Modal Logic Theory for Pathology Inference. 3/16/2009.

MODAL LOGIC THEORY
FOR PATHOLOGY INFERENCE.
DRAFT COPY ONLY.
3/16/2009.
G. William Moore, MD, PhD.
Lawrence A. Brown, MD.
Robert H. Burger, MD, MPA.
Grover M. Hutchins, MD.
Robert E. Miller, MD.
http://www.netautopsy.org/modlthry.htm

SCREEN 1. DISCLAIMER.

United States Government Work, uncopyrighted, public-domain, DRAFT COPY ONLY. This document does not necessarily represent the views or policies of any United States Government agency. This document is provided "as is", without warranty of any kind, express or implied, including but not limited to the warranties of merchantability, fitness for a particular purpose and non-infringement. In no event shall the authors be liable for any claim, damages or other liability, whether in an action of contract, tort or otherwise, arising from, out of, or in connection with the document or the use or other dealings made with the document.

SCREEN 2. ABSTRACT.

Pathology studies the etiology and pathogenesis of disease. Anatomic pathology is devoted to the gross anatomy and microanatomy of diseased organs, for rendering diagnoses, and for acquiring new knowledge about disease biology. A major function of the anatomic pathologist is to issue diagnostic reports on samples from diseased tissue. The aggregate collection of these reports contains a wealth of information related to almost every serious human disease.

Any data-mining program must incorporate the fundamental constraints on data acquisition in routine medical practice. It may be unnecessary, uneconomic, technically unfeasible, or unethical to fill in all possible data-items in a rectangular database. Existing clinical databases should include formal considerations: for missing values, patient consent, patient risk, and provider alerts. This report proposes a basic theory of clinicopathologic inference.

This report proposes a mathematically consistent theory of clinicopathologic inference. There are two types of propositions: data, set D; and medical entities, set E. Data are binary propositions (i.e., true/false); and medical entities (or medical threats) are fuzzy propositions. Classically, a fuzzy proposition assumes truth-values, v, along the closed interval, [0,1], where v=0 is false and v=1 is true. For convenience in the present formulation, propositions assume certainty levels, $¹, $², $³, ..., where certainty level $^k corresponds to fuzzy value (1 - 2^-k); so that certainty level $¹ corresponds to fuzzy value ½; certainty level $² corresponds to fuzzy value ¾; certainty level $³ corresponds to fuzzy value ⅞, etc.

There are three ethical operators in our model: certainty ($); value (#); and payment (!); and nine rules of ethical data collection, based upon the general princiople that data should be collected whenever a medical condition sufficiently threatens the patient and the patient gives informed consent; and data should not be collected if either condition fails, i.e., there is no significantly threatening condition, or else the patient does not give informed consent.

What for? There is an emerging technology of software agents, or spiders that crawl through the worldwide web or other computer resources, looking for cases needing followup, and other medical anomalies. The language for constructing and organizing these software agents is RDF........ The use of these software agents should be constrained by minimal ethical considerations, consisting of fuzzy certainty, value, and payment for the relevant medical entities. The basic framework includes: increasing certainty of medical threats (Rules 1,2,3); Hippocratic principles (first do no harm; treat if indicated) (Rules 4,5); and ethical data collection (Rules 6,7,8,9). Ethical data collection is the idea that there is an ontology for medical threats; the physician may be concerned (vexed)) enough to collect data on a perceived medical threat; that data, once obtained, are never lost; and the use of Sutton's Law (Zebra Rule) to guide further threat assessment.

There are nine rules of relationship in this system: (1) complementizer negation/homomorphism; (2) fuzzy asymmetry; (3) crisp data; (4) Hippocrates-first; (5) Hippocrates-reverse; (6) ontology; (7) vexation; (8) ethical data collection; and (9) Schrödinger's cat.

The theory employs modal/fuzzy/multivalued logic operators of know-whether/certainty ($), value-to-know-whether (#), and pay-to-know-whether (!). There is an atomset of distinct, atomic propositions (atoms, A), each of which has a definite true-false status. Quantitative, interval, ranked, and categorical data are interpreted as collections of true-false statements. Each atomic proposition, a, is either a datum (complaints, history, physical findings, laboratory values, statements of consent, etc.); or a medical entity (cancer, inflammation, necrosis, etc.). No datum is an entity and no entity is a datum. The negation of a datum is a datum; and the negation of an entity is an entity. To each atom, a, there exists known-to-the-k-a, denoted $^ka, for every integer, k, up to a maximum, M>k; and additionally for each datum, d, there exists value-to-know-d, denoted #d; and pay-to-know-d, denoted !d. A datum, d, is Hippocratic-first (do-no-harm) if and only if (not-#d implies not-!d), i.e., don't-value-d implies don't-pay-d; and Hippocratic-reverse if and only if ((not-$d and #d) implies !d), i.e., don't-know-d and value-to-know-d implies pay-to-know-d. A medical entity e, may be ontologic (exists) and vexative (worrisome) based upon previously collected data.

The theory is mathematically consistent; and satisfies Occam's Razor, namely, that no entities are known without data. The Hippocratic-first, Hippocratic-reverse, ontologic, and vexative properties are consistent if data are entered consensually, consecutively, and consistently, i.e., no datum is entered after its negation has been entered. The computer algorithm for solving this system concludes within polynomial time.

This report introduces a mathematical system for managing medical concepts and data. Modal/fuzzy/multivalued logic operators expand the purview of classical symbolic logic, to accommodate technical, economic, and consent-based constraints on clinicopathologic data collection. The theory supports such medical concepts as: do-no-harm; treat-if-valuable; disease ontologies; worrisome findings; and levels of certainty.

The theory is completely general, and permits definitions of patient injury that include possible death, morbidity, inconvenience, financial constraints, or loss-of-privacy; and definitions of value-to-know that may differ among observers (patient, physician, insurer, national health policy, research protocol). Mathematical theories can serve to organize medical knowledge and patient data, and improve the scheduling and effectiveness of data collection and surveillance in large clinicopathologic data systems.

RATIONALE.

Natural science may be regarded as the pursuit of truth, based upon observations, or data. Scientific, or evidence-based medicine, involves the collection and organization of data for the relief of human suffering. While pure science seeks only the truth, medical science has two significant, additional constraints: value and payment. Value is the benefit to the patient of obtaining a particular fact or applying a particular therapy. Payment is the aggregate expense to the patient of obtaining this fact or therapy, in inconvenience, money, pain, and/or risk of morbidity and mortality.

The present model for medical analysis recognizes two classes of binary (yes/no) logic propositions: data, D, and medical entities, E. Each datum, d∈D, such as serum prostatic specific antigen above a particular upper bound, has a payment, !d, that must be justified by a corresponding value, #d, that justifies the payment for collection. A datum is either entirely certain, +$d, or entirely uncertain, -$d.

By contrast, a medical entity, e∈E, such as "prostate cancer", is a theoretical construct supported by observations, that is never entirely certain. Increasing levels of certainty for a threatening medical entity, such as cancer, might justify progressively invasive data collection. For example, a sixty-year-old man who has not had a serum prostatic specific antigen or digital rectal examination performed for over a decade might justify performing one or both of these tests (mildly invasive). A positive result on either test raises the suspicion for prostate cancer, and might justify a (more invasive) prostate biopsy. However, the suspicion for prostate cancer in an asymptomatic sixty-year-old man with no other relevant findings, does not justify an immediate prostate biopsy.

Why construct a mathematical formalism for a few, very ordinary ideas in medicine? First, because a lot of the folk-ideas of medicine (Sutton's Law, Zebra Rule, Hippocrates' Rules, Value, Payment, St. Peter's Rule, etc.) are not well-formalized. As late as the 1980s, there was no formal definition for intention (not intension) (see Searle[]). Yet, clinical medicine involves the intention of the patient, the intention of the physician, as well as that of third-party-payers, health policy makers, etc. Despite all the advances in astrophysics, cosmology, and evolutionary biology, there is still no decent definition of free will (see Wilson[], Hawking[]); yet free will (or at least the perception of free will) is a major feature of medical care and medical ethics.

Medical care records are rapidly becoming computerized, and, alas all-to-slowly, becoming standardized. The U. S. Veterans Affairs medical centers are a leader. At the Baltimore VA Maryland Health Care System (VAMHCS), nearly all records have been computerized since 2000, including ethics records, such as patient consent and patient competence-to-consent. Quality assurance processes within the institution depend upon these records, to assure compliance of the institution to high standards of care. Although the goal of fully-automated quality assurance processes is still elusive, we can foresee the day when formal computer systems survey large collections of records, to monitor compliance with optimal standards of care. The trouble is: computer programs, by themselves, have no judgment or ethics. We physicians need to formulate the basic principles of judgment and ethics, in order to survey electronic medical records for possible anomalies in these standards.

Why bother with mathematical consistency? So that, when a computer program surveys these records, barring programming errors, one can be certain that one doesn't have a statement that is both true and false at the same time (the definition of mathematical inconsistency). It's not enough to "try out a few examples". One must verify that the actual basis for the calculations is consistent.

MODAL LOGIC:
PROSTATE CANCER EXAMPLE.

1. Modal logic is an expanded form of classical logic, in which Aristotle's (384-322 BC) Law of Excluded Middle is conditionally/partially suspended.

2. The term refers to subjunctive mood (Latin: modus subjunctivus in classical grammar.

3. In classical logic, a proposition, p, is either true or false. In modal logic, proposition, p, is either necessarily true, denoted □p; necessarily false, denoted □~p; or possibly true, denoted ◇p, where:

◇p = ~□~p.
□p = ~◇~p.

4. Plato (428-347 BC, Greek philosopher) and Avicenna (980-1037, Persian physician and mathematician) were early contributors.

5. Modern contributors: Jan Lukasiewicz (1883-1964, Polish logician), C. I. Lewis (1883-1964), Sadegh-zadeh, and Zadeh.

6. Deontic modal logic:

6.1. Deontic Necessity: it is mandatory to do p.

6.2. Deontic Possibility: it is permitted to do p.

6.3. Deontic Passive Negation: p is not mandatory to do.

There is also: temporal modal logic (time), doxastic modal logic (belief), ....

7. Prostate cancer example. Let p=prostate cancer. Then:

7.1. A 60-year-old man who hasn't seen a doctor for ten years: □p unless □²~p,
7.2. Serum prostate specific antigen is positive: □²p unless □³~p,
7.3. Needle biopsy of the prostate is negative: □³~p unless □⁴p, etc.

At each step, uncertainty about a threatening medical condition, namely, prostate cancer, justifies gathering additional data: □p justifies drawing serum prostate specific antigen; □²p justifies performing prostate biopsy, etc.

FREQUENTLY ASKED QUESTIONS.

Question 1. Modal logic has been around, in one form or another, for over a century (Łukasiewicz). What is so special about the present version?
Answer. The present version of modal logic attempts to explain a stepwise approach to medical diagnosis, in which every data-collection step on a patient gets one closer to diagnostic certainty. For a diagnosis, p, one may know the diagnosis as necessarily p, denoted □p, necessarily necessarily p, denoted □□p, necessarily necessarily necessarily p, denoted □□□p, etc. In this formulation, one never achieves diagnostic certainty. This formulation corresponds to the medical reality that a medical diagnosis is never certain, but rather, certain to a degree that one is ethically entitled to take another step, such as run additional tests or begin treatment. Even some autopsy diagnoses are not necessarily certain: there are autopsy blocks that are processed by newer methods (such as DNA analysis) not available at the original autopsy, which yield additional diagnoses. Example: DNA analysis of autopsy blocks in victims from the 1917-1918 worldwide influenza pandemic.

Question 2. Why is it that the masters of Modal Logic (Łukasiewicz, Lewis, Zadeh, Zeman, Snyder) missed this particular variation of modal logic?
Answer. Perhaps because the present formulation has an infinite regress of necessarilies, □□□ □..., for which the early inventors of modal logic did not have a suitable philosophical analogy.

Question 3.
Answer.

Question 4.
Answer.

Question 5.
Answer.

Question 6.
Answer.

Question 7.
Answer.

Question 8.
Answer.

Question 9.
Answer.

Question 10.
Answer.

SCREEN 3. TABLE OF CONTENTS.

SCREEN 4. SKETCH OF MATHEMATICAL MODEL.

Return to Table of Contents.

0. Seven general theorems are stated and proved in this mathematical model, along with associated lemmas and corollaries. There is a live proof program in the manuscript, in which simple examples and theorems may be tested. The reader is invited to try out his/her own examples. The live proof program has been tested on 200 theorems from Zeman's Modal Logic. See Appendix H:

http://www.netautopsy.org/mucoarch.htm

1. There is a relationship between modal logic (necessarily, possibly) and fuzzy set theory, such that greater fuzzy membership implies higher levels of modal-certainty.

2. Ethical data collection (Rule 8) leads to consistent entity inferences.

3. An empty system is consistent, and implies no entities; for stepwise data collection, less data imply less entities (Occam's Razor, William of Ockham, 1285-1349, English logician and Franciscan friar, Latinized: Occam).

4.In-between theorem. Analogous to between in Euclidean geometry. If you have sufficient data to imply necessarily^k entity, then you have sufficient data to imply necessarily^k-1 entity.

5. Resource Description Framework (RDF): general syntax for writing computer-parsable ordered triples, that export meaning among databases on the semantic worldwide web, by binding a described datum to a specified subject. Internet web-crawler programs can interrogate multiple RDF documents, and draw inferences from these ordered triples. RDF-classes: Strict monoparental hierarchy; An RDF-class hierarchy is mathematically consistent.

6. RDF Theorems::
Theorem §6.1. Consistency of RDF classes.
Theorem §6.2. Identity. Class p implies p.
Theorem §6.3. Or-expansion. If p implies q, then p implies q or q or q or q....
Theorem §6.4. Telescoping.
Theorem §6.5. Contextualization.
Theorem §6.6. Intercalation.
Theorem §6.7. Retirement.

7. Token Cube / Neyman-Pearson Condition (Jerzy Neyman, 1894-1981, Polish-American statistician; Egon S. Pearson, 1895-1980, British statistician). Extension of classical contingency table analysis, which compensates for metaknowledge in a contingency table; and deals with zerodivide in chisquare test, χ² contingency table analysis. The essential argument of the Neyman-Pearson Condition is that greater power (=(1-β)) forces greater Type I Error (=α).

SCREEN 5. WORD MODEL: OUTLINE.

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1. Rule 1. Complementizers: Absorb negation; homomorphic in logical-and. A complementizer is a grammatical element, such as that, whether, which, who, where, when, how,..., in a sentence, that connects an independent (main) clause to a dependent clause. For example:

it is said that Homer was blind

where it is said is the main clause; Homer was blind is the dependent clause (Homer, 8th century BC, Greek poet); and that is the complementizer. In this sentence, the complementizer, that, is negation-sensitive, that is, it is said that Homer was blind is not the same as it is said that Homer was not blind. By contrast, the complementizer, whether, is negation-insensitive, that is, it is said whether Homer was blind is the same as it is said whether Homer was not blind.

The present mathematical model has three negation-insensitive complementizers, namely:

$: it is certain/known whether
#: it is of value to know whether
!: payment to know whether

These complementizers, $, #, !, absorb negation. That is, for propositions p, q:

$p = $+p = $-p; #p = #+p = #-p; and !p = !+p = !-p.

These complementizers are homomorphic in logical-and. That is, for propositions p, q:

$(p&q)=$p&$q; #(p&q)=#p&#q; and !(p&q)=!p&!q.

2. Rule 2. Fuzzy Asymmetry. Fuzzy set theory (Zadeh, 1965) is a generalization of classical/crisp set theory, that represents different levels of certainty for the same concept. Element p has partial membership in set P, denoted pμ_vP, where v assumes any value along closed interval, v ∈ [0,1]. Fuzzy is not probability. Despite its quirky name, fuzzy is serious mathematics. Fuzzy set theory has an asymmetry property: If pμ_vP, and v>w, then pμ_wP. Classical set theory is the special case of fuzzy set theory, in which either v=0 or v=1.

3. Rule 3. Crisp Data. In our mathematical model, data are crisp/classical and entities are fuzzy.

4. Rule 4. Hippocrates-first. Hippocrates (460-370 BC, Greek physician, father of medicine) is famous for the medical dictum: first do no harm, often given in the form of Galen's (129-200, Greco-Roman physician) Latin translation: primum nón nocére.

5. Rule 5. Hippocrates-reverse A converse doctrine, also formulated by Hippocrates, that one must offer treatment to the patient if one is available: treat if you can.

6. Rule 6. Ontology (Platonic description of essential reality (Smith, 1996); Plato, 424-348 BC, Greek philosopher; Greek: οντως = ontós = real, actual; λογος = logos = word, study); is a description of the core beliefs for a field of study, in this case, ethical clinical medicine. The central idea in our model is that a collection of data, Δ, implies an entity, e, at a certainty level k, commensurate with the extent and quality of data given.

7. Rule 7. Vexation (Latin: vexari: to worry) corresponds to the worry list that every physician carries around in his/her mind, regarding patients requiring additional tests, therapy, or followup. In our mathematical model, entity e at certainty level k implies value-to-know the additional datum, d.

8. Rule 8. Ethical Data Collection. In our mathematical model, a datum, d, is collected ethically if and only if:

1. the datum is never collected;
2. payment is made and the datum is true (+d and +$d and +!d);
3. payment is made and the datum is false (-d and +$d and +!d); or
4. payment is made and the attempt fails (+!d only).

Each step at which payment is made (+!d), must be justified by value, (+#d), in the previous step.

9. Rule 9. Schrödinger's cat (Erwin Schrödinger, 1887-1961, Nobel Prize Physics, 1933) is a disappearing cat in a box. According to quantum mechanical theory, a probabilistic event, such as a radioactive decay, doesn't have a consequence (i.e., the cat neither lives nor dies) until the event is observed. In our model, an entity is not certain (Rule 6, Ontology) at a particular certainty-level until all higher certainty levels are (provisionally) excluded. In contrast to Schrödinger's cat, which involves a single physical event in which the cat lives or dies, in our model, there is a stepwise process of data collection, and corresponding cat's box openings or Schrödinger openings at each step, where the cat may die and then come back to life in subsequent data collection steps. Also known as: Sutton's Law (Willie Sutton, 1901-1980, American Bank Robber, "Slick Willie"); Zebra Rule; Black Swan; Albino crow; etc.

10. Rule 10. Neyman-Pearson Condition . (Jerzy Neyman, 1894-1981, Polish-American statistician; Egon S. Pearson, 1895-1980, British statistician). The Neyman-Pearson Condition is the condition that when performing a hypothesis test between two point hypotheses H₀: θ=θ₀ and H₁: θ=θ₁, then the likelihood-ratio test that rejects H₀ in favor of H₁ when

Λ(x) = (L(θ₀|x) / L(θ₁|x)) < η, where P(Λ(X)<η|H₀)=α,

SCREEN 6. INTRODUCTION.

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1. Data-mining in Anatomic Pathology: use of public data for drawing medical conclusions (Moore et al, 2001).

2. Constraints: patient privacy, missing values.

3. Data-mining program for pathology: incorporate ethical/technical constraints of routine medical practice.

4. At a fully-computerized medical institution, such as the Baltimore VA Maryland Health Care System, pathology data are used for quality assurance of clinical services.

5. Completing a rectangular database: may be unnecessary, uneconomic, technically unfeasible, or unethical, to collect all possible data for all possible data-cells in the table.

6. Formal considerations for missing values, patient consent, patient risk, and provider alerts.

7. Set theory definitions of atoms, data, and medical entities [7,8,9,10].

8. Fuzzy/multivalued concepts: (Zadeh, 1965).

9. Modal/fuzzy complementizers: know-whether ($), value-to-know-whether (#), and pay-to-know-whether (!) [Moore et al, 1980].

SCREEN 7. HYPOTHETICAL AUTOPSY REPORT.

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Male. Caucasian. 1.91 m. 95.5 kg.
b. 8/27/1908. d. 1/22/1973.
Occupation: U.S. Congressman, U.S. Senator, U.S. President.
Status post: Appendectomy.
Status post: Cholecystectomy.
History of: Renal Calculi.
Myocardial Infarct, 1955.
Myocardial Infarct, April, 1972.
Myocardial Infarct, January 22, 1973.
Marked Generalized Atherosclerosis.

Who is this person? [DeGregorio, 1997]

SCREEN 8. UMLS-ENCODED
HYPOTHETICAL AUTOPSY REPORT

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U. S. National Library of Medicine Unified Medical Language System: (USNLM, 2004).

Male. Caucasian. 1.91 m. 95.5 kg. {C0024554}.
b. 8/27/1908. d. 1/22/1973. {C0021132}.
Occupation: U.S. Congressman, U.S. Senator, U.S. President. {C0032382}.
Status post: Appendectomy. {C0003611}.
Status post: Cholecystectomy. {C0008320}.
History of: Renal Calculi. {C0022650}.
Myocardial Infarct, 1955. {C0027051}.
Myocardial Infarct, April, 1972. {C0027051}.
Myocardial Infarct, January 22, 1973. {C0027051}.
Marked Generalized Atherosclerosis. {C0205082,C0205046,C0205246}.

Privacy: Does the patient have a positive syphilis test?

Summary/Set theory definition: {{C0024554}, {C0021132}, {C0032382}, {C0003611}, {C0008320}, {C0022650}, {C0027051}, {C0027051}, {C0027051}, {C0205082,C0205046,C0205246}}.

SCREEN 9. HIPAA:
HEALTH INSURANCE
PORTABILITY AND ACCOUNTABILITY ACT.

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1. U. S. Health Insurance Portability and Accountability Act. 1996. (HIPAA, Kennedy-Kassebaum Bill, H.R. 3103 of 104th U. S. Congress).

2. Regulates all individually identifiable medical records in the USA.

3. Final Rule in force since April 14, 2003.

4. Huge fines for non-compliance: $25,000 for each record disclosed unintentionally; more for intentional disclosures or disclosures involving commercial gain.

5. Some research studies involving statistics require individual data.

6. For public research databases, no patient medical record may be individually identifiable.

7. U. S. Code of Federal Regulations. 1995.

SCREEN 10. PRIVACY AND
CLINICOPATHOLOGIC RESEARCH. (Moore et al, 2001)

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1. Some research studies involving statistics require individual patient data.

2. Published, grouped data may not contain all the detail necessary to evaluate the statistical analysis methods. Therefore, it would be valuable if individual data were published on the internet, so that the statistical analysis methods could be verified by the public at large.

3. Strong Privacy: The patient him/herself cannot identify his/her own medical record. Therefore, there may be at least c exact duplicates in the published record, where c is the conspiracy threshold. That is, a conspiracy of c patients could get together and demonstrate that their records, as a group, have been exposed/published on the internet.

4. Weak Privacy: The public part of a patient's record cannot be uniquely identified. Therefore, there must be c exact duplicates in the public variables of the published record.

5. Dangers of Weak Privacy: embarrassment to the patient, even if logically unfounded; sense by the patient that his/her records are public, even if they are not; if one private part is accidentally disclosed, then the remainder of the record is exposed. (See: "syphilis" example, Screen 8.)

6. Detail must be blurred just enough so that one patient can be mistaken for c other patients.

7. It is a bad idea statistically, as well as fraudulent and confusing, to create additional, phantom patients. I'm not sure that we currently have the statistical apparatus to manage even controlled, intentional fraud. (But see: Berman (2007)).

SCREEN 11. AUTOPSY EXAMPLE:
SICKLE CELL CRISIS.

Φ, Unexplained:→ Ψ, Pain Crisis:↓	No	Yes	TOTAL
Yes			20
No			51
TOTAL	58	13	71

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1. Pain crisis in sickle cell disease is an episode of poorly-localized abdominal pain, that requires major pain medications for relief. There are no characteristic morphologic features corresponding to pain crisis in sickle cell disease.

2. Can pain crisis in sickle cell disease be recognized statistically at autopsy? Is it a cause of death?

3. Parfrey NA, Moore GW, Hutchins GM.
Is pain crisis a cause of death in sickle cell disease?
Am J Clin Pathol. 1985 Aug;84(2):209-212.

4. 71 autopsied cases of sickle cell disease in the autopsy files of The Johns Hopkins Medical Institutions with adequate clinical histories. 9/20 (45%) patients died in pain, death unexplained at autopsy; 4/51(8%) patients died without pain, death unexplained at autopsy.

5. Is there a significant correlation between unexplained death and pain crisis?

Click on the SUBMIT button.

6. No-explanation-at-autopsy is the gold-standard, Φ; and pain-crisis is the new hypothesis, Ψ being investigated.

7. Try out your own values.

SCREEN 12. CONTINGENCY TABLE ANALYSIS:
BASIC DEFINITION.

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1. Contingency table analysis (Screen 11, above) is a powerful method for comparing frequency data in patients with two different data-sources, Φ and Ψ (Pearson, 1904; Upton and Cook, 2006) (Karl Pearson, 1857-1936, British statistician).

2. The simplest contingency table is a rectangular table of binary (false/true) observations on patients, with two rows, two columns, and 2×2=4 cells. Columns correspond to an existing biomedical test, Φ; (death explained at autopsy); and columns correspond to a newer test, Ψ (pain crisis), as follows:


                        _____________
                 True:  |  c  |  d  |
             Ψ          |_____|_____|
                 False: |  a  |  b  |
                        |_____|_____|
                         False True
                              Φ

Classical (Two-dimensional) Contingency Table. Fig. 3490.

3. In this contingency table, cell a represents the set of patients where both test Φ and test Ψ are false (true negatives, TN); cell b represents the set of patients where test Φ is true and test Ψ is false (false negatives, FN); cell c represents the set of patients where test Φ is false and test Ψ is true (false positives, FP); and cell d represents the set of patients where both test Φ and test Ψ are true (true positives, TP).


                        _____________
                 True:  |  FP |  TP |
             Ψ          |_____|_____|
                 False: |  TN |  FN |
                        |_____|_____|
                         False True
                              Φ

That is, the lower-left and upper-right cells form the true diagonal of this table; and the upper-left and lower-right cells form the error diagonal.

4. We may calculate marginal totals, w, v, x, y; and a grand total, z, for this table, where v=a+b, w=c+d, x=a+c, y=b+d, and z=v+w=x+y=a+b+c+d.


                        _____________
                 True:  |  c  |  d  |  w
             Ψ          |_____|_____|
                 False: |  a  |  b  |  v
                        |_____|_____|  
                           x     y     z
                         False True
                              Φ

5. In classical statistics, test Φ compared to test Ψ is evaluated by the chisquare test, χ², or by the Fisher exact test (Ronald A. Fisher, 1890-1962, British statistician), based upon the squared-normal or binomial distributions, respectively. In the null hypothesis (the statistical straw man), it is assumed that tests Φ and Ψ are statistically independent.

SCREEN 13. CONTINGENCY TABLE ANALYSIS:
HYPOTHETICAL EXAMPLE.

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1. In classical contingency table analysis, there is a 2×2 rectangular table, in which test Φ (columns) represents the definitive but costly test for a medical entity (e.g., prostate biopsy); and test Ψ (rows) represents a newer, less costly, less painful test for the same medical entity (e.g., serum prostate specific antigen). Suppose that we have data for both these tests on 10,000 patients, and the contingency table is as follows:


                        __________________
                 True:  | 200=c  |  90=d |    290
             Ψ          |________|_______|
                 True:  | 9700=a |  10=b |   9700
                        |______ _|_______|           
                          9700     100    10,000
                            False True
                                 Φ

2. Suppose further that we have adjusted the new test, Ψ, such that we are willing to accept a 200:10 = 20:1 ratio of false_positives:false_negatives, as shown. That is, a false-negative is much more dangerous to the patient than a false-positive, since a false-negative means that the patient is not followed-up until until the next regular screening interval; whereas a false-positive only requires the more expensive test, Φ, but at least doesn't lose the patient to follow-up.

3. Suppose that we are already convinced that tests Φ and Ψ are highly correlated (i.e., not independent), so that the classical χ² and Fisher exact tests (Ronald A. Fisher, 1890-1962, British statistician) are not useful at this point.

4. Finally, we know that the medical entity, prostate cancer, affects much less than half the population sampled, so that (a+c)>(b+d) and c>b. Whence we may conclude that the cell totals satisfy: a>c>d>b. (Proof:......).

5. Furthermore, if we know that the actual frequency of the disease in the general population is <190 (here, 100/10,000, then we would set c/a>1% (Proof:......).

6. In the token swap test, we set the null hypothesis at b=0. Then the null hypothesis becomes:


                        _________________
                 False: |  c-b  |  d+b  |    w
             Ψ          |_______|_______|
                 True:  |  a+b |     0  |    v
                        |_______|_______|           
                             x       y       z
                            False True
                                 Φ

7. None of the null hypothesis cell totals are negative (Proof: because c>b). The marginal totals are preserved, and in particular, the ratio of Φ-positives to Ψ-positives is preserved. The token swap algorithm then addresses the question whether b is unacceptably large, based upon its distance from zero.

Null hypothesis:


                        _________________
                 False: |  190  |  100  |    290
             Ψ          |_______|_______|
                 True:  | 9700 |     0  |   9700
                        |_______|_______|           
                          9700     100    10,000
                            False True
                                 Φ

SCREEN 14. CONTINGENCY TABLE ANALYSIS:
THREE-DIMENSIONAL TABLE (CONTINGENCY CUBE).

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1. Many scenarios in medicine are more complex than established test Φ versus new test Ψ, in determining the presence of medical entity e. Some patients are in higher risk groups than other patients, and one is more suspicious of a false negative or false positive, based upon this ancillary, risk-biased information.

2. Therefore, we propose a third logical variable, test Ω, as a gold standard that encapsulates everything that we know about each patient. The apparatus for managing this heterogenous test Ω information is given by the medical model below.

3. Suppose that we have a three-dimensional contingency cube, where test Φ is the horizontal axis, test Ψ is the vertical axis, and test Ω is the depth axis:

Three-dimensional Contingency Table (Figure 3480).

4. There are eight cells (subcubes) in a contingency cube: a, b, c, d, e, f, g, h: with cells a, b, c, d in the Ω-front plane, as before; and corresponding cells e, f, g, h, respectively, in the Ω-back plane.


    Cell    Φ   Ψ   Ω    Diagonal:
       a    F   F   F    True.
       b    T   F   F    Favor Ψ.
       c    F   T   F    Favor Φ.
       d    T   T   F    Error.
       e    F   F   T    Error.
       f    T   F   T    Favor Φ.
       g    F   T   T    Favor Ψ.
       h    T   T   T    True.

5. There are four diagonals. In the true diagonal, ah, all three tests, Φ, Ψ, and Ω, agree, i.e., all three tests are either all true (cell a) or all false (cell h). In the error diagonal, de, both test Φ and test Ψ disagree equally with the gold standard, test Ω. In addition, there is a favor Φ diagonal, cf, in which test Φ agrees with the gold standard but test Ψ disagrees with the gold standard, test Ω; and favor Ψ diagonal, bg, in which test Ψ agrees with the gold standard but test Ψ disagrees with the gold standard, test Ω.

TOKEN SWAP CUBE : PLANAR PROJECTIONS.

Three-dimensional swap from Ψ to Φ: b → c and g → f.

Three-dimensional swap from Φ to Ψ: c → b and f → g.

Collapse/project the cube into three margin-neutral token squares:


                        _________________
                 True:  |  c+g  |  d+h  |
             Ψ          |_______|_______|
                 False: |  a+e  |  b+f  |
                        |_______|_______|
                         False   True
                              Φ


                        _________________
                 True:  |  e+g  |  f+h  |
             Ω          |_______|_______|
                 False: |  a+c  |  b+d  |
                        |_______|_______|
                         False   True
                              Φ


                        _________________
                 True:  |  e+f  |  g+h  |
             Ω          |_______|_______|
                 False: |  a+b  |  c+d  |
                        |_______|_______|
                         False   True
                              Ψ

SCREEN 15. CONTINGENCY TABLE ANALYSIS:
PROBLEMS WITH CLASSICAL TESTS.

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Classical contingency table analysis has several problems in biomedical applications:

1. Classical contingency table analysis assumes statistical independence between methods Φ and Ψ.

2. Expected values for cell totals must be non-zero and not close to zero.

3. There is no way to include/accommodate ancillary information, that might be known about patients in the study.

4. There is no distinction between knowable errors, based upon ancillary information; and unknowable errors.

5. Every classification has an irreducible number of unknowable errors.

6. Classical statistics has no accommodation for missing values.

SCREEN 16. CONTINGENCY TABLE ANALYSIS:
BALANCED TABLE.

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A contingency table is a rectangular table, with two rows and two columns [95,96,97,98].

2. Rows represent an existing gold standard, g; and columns represent a hypothesis, h

3.

Φ→ Ψ↓	-	+	Total
-	c	d	v
+	a	b	w
Total	x	y	z

4. In the above example, the explanation-at-autopsy is the gold-standard = Φ; and pain-crisis is the hypothesis = Χ being investigated.

5. In a simple example, consider a BALANCED 2×2CT in which there are 100 patients, all told, of which 90 patients are gold standard negative, Φ- and 10 patients are gold standard positive, Φ+. Further, suppose that 50 patients are hypothesis negative, Ψ- and 50 patients are hypothesis positive, Ψ+, as follows:
BALANCED

Φ→ Ψ↓	Φ-	Φ+	Total
Ψ+	45	5	50
Ψ-	45	5	50
TOTAL	90	10	100

6. In this example, gold-standard ± is uncorrelated to hypothesis ±. The individual data cells in the table contain tokens, that represent individual patients, characterized by nothing more than their Φ±Ψ± status. In the example, the observed cell totals are: Φ-Ψ- = 45 tokens; Φ-Ψ+ = 5 tokens; Φ+Ψ- = 45 tokens; Φ+Ψ+ = 5 tokens. The marginal totals are: Φ- = 90; Φ+ = 10; Ψ- = 50; Ψ+ = 50. The grand total, z, is 100.

7. The BALANCED/EXPECTED CELL TOTALS are obtained as cross-products of the marginal totals, as follows:

Expected Φ-Ψ- = (Φ-×Ψ-)/z = 90×50/100 = 45;
Expected Φ-Ψ+ = (Φ-×Ψ+)/z = 10×50/100 = 5;
Expected Φ+Ψ- = (Φ+×Ψ-)/z = 90×50/100 = 45;
Expected Φ+Ψ+ = (Φ+×Ψ+)/z = 10×50/100 = 5.

8. Classical statistical analyses of a (2×2CT) are afforded by the CHISQUARE TEST (CST) and FISHER EXACT TEST (FXT), based upon statistical sampling assumptions (Ronald A. Fisher, 1890-1962, British statistician).

9. The TOKEN SWAP TEST (TST) is a statistical-type significance test, that measures the likelihood of MISCLASSIFICATIONS in a 2×2CT.

SCREEN 17. CONTINGENCY TABLE ANALYSIS:
UNBALANCED TABLE.

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1. Now consider an UNBALANCED 2×2CT, with the SAME MARGINAL TOTALS as above.
The least-unbalanced example has only a single token misclassified:

UNBALANCED: BALANCED+1

.	Φ-	Φ+	TOTAL
Ψ+	46	44	90
Ψ-	4	6	10
TOTAL	50	50	100

The second-least-unbalanced example has two tokens misclassified:

UNBALANCED: BALANCED+2

.	Φ-	Φ+	TOTAL
Ψ-	47	43	90
Ψ+	3	7	10
TOTAL	50	50	100

... and so forth.

2. How unbalanced can the observed data-cells be, before we suspect that there is a genuine relationship between the gold-standard g, and the hypothesis, h? That is, how unbalanced can the observed data-cells be, before one rejects the null hypothesis?

3. The CHISQUARE TEST (CST) and FISHER EXACT TEST (FXT) are based upon statistical sampling assumptions (Ronald A. Fisher, 1890-1962, British statistician).

4. The TOKEN SWAP TEST does not depend upon the usual statistical assumptions of repeated, random sampling from a source population.

SCREEN 18. TOKEN SWAP TEST: MISCLASSIFICATION PARADIGM.

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1. TOKEN SWAP SIGNIFICANCE EXAMPLE. In the following example, it requires five TOKEN SWAPS to transform the expected into the observed contingency table:
EXPECTED

.	NO	YES	TOTAL
YES	16	4	20
NO	42	9	51
TOTAL	58	13	71

⇒⇒⇒
EXPECTED+1

.	NO	YES	TOTAL
YES	15	5	20
NO	43	8	51
TOTAL	58	13	71

⇒⇒⇒
EXPECTED+2

.	NO	YES	TOTAL
YES	14	6	20
NO	44	7	51
TOTAL	58	13	71

⇒⇒⇒
EXPECTED+3

.	NO	YES	TOTAL
YES	13	7	20
NO	45	6	51
TOTAL	58	13	71

⇒⇒⇒
EXPECTED+4

.	NO	YES	TOTAL
YES	12	8	20
NO	46	5	51
TOTAL	58	13	71

⇒⇒⇒
EXPECTED+5
=OBSERVED

.	NO	YES	TOTAL
YES	11	9	20
NO	47	4	51
TOTAL	58	13	71

2. In the zeroth token-swap, the chances that the EXPECTED-to-EXPECTED+1 swaps could have taken place AT RANDOM are: (9×16) _________________________ (9×16)+(4×42)
that is, the number of possible of EXPECTED-to-EXPECTED+1 swaps, divided by (the number of possible EXPECTED-to-EXPECTED+1 swaps plus the number of possible EXPECTED-to-EXPECTED-1 swaps), without altering the marginal totals.

3. In the zeroth token-swap, the chances that the EXPECTED-to-EXPECTED-1 swaps could have taken place AT RANDOM are: (4×42) _________________________ (9×16)+(4×42)

4. In the first right token-swap, the chances that the EXPECTED+1-to-EXPECTED+2 swaps could have taken place AT RANDOM are: (8×15) _________________________ (8×15)+(5×43)

5. In the first left token-swap, the chances that the EXPECTED+1-to-EXPECTED swaps could have taken place AT RANDOM are: (5×43) _________________________ (8×15)+(5×43)
and so forth.

6. When the EXPECTED has swapped up to the OBSERVED table, without altering the marginal totals, and the proportion of such swaps is less than 5%, then the result is significant.

7. If the result is not significant, then we say that the observed 2×2CT is NOT SO DIFFERENT from the expected 2×2CT, that occasional misclassifications by a medical observer could account for the differences.

SCREEN 19. CONTINGENCY TABLE ANALYSIS.
NEYMAN-PEARSON CONDITION.

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1. In statistics, the Neyman-Pearson Condition (Jerzy Neyman, 1894-1981, Polish-American statistician; Egon S. Pearson, 1895-1980, British statistician) is the condition that when performing a hypothesis test between two point hypotheses H₀: θ=θ₀ and H₁: θ=θ₁, then the likelihood-ratio test that rejects H₀ in favor of H₁ when

Λ(x) = (L(θ₀|x) / L(θ₁|x)) < η, where P(Λ(X)<η|H₀)=α

is the most powerful test of size α for a threshold η, where (L(θ₀|x) / L(θ₁|x)) is the likelihood ratio (or more generally, any statistical test inequality comparison); η designates the so-called critical region for the test, and α is the significance level for Type I (false positive) Error.

If the test is most powerful for all θ₁ ∈ Θ₁, then it is said to be uniformly most powerful (UMP). The essential argument of the Neyman-Pearson Condition is that greater power (=(1-β)) forces greater Type I Error (=α).

2. In practice, the likelihood ratio itself is not actually used in the test. Instead one computes the ratio to see how the key statistic in it is related to the size of the ratio (i.e. whether a large statistic corresponds to a small ratio or to a large one).

3. Neyman J, Pearson E.
On the Problem of the Most Efficient Tests of Statistical Hypotheses.
Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character. 1933;231:289-337.

4. cnx.org: Neyman-Pearson criterion:
http://cnx.org/content/m11548/latest/

SCREEN 20. CONFIDENCE REGIONS:
NEYMAN-PEARSON CONDITION.

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1. The Neyman-Pearson Condition involves the notion of confidence intervals, which reverse the traditional notion of hypothesis testing. In traditional hypothesis testing with a symmetric random variable, such as the normal distribution with population mean, μ, and population standard deviation, σ, we determine the probability whether a sample mean, X, lies within a fixed interval, say, X ± ησ, about the population mean, μ, i.e., the probability that X∈[μ-ησ,μ+ησ], or μ-ησ < X < μ+ησ:

Figure 3485.

2. In many cases, however, we don't really care about which proportion (probability) of values of X fall within this interval. Rather, we may have a good sense of the value of the population standard deviation, σ, but a poor sense regarding that of the population mean, μ. Furthermore, we may wish to estimate the value for μ, based upon our knowledge of X and σ.

3. Let us reverse the question to its algebraic equivalent, namely, whether σ lies in the interval, say, ±ησ, about X, i.e., σ ∈ [X -ησ, X +ησ] or X -ησ < σ < X +ησ:

Figure 3486.

Proof that (1): X -ησ < σ < X +ησ is equivalent to (2): μ-ησ < X < μ+ησ.
Expression (1) consists of expressions (1a): X -ησ < σ and (1b): σ < X +ησ. Add ησ to expression (1a) and -ησ to expression (1b), to obtain: X < μ+ησ and μ-ησ < X , which yield (2) . Q.E.D.

4. This reversal may seem like a peculiar probabilistic formulation, since X is subject to random fluctuations, whereas the population mean, μ, is fixed. Neyman and Pearson proposed the following interpretation in their theory of confidence intervals. The probability value, α, represents the probability that the random interval, X ± ησ, with bracket μ, as shown in Figure 3463:

Figure 3463.

Here, we show 20 trials, each of size N, where 1/20 (probability 5%) of the trial confidence bars fall outside the desired population mean, μ.

5. Of course, the population standard deviation, σ, is typically not known, but may be estimated as the sample standard deviation, S, divided by √N, where S/√N is the sample standard error, for trial-size, N. This sample standard error may vary from trial-to-trial, where the error bars are different sizes, corresponding to different values for S, as shown in Figure 3464:

Figure 3464. 6. The parameter, η, satisfies the Student t distribution for (N-1) degrees of freedom. The Neyman-Pearson condition asserts that....

7. The token swap test is a non-statistical test, in which there is no assumption of sampling; rather, probabilities are calculated from data internal to the contingency table itself. For this interpretation of the Neyman-Pearson condition, we must demonstrate that, for a given initial hypothesis, in which the marginal and grand totals are fixed and specified, a greater value for η, corresponds to a smaller value for α.

8. The essential argument of the Neyman-Pearson Condition is that greater power (=(1-β)) forces greater Type I Error (=α). For example, in a Gaussian distribution with two hypotheses, θ₀ (null hypothesis) and θ₁ (alternative hypothesis), the Type I error is designated as α and the Type II error is designated as β:

Figure 3477. The power, = (1-β), of the hypothesis test increases, at the expense of increasing the Type I error:

Figure 3478.

SCREEN 20A. CONFIDENCE REGIONS:
NEYMAN-PEARSON CONDITION.

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1. The easiest way to understand the Neyman-Pearson Condition is to consider two curves:

Figure 3477. Figure 3489.

The left curve, θ₀, corresponds to the null hypothesis; and the right curve, θ₁, corresponds to the alternative hypothesis.

2. A vertical line, η, is drawn between the two curves.

3. The shaded area ///// under the left curve, θ₀, that lies right of line η, represents Type I Error = α error = false positives, assuming that the null hypothesis is true.

4. The shaded area \\\\\ under the right curve, θ₁, that lies left of line η, represents Type II Error = β error = false negatives, assuming that the alternative hypothesis is true.

5. The power of a statistical test with respect to the alternative hypothesis is denoted, (1 - β).

6. If one increases the power of the alternative hypothesis, this is done at the expense of increasing the α error of the null hypothesis.

7. The Neyman-Pearson Condition is the property that hypotheses θ₀ and θ₁ are chosen to maximize the power of θ₁, for a given θ₀ and a given α error.

8. In the token swap test, the bell-shaped curves are replaced with discrete histograms:

Figure 3479.

The red line shown here is the η-line. The left histogram is predominantly the null hypothesis; and the right histogram is predominantly the alternative hypothesis.

SCREEN 21. CONTINGENCY TABLE ANALYSIS:
PROOF OF THE NEYMAN-PEARSON CONDITION.

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The essential argument of the Neyman-Pearson Condition is that greater power (=(1-β)) forces greater Type I Error (=α).

Lemma 1. In a 2×2 contingency table with given marginal totals, the frequency of cell d determines the frequencies of the other cell totals, a, b, and c.
Proof. Consider any value of d, where v, w, x, and y are determined. Then b=y-d, c=w-d, and a=x-c.

Lemma 2. In a 2×2 contingency table, let F^k_j, for 0<F^k_j<1, represent the proportion of tokens at frequency j in cell d after k swaps; for D, the expected value of cell d, let F⁰_D=1, and F⁰_j≠D=0. Then:

(1) F^k_j=0 for j<(D-k) and j>(D+k).

(2) F^k_(D-k)>0 and F^k_(D+k)>0.

(3) F^(k+1)_(D-k-1) < F^k_(D-k) and F^(k+1)_(D+k+1) < F^k_(D+k)

Proof. Part (1). Let k=1. Then:
F¹_(D+1) = [F⁰_D×(CB/(AD+CB)) + F⁰_(D+2)×...] where [F⁰_(D+2)=0;
and F¹_(D-1) = [F⁰_D×(AD/(AD+CB)) + F⁰_(D-2)×...] where F⁰_(D-2)=0.
By definition, F¹_j = [F⁰_(j-1)×...+ F⁰_(j+1)×...].
For j<(D-k), then F⁰_(j-1) = F⁰_(<D-2)=0 and F⁰_(j+1) = F⁰_(<D)=0.
For j>(D+k), then F⁰_(j-1) = F⁰_(>D)=0 and F⁰_(j+1) = F⁰_(>D+2)=0.

Let the lemma be true for k. Then.....

Proof. Part (2). Let k=1. Then:

Proof. Part (3). Let k=1. Then:

Theorem 1. The token swap test satisfies the Neyman-Pearson Condition.
Proof. ...........

SCREEN 22. THE ARGUMENT.

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1. Atomic statements of the medical model are propositions, i.e., statements that are either true, false, or uncertain. The negation of a proposition is also a proposition; the double-negation of a proposition equals the original proposition, i.e., --p=+p. We recognize two mutually exclusive sets of propositions: data, set D; and medical entities, set E. The negation of every datum is a datum, i.e., +d ∈ D implies -d ∈ D; and the negation of every medical entity is a medical entity, i.e., +e ∈ E implies -e ∈ E.

2. A datum is understood as a fixed event, with a fixed date/time and a localization on the patient, as for example, a serum potassium of 2.6 mEq/dL on January 1, 2007, at 8:00 AM; or a 0.5 cm pearly papule biopsied from the left nasal ala on January 1, 2007, at 8:00 AM.

3. A medical entity is an inferred truth, such as heart failure or basal cell carcinoma. A datum is either absolutely true, absolutely false, or absolutely uncertain. A medical entity is fuzzily true or fuzzily false, based upon inferences drawn from a data vector, Δ = {+d₁, +d₂, ... +d_n}, available at a particular time.

4. The relationship of medical entities to data is specified by an ontology (Rule 6) of accepted core beliefs in medicine. For example, a pearly papule and a confirmatory pathology report from the biopsy implies basal cell carcinoma, say, at a fuzzy level of 7/8 (or a certainty level of 3, see below).

5. Not every pearly papule of the nose is examined by a physician; and the physician does not biopsy every pearly papule that he/she examines. The patient must be worried enough about the papule to schedule a doctor's appointment; and the physician must be worried enough about the papule to justify a diagnostic biopsy. Rule 7 is the Vexative Rule (Latin: vexari = to worry), that provides justifications for obtaining particular data. It is assumed that every datum obtained has some payment, however small, in injury, pain, money, inconvenience, or risk of morbidity or mortality to the patient.

6. Rule 8, or Sutton's Law (go where the money is) (Willie Sutton, 1901-1980, American Bank Robber, nicknamed "Slick Willie") is the rule of jumping to conclusions based upon incomplete data (Brewka, 1997), also known as the Zebra Rule (if you hear hoofbeats in the street, think of horses not zebras). Medical reasoning inevitably involves decisions under uncertainty. One collects limited data, from which one must draw an initial conclusion. One has a a complementary/converse ethical mandate (Rule 5) to treat a threatening disease condition if there is compelling (but not absolute) evidence for it. On the other hand, one has the ethical mandate (Rule 4, first do no harm) not to collect unnecessary data, that might harm the patient physically, mentally, or financially. Therefore, there will be instances in which one initially jumps to the most likely but wrong conclusion, based upon data that are obtained subsequently.

In Petersdorf and Beeson's (1961) original paper on Sutton's Law, namely, (Fevers of Unexplained Origin)), these events are clinical findings suggesting one infectious agent that are superseded by subsequent culture results. In medical slang, these unexpected reversals are called zebras (Groopman, 2007). (Willie Sutton, 1901-1980, American Bank Robber; the original "Slick Willie": nickname for U. S. President Bill Clinton).

SCREEN 23. SCHRÖDINGER'S CAT.

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1. In classical propositional logic, these infrequent reversals of usual conclusions (which, cumulatively, occur rather often in medical practice) result in a mathematical inconsistency, i.e., a proposition that is both true and false, a mathematical abomination. This inconsistency may be avoided by requiring that conclusions be interpreted as medical entities, that are fuzzily true, but may be overturned by subsequent data.

2. The companion concept for overturning a plausible conclusion based upon subsequent data collection is Schrödinger's Cat:

"... There is a famous thought experiment called Schrödinger's cat. A cat is placed in a sealed box. There is a gun pointing at it, and it will go off if a radioactive nucleus decays. The probability of this happening is fifty percent. (Today no one would dare propose such a thing, even purely as a thought experiment, but in Schrödinger's time they had not heard of animal liberation.)

"If one opens the box, one will find the cat either dead or alive. But before the box is opened, the quantum state of the cat will be a mixture of the dead cat state with a state in which the cat is alive. This some philosophers of science find very hard to accept. The cat can't be half shot and half not-shot, they claim, any more than one can be half pregnant. Their difficulty arises because they are implicitly using a classical concept of reality. In this view, an object has not just a single history but all possible histories. In most cases, the probability of having a particular history will cancel out with the probability of having a very slightly different history; but in certain cases, the probabilities of neighboring histories reinforce each other. It is one of these reinforced histories that we observe as the history of the object.

"In the case of Schrödinger's cat, there are two histories that are reinforced. In one the cat is shot, while in the other it remains alive. In quantum theory both possibilities can exist together. But some philosophers get themselves tied in knots because they implicitly assume that the cat can only have one history."

From:

Hawking S.
Black Holes and Baby Universes and Other Essays.
New York: Bantam Books. 1993;:. Pages 44-45.
ISBN 0-553-37411-7, 182 pages.

3. In our formulation, as with the boxed Schrödinger's Cat, no medical entity is every absolutely certain [other than possibly in the mind of God, because God presumably works with a larger data vector than we mortals can ever know. Or, medical entities are perhaps also uncertain even in the mind of God, and the certainty model itself has been imposed upon God by arrogant humans. In any event, Schrödinger's Cat always has an encore in our formulation.]

4. In Schrödinger's Cat, one irrevocably determines the life-status of the cat when the cat's box is opened. In our mathematical model, one determines the status of medical entities when you apply Sutton's Law, i.e., jump to the most likely conclusion, given the data that you have on hand. In our mathematical model, this Schrödinger Opening of the cat's box unleashes an ethical mandate (Rule 7, Vexative) to collect additional data. In Schrödinger's formulation, the cat's box is opened exactly once. In our mathematical model, the cat's box is opened once; vexative data are collected; the cat's box is closed (i.e., Sutton's Law is suspended again); the cat's box is opened again; additional vexative data are collected; the cat's box is closed again, ....

SCREEN 24. SUMMARY OF RULES:
SET THEORY FORMULATION.

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0. The logic in this report is based upon classical logic, with the following three complementizers: payment (!); value(#); and knowledge/certainty($). That is, the harm/payment created by achieving higher levels of knowledge/certainty must be balanced by the value in obtaining that knowledge/certainty.

1. Rule 1. Complementizers: Absorb negation, homomorphic in logical-and. = complementizer-positive. That is: negative-negative-p equals p; know-negative-x equals know-p; pay-negative-p equals pay-p; value-negative-x equals value-p. Homomorphic in logical-and...........

2. Rule 2. Fuzzy asymmetry. More-certain implies less-certain. Certain^k+1p implies certain^kp.
Nandset definition: {-$^kp,+$^k+1p}.

3. Rule 3. Data are crisp. You either know a datum or not.
Nandset definition: {+$d,-$^∞d}.

4. Rule 4. Hippocrates-first (Hippocrates, 460-370 BC, Greek physician, father of medicine). That is, payment-datum implies value-datum. (Contrapositively: no-value-datum implies no-payment-datum.)
Nandset definition: {-#d,+!d}

5. Rule 5. Hippocrates-reverse. Treat if you can. Not-know-datum and value-datum implies harm-datum.
Nandset definition: {-$d,+#d,-!d}.

6. Rule 6. Ontology. If you know certain entities and data, then this generates the knowledge/certainty of an additional entity. For example, if this patient has an elevated serum-prostatic-specific-antigen, then you become more certain that the patient has prostate cancer.
Nandset definition: {+$^kΔ,Δ,..,-e,-$^k+1e} and {+$^kΔ,Δ,..,-$^ke}.

7. Rule 7. Vexative. If you know certain entities and data, then this generates value for an additional datum. That is, you become vexed by your ignorance of that additional datum. For example, if you know that an elderly male patient has not had a serum-prostatic-specific-antigen in the past five years, you become vexed regarding that missing-datum.
Nandset definition: {+$^ke,e,-$d,-#d,-$^k+1e}.

8. Rule 8. Ethical Data Registration. For each datum, there is a data-collection step, J, at which the datum is collected and is true; or the datum is collected and is false; or the datum collection attempt fails and the datum is unknown. Otherwise, the datum is never attempted and never collected. That is, for d ∈ D, there exists at most one J, 1 < J < H, at which (8.1.1) +$d, +d, +!d are true; or else (8.1.2) +$d, -d, +!d are true; or else (8.1.3) -$d, +!d are true. (8.2) Otherwise, for every J, 1 < J < H, -$d, +$d, -#d, +#d, -!d, +!d are all not entered into (S_J - S_J-1). The nandsets for Rule 8 are: (8.1.1) {-$d}, {-d}, {-!d} ∈ (S_J - S_J-1); or else (8.1.2) {-$d}, {+d}, {-!d} ∈ (S_J - S_J-1); or else (8.1.3) {+$d}, {-!d} ∈ (S_J - S_J-1). (8.2) Otherwise, {+$d}, {-$d}, {+#d}, {-#d}, {+!d}, {-!d} ~∈ S_J - S_J-1).

9. Rule 9. Schrödinger's Rule. At data-collection-step J, we create a set, O_J, the SCHRÖDINGER OPENING. The nandset for -$^kω, namely, {+$^kω}, is placed in O_J if and only if the nandset for +$^kω, namely, {-$^kω}, is NOT a member of the logical consequences of the data-collection-step, denoted ∫ (for logical "summation"). That is, anything that is uncertain at data-collection-step J is declared uncertain in O_J. If the cat's life is uncertain at data-collection-step J, then it is declared uncertain in O_J. However, the cat may spring alive again at data-collection-step (J+1). Watch closely: the reasoning is a little tricky.

Rule 9, Schrödinger's Rule: It is true that -$^kω for O_J if and only if +$^kω is not a logical consequence, denoted ∫ (for logical "summation"), of S_J. The nandset for Rule 9 is: {+$^kω} ∈ O_J if and only if {-$^kω} ~∈ ∫S_J, where ∫ represents logical consequences (for logical "summation").

SCREEN 25. METHOD OF PROOF:
ILLUSTRATED TABLES.

Return to Table of Contents.

1. There are two mutually exclusive classes of propositions: data, D and medical entities, E.

2. There are nine rules of relationship among these propositions.

3. Each rule corresponds to one or more nandsets. (Screen 24).

4. Nandsets are: green (quarantined), yellow (conditional), or red (absolute).

5. Proof consists of constructing a quarantine for a claimed theorem, and showing that the nine rules do not violate the quarantine.

6. Proof Example: The empty dataset is consistent.

7. Proof Example: Occam's Razor is satisfied for medical entities in the empty dataset (Occam, William of Ockham, 1285-1349, English logician and Franciscan friar).

stru3403.xls
stru3404.xls
stru3405.xls
stru3406.xls

Data Empty (Fig. 3403):

Data Positive (Fig. 3404):

Data Negative (Fig. 3405):

Data Failure (Fig. 3406):

SCREEN 26. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 1.
60 YEAR OLD MALE.

Return to Table of Contents.

A 60 year old male patient makes an appointment and visits a physician for the first time in the past ten years. Since the patient makes the appointment, we assume that the physician has permission (+#d1), and obtains the patient's age and sex, i.e., +$d1, +d1.

Prostate example, Step 1. Live Proof:

d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Step 1  : +0^
 Rule 3.1:    +0^
         :       +$$e^
         :          +$e^
         :       -$$e^
 Rule 3.1:    +0^
         :       +$$$e^
         :          +$$e^
         :       -$$$e^
 Rule 4.1:    +0^
         :       -#d1^
         :          -!d1^
         :       +#d1^
 Rule 5.1:    +0^
         :       -$d1^
         :          +#d1^
         :             +!d1^
         :          -#d1^
         :       +$d1^
 Rule 6.1:    +0^
         :       +d1^
         :          +$d1^
         :             -e^
         :                +$$e^
         :             +e^
         :          -$d1^
         :       -d1^
         :    +0^
         :       +d1^
         :          +$d1^
         :             +$e^
         :          -$d1^
         :       -d1^
 Rule 7.1:    +0^
         :       -$d2^
         :          -#d2^
         :             -e^
         :                +$e^
         :                   +$$e^
         :                -$e^
         :             +e^
         :          +#d2^
         :       +$d2^
 Rule 8.1:    +0^
         :       +#d1^
         :    +0^
         :       +$d1^
         :    +0^
         :       +!d1^
         :    +0^
         :       +d1^
 Rule 9.1:    +0^
         :       -$d2^
         :    +0^
         :       -$d3^
         :    +0^
         :       -$$e^
         :    +0^
         :       -$$$e^

Solution: +#d1 , +$d1 , +!d1 , +d1 , -$d2 , -$d3 , -$$e , -$$$e , +e , +$e , -$d2 , -$d3.

Prostate example, Step 1. Live Proof:
Restated with intuitive notation:
d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Step 1  : +0^
 Rule 3.1:    +0^
         :       +$$hasprca^
         :          +$hasprca^
         :       -$$hasprca^
 Rule 3.1:    +0^
         :       +$$$hasprca^
         :          +$$hasprca^
         :       -$$$hasprca^
 Rule 4.1:    +0^
         :       -#malesixty^
         :          -!malesixty^
         :       +#malesixty^
 Rule 5.1:    +0^
         :       -$malesixty^
         :          +#malesixty^
         :             +!malesixty^
         :          -#malesixty^
         :       +$malesixty^
 Rule 6.1:    +0^
         :       +malesixty^
         :          +$malesixty^
         :             -hasprca^
         :                +$$hasprca^
         :             +hasprca^
         :          -$malesixty^
         :       -malesixty^
         :    +0^
         :       +malesixty^
         :          +$malesixty^
         :             +$hasprca^
         :          -$malesixty^
         :       -malesixty^
 Rule 7.1:    +0^
         :       -$psapositive^
         :          -#psapositive^
         :             -hasprca^
         :                +$hasprca^
         :                   +$$hasprca^
         :                -$hasprca^
         :             +hasprca^
         :          +#psapositive^
         :       +$psapositive^
 Rule 8.1:    +0^
         :       +#malesixty^
         :    +0^
         :       +$malesixty^
         :    +0^
         :       +!malesixty^
         :    +0^
         :       +malesixty^
 Rule 9.1:    +0^
         :       -$psapositive^
         :    +0^
         :       -$prostatectomyca^
         :    +0^
         :       -$$hasprca^
         :    +0^
         :       -$$$hasprca^

Solution: +#malesixty , +$malesixty , +!malesixty , +malesixty , -$psapositive , -$prostatectomyca , -$$hasprca , -$$$hasprca , +hasprca , +$hasprca.

SCREEN 27. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 2.
60 YEAR OLD MALE, ELEVATED PSA.

Return to Table of Contents.

Prostate example, Step 2. Live Proof:

d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Solution: +#d1 , +!d1 , +$d1 , +d1 , +#d2 , +$d2 , +!d2 , +d2 , -$d3 , -$$$e , -$$$$e , +$e , +e , +$$e.

Prostate example, Step 2. Live Proof:

d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Solution: +#malesixty , +!malesixty , +$malesixty , +malesixty , +#psapositive , +$psapositive , +!psapositive , +psapositive , -$prostatectomyca , -$$$hasprca , -$$$$hasprca , +$hasprca , +hasprca , +$$hasprca.

SCREEN 28. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 2a.
60 YEAR OLD MALE, ELEVATED PSA.

Return to Table of Contents.

Prostate example, Step 2a. Live Proof:

d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Solution: +#d1 , +!d1 , +$d1 , +d1 , +#d2 , +$d2 , +!d2 , -d2 , -$d3 , -$$$e , -$$$$e , +$e.

Prostate example, Step 2a. Live Proof:

d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Solution: +#malesixty , +!malesixty , +$malesixty , +malesixty , +#psapositive , +$psapositive , +!psapositive , -psapositive , -$prostatectomyca , -$$$hasprca , -$$$$hasprca +$hasprca.

SCREEN 29. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 2b.
60 YEAR OLD MALE, ELEVATED PSA.

Return to Table of Contents.

Prostate example, Step 2b. Live Proof:

d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Step 2  : +0^
 Rule 3.1:    +0^
         :       +$$e^
         :          +$e^
         :       -$$e^
 Rule 3.2:    +0^
         :       +$$$e^
         :          +$$e^
         :       -$$$e^
 Rule 3.3:    +0^
         :       +$$$$e^
         :          +$$$e^
        :       -$$$$e^
 Rule 4.1:    +0^
         :       -#d1^
         :          -!d1^
         :       +#d1^
 Rule 4.2:    +0^
         :       -#d2^
         :          -!d2^
         :       +#d2^
 Rule 5.1:    +0^
         :       -$d1^
         :          +#d1^
         :             +!d1^
         :          -#d1^
         :       +$d1^
 Rule 5.2:    +0^
         :       -$d2^
         :          +#d2^
         :             +!d2^
         :          -#d2^
         :       +$d2^
 Rule 6.1:    +0^
         :       +d1^
         :          +$d1^
         :             -e^
         :                +$$e^
         :             +e^
         :          -$d1^
         :       -d1^
         :    +0^
         :       +d1^
         :          +$d1^
         :             +$e^
         :          -$d1^
         :       -d1^
 Rule 6.2:    +0^
         :       +d2^
         :          +$d2^
         :             -e^
         :                +$$$e^
         :             +e^
         :          -$d2^
         :       -d2^
         :    +0^
         :       +d2^
         :          +$d2^
         :             +$$e^
         :          -$d2^
         :       -d2^
 Rule 6.1:    +0^
         :       -d1^
         :          +$d1^
         :             +e^
         :                +$$e^
         :             -e^
         :          -$d1^
         :       +d1^
         :    +0^
         :       -d1^
         :          +$d1^
         :             +$e^
         :          -$d1^
         :       +d1^
 Rule 6.2:    +0^
         :       -d2^
         :          +$d2^
         :             +e^
         :                +$$$e^
         :             -e^
         :          -$d2^
         :       +d2^
         :    +0^
         :       -d2^
         :          +$d2^
         :             +$$e^
         :          -$d2^
         :       +d2^
 Rule 7.1:    +0^
         :       -$d2^
         :          -#d2^
         :             -e^
         :                +$e^
         :                   +$$e^
         :                -$e^
         :             +e^
         :          +#d2^
         :       +$d2^
 Rule 7.2:    +0^
         :       -$d3^
         :          -#d3^
         :             -e^
         :                +$$e^
         :                   +$$$e^
         :                -$$e^
         :             +e^
         :          +#d3^
         :       +$d3^
 Rule 7.1:    +0^
         :       -$d2^
         :          -#d2^
         :             +e^
         :                +$e^
         :                   +$$e^
         :                -$e^
         :             -e^
         :          +#d2^
         :       +$d2^
 Rule 7.2:    +0^
         :       -$d3^
         :          -#d3^
         :             +e^
         :                +$$e^
         :                   +$$$e^
         :                -$$e^
         :             -e^
         :          +#d3^
         :       +$d3^
 Rule 8.1:    +0^
         :       +#d1^
         :    +0^
         :       +!d1^
         :    +0^
         :       +$d1^
         :    +0^
         :       +d1^
 Rule 8.2:    +0^
         :       +#d2^
         :    +0^
         :       +$d2^
         :    +0^
         :       +!d2^
         :    +0^
         :       -d2^
 Rule 9.2:    +0^
         :       -$d3^
         :    +0^
         :       -$$$e^

Solution: +#d1 , +!d1 , +$d1 , +d1 , +#d2 , +$d2 , +!d2 , -d2 , -$d3 , -$$$e , -$$$$e , +$e , -e , +$$e , +#d1 , +!d1 , +$d1 , +d1 , +#d2 , +$d2 , +!d2 , -d2 , -$d3 , -$$$e.

Prostate example, Step 2b. Live Proof:

d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Step 2  : +0^
 Rule 3.1:    +0^
         :       +$$hasprca^
         :          +$hasprca^
         :       -$$hasprca^
 Rule 3.2:    +0^
         :       +$$$hasprca^
         :          +$$hasprca^
         :       -$$$hasprca^
 Rule 3.3:    +0^
         :       +$$$$hasprca^
         :          +$$$hasprca^
         :       -$$$$hasprca^
 Rule 4.1:    +0^
         :       -#malesixty^
         :          -!malesixty^
         :       +#malesixty^
 Rule 4.2:    +0^
         :       -#psapositive^
         :          -!psapositive^
         :       +#psapositive^
 Rule 5.1:    +0^
         :       -$malesixty^
         :          +#malesixty^
         :             +!malesixty^
         :          -#malesixty^
         :       +$malesixty^
 Rule 5.2:    +0^
         :       -$psapositive^
         :          +#psapositive^
         :             +!psapositive^
         :          -#psapositive^
         :       +$psapositive^
 Rule 6.1:    +0^
         :       +malesixty^
         :          +$malesixty^
         :             -hasprca^
         :                +$$hasprca^
         :             +hasprca^
         :          -$malesixty^
         :       -malesixty^
         :    +0^
         :       +malesixty^
         :          +$malesixty^
         :             +$hasprca^
         :          -$malesixty^
         :       -malesixty^
 Rule 6.2:    +0^
         :       +psapositive^
         :          +$psapositive^
         :             -hasprca^
         :                +$$$hasprca^
         :             +hasprca^
         :          -$psapositive^
         :       -psapositive^
         :    +0^
         :       +psapositive^
         :          +$psapositive^
         :             +$$hasprca^
         :          -$psapositive^
         :       -psapositive^
 Rule 6.1:    +0^
         :       +malesixty^
         :          -$malesixty^
         :             +hasprca^
         :                +$$hasprca^
         :             -hasprca^
         :          +$malesixty^
         :       -malesixty^
         :    +0^
         :       +malesixty^
         :          +$malesixty^
         :             +$hasprca^
         :          -$malesixty^
         :       -malesixty^
 Rule 6.2:    +0^
         :       -psapositive^
         :          +$psapositive^
         :             +hasprca^
         :                +$$$hasprca^
         :             -hasprca^
         :          -$psapositive^
         :       +psapositive^
         :    +0^
         :       -psapositive^
         :          +$psapositive^
         :             +$$hasprca^
         :          -$psapositive^
         :       +psapositive^
 Rule 7.1:    +0^
         :       -$psapositive^
         :          -#psapositive^
         :             -hasprca^
         :                +$hasprca^
         :                   +$$hasprca^
         :                -$hasprca^
         :             +hasprca^
         :          +#psapositive^
         :       +$psapositive^
 Rule 7.2:    +0^
         :       -$prostatectomyca^
         :          -#prostatectomyca^
         :             -hasprca^
         :                +$$hasprca^
         :                   +$$$hasprca^
         :                -$$hasprca^
         :             +hasprca^
         :          +#prostatectomyca^
         :       +$prostatectomyca^
 Rule 7.1:    +0^
         :       -$psapositive^
         :          -#psapositive^
         :             +hasprca^
         :                +$hasprca^
         :                   +$$hasprca^
         :                -$hasprca^
         :             -hasprca^
         :          +#psapositive^
         :       +$psapositive^
 Rule 7.2:    +0^
         :       -$prostatectomyca^
         :          -#prostatectomyca^
         :             +hasprca^
         :                +$$hasprca^
         :                   +$$$hasprca^
         :                -$$hasprca^
         :             -hasprca^
         :          +#prostatectomyca^
         :       +$prostatectomyca^
 Rule 8.1:    +0^
         :       +#malesixty^
         :    +0^
         :       +!malesixty^
         :    +0^
         :       +$malesixty^
         :    +0^
         :       +malesixty^
 Rule 8.2:    +0^
         :       +#psapositive^
         :    +0^
         :       +$psapositive^
         :    +0^
         :       +!psapositive^
         :    +0^
         :       -psapositive^
 Rule 9.2:    +0^
         :       -$prostatectomyca^
         :    +0^
         :       -$$$hasprca^

Solution: +#malesixty , +!malesixty , +$malesixty , +malesixty , +#psapositive , +$psapositive , +!psapositive , -psapositive , -$prostatectomyca , -$$$hasprca , -$$$$hasprca , +$hasprca , +$hasprca , -hasprca , +$$hasprca , -psapositive , -$prostatectomyca , -$$$hasprca.

SCREEN 30. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 3.
60 YEAR OLD MALE, ELEVATED PSA, POSITIVE PROSTATE BIOPSY.

Return to Table of Contents.

d1 = Patient is a 60 old male, malesixty.
d2 = Perform PSA test, psapositive.
d3 = Perform prostatectomy, prostatectomyca.
e = Has prostate carcinoma, hasprca.

Step 2  : +0^
 Rule 3.1:    +0^
         :       +$$hasprca^
         :          +$hasprca^
         :       -$$hasprca^
 Rule 3.2:    +0^
         :       +$$$hasprca^
         :          +$$hasprca^
         :       -$$$hasprca^
 Rule 3.3:    +0^
         :       +$$$$hasprca^
         :          +$$$hasprca^
         :       -$$$$hasprca^
 Rule 4.1:    +0^
         :       -#malesixty^
         :          -!malesixty^
         :       +#malesixty^
 Rule 4.2:    +0^
         :       -#psapositive^
         :          -!psapositive^
         :       +#psapositive^
 Rule 4.3:    +0^
         :       -#prostatectomyca^
         :          -!prostatectomyca^
         :       +#prostatectomyca^
 Rule 5.1:    +0^
         :       -$malesixty^
         :          +#malesixty^
         :             +!malesixty^
         :          -#malesixty^
         :       +$malesixty^
 Rule 5.2:    +0^
         :       -$psapositive^
         :          +#psapositive^
         :             +!psapositive^
         :          -#psapositive^
         :       +$psapositive^
 Rule 5.3:    +0^
         :       -$prostatectomyca^
         :          +#prostatectomyca^
         :             -!prostatectomyca^
         :          -#prostatectomyca^
         :       +$prostatectomyca^
 Rule 6.1:    +0^
         :       +malesixty^
         :          +$malesixty^
         :             -hasprca^
         :                +$$hasprca^
         :             +hasprca^
         :          -$malesixty^
         :       -malesixty^
         :    +0^
         :       +malesixty^
         :          +$malesixty^
         :             +$hasprca^
         :          -$malesixty^
         :       -malesixty^
 Rule 6.2:    +0^
         :       +psapositive^
         :          +$psapositive^
         :             -hasprca^
         :                +$$$hasprca^
         :             +hasprca^
         :          -$psapositive^
         :       -psapositive^
         :    +0^
         :       +psapositive^
         :          +$psapositive^
         :             +$$hasprca^
         :          -$psapositive^
         :       -psapositive^
 Rule 6.3:    +0^
         :       +prostatectomyca^
         :          +$prostatectomyca^
         :             -hasprca^
         :                +$$$hasprca^
         :             +hasprca^
         :          -$prostatectomyca^
         :       -prostatectomyca^
         :    +0^
         :       +prostatectomyca^
         :          +$prostatectomyca^
         :             +$$$hasprca^
         :          -$prostatectomyca^
         :       -prostatectomyca^
 Rule 6.1:    +0^
         :       +malesixty^
         :          +$malesixty^
         :             +hasprca^
         :                +$$hasprca^
         :             -hasprca^
         :          -$malesixty^
         :       -malesixty^
         :    +0^
         :       +malesixty^
         :          +$malesixty^
         :             +$hasprca^
         :          -$malesixty^
         :       -malesixty^
 Rule 6.2:    +0^
         :       +psapositive^
         :          +$psapositive^
         :             +hasprca^
         :                +$$$hasprca^
         :             -hasprca^
         :          -$psapositive^
         :       -psapositive^
         :    +0^
         :       +psapositive^
         :          +$psapositive^
         :             +$$hasprca^
         :          -$psapositive^
         :       -psapositive^
 Rule 6.3:    +0^
         :       +prostatectomyca^
         :          +$prostatectomyca^
         :             +hasprca^
         :                +$$$hasprca^
         :             -hasprca^
         :          -$prostatectomyca^
         :       -prostatectomyca^
         :    +0^
         :       +prostatectomyca^
         :          +$prostatectomyca^
         :             +$$$hasprca^
         :          -$prostatectomyca^
         :       -prostatectomyca^
 Rule 7.1:    +0^
         :       -$psapositive^
         :          -#psapositive^
         :             -hasprca^
         :                +$hasprca^
         :                   +$$hasprca^
         :                -$hasprca^
         :             +hasprca^
         :          +#psapositive^
         :       +$psapositive^
 Rule 7.2:    +0^
         :       -$prostatectomyca^
         :          -#prostatectomyca^
         :             -hasprca^
         :                +$$hasprca^
         :                   +$$$hasprca^
         :                -$$hasprca^
         :             +hasprca^
         :          +#prostatectomyca^
         :       +$prostatectomyca^
 Rule 7.1:    +0^
         :       -$psapositive^
         :          -#psapositive^
         :             +hasprca^
         :                +$hasprca^
         :                   +$$hasprca^
         :                -$hasprca^
         :             -hasprca^
         :          +#psapositive^
         :       +$psapositive^
 Rule 7.2:    +0^
         :       -$prostatectomyca^
         :          -#prostatectomyca^
         :             +hasprca^
         :                +$$hasprca^
         :                   +$$$hasprca^
         :                -$$hasprca^
         :             -hasprca^
         :          +#prostatectomyca^
         :       +$prostatectomyca^
 Rule 8.1:    +0^
         :       +#malesixty^
         :    +0^
         :       +!malesixty^
         :    +0^
         :       +$malesixty^
         :    +0^
         :       +malesixty^
 Rule 8.2:    +0^
         :       +#psapositive^
         :    +0^
         :       +$psapositive^
         :    +0^
         :       +!psapositive^
         :    +0^
         :       +psapositive^
 Rule 8.3:    +0^
         :       +#prostatectomyca^
         :    +0^
         :       +$prostatectomyca^
         :    +0^
         :       +!prostatectomyca^
         :    +0^
         :       +prostatectomyca^
 Rule 9.3:    +0^
         :       -$$$$hasprca^

Solution: +#malesixty , +!malesixty , +$malesixty , +malesixty , .

SCREEN 31. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

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SCREEN 32. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

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SCREEN 33. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

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SCREEN 34. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

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SCREEN 35. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

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SCREEN 36. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

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Definition 1. x is a logical consequence of X if and only if for every t∈T such that x⊆t, there exists a y ∈ X such that y⊆t.

Definition 2. ∫X is the set of all logical consequences of X.

Theorem 1. X ⊆ ∫X.
Proof: Consider any x∈X. Claim: x∈∫X. Consider any t∈T such that x⊆t. Then there exists a y∈X, namely, y=x, such that y=x⊆t. Q.E.D.

Definition 3. Ethical-data-sequence, B₀, B₁, B₂,..., B_H:
Definition 3.1.: B₀ is the set of nandsets specified by Rules 1, 2, 3, 4, 5, 6, and 7.
Definition 3.2.: For 1 <I<H, B_I - B_(I-1) contains exactly the nandsets for a single datum collected according to Rule 8.

Definition 4. Schrödinger cover,....

Theorem 2. B₀ is consistent: Ø ~∈∫B₀.
Proof:

Theorem 3. No $d is true for ∫B₀. Occam's Razor: No data are implied without data: {-$d} ~∈∫B₀.
Proof:

Theorem 4. No $e is true for ∫B₀. Occam's Razor: No entities are implied without data: {-$e} ~∈∫B₀.
Proof:

Theorem 5. No #d is true for ∫B₀. Occam's Razor: No data are needed without other data: {-#d} ~∈∫B₀.
Proof:

Theorem 6. Ø ~∈∫B_H
Proof:

Theorem 7. {+$d} ∈ C_I if and only if {+d} ~∈ B_I and {-d} ~∈ B_I.
Proof:

Theorem 8. if {-$e} ~ ∈ ∫B_IC_I, then {+e} ~∈ ∫B_IC_I and {-e} ~∈ ∫B_IC_I.
Proof:

Theorem 9. Consistency of B_IC_I. Ø ~∈ ∫C_IB_I
Proof:

Theorem 10. ∫B_IC_I is Hippocratic-first if and only if B₀ is Hippocratic-first.
Proof:

Theorem 11. ∫B_IC_I is Hippocratic-reverse if and only if B₀ is Hippocratic-reverse.
Proof:

Theorem 12. ∫B_IC_I is ontologic if and only if B₀ is ontologic.
Proof:

Theorem 13. ∫B_IC_I is vexative if and only if B₀ is vexative.
Proof:

Definition 5. Necessarily. +□p = (+$p & +p).

Definition 6. Possibly. +◇p = -□-p.

Rule 1a. Complementizer Negation. +$+p = +$-p.

Rule 1b. Complementizer Homomorphism: +$(+p & +q) = (+$+p & +$+q).

Rule 2. Fuzzy Asymmetry: $$p ⇒ $p.

Theorem 14. $□p = +$$p.
Proof: $□p = +$($p&p) = (+$$p&$p) = +$$p. Q.E.D.

Theorem 15. +□□p = (+$$p&+p).
Proof:+□□p = (+$□p & +□p) = (+$$p & +$p & +p) = (+$$p & +p) = (+$$p&+p). Q.E.D.

Theorem 16. +◇p = -$p | +p.
Proof: ◇p = -□-p = -($-p & -p) = (-$p | +p).

Theorem 17. +◇◇p = ◇p = (+$$p & +p).
Proof: +◇◇p = +◇(-$p|p) = -$p(-$p|p) |-$p | +p = (-$$p&-$p)|-$p|+p = = +◇p.

Theorem 18. Contrapositive.

 | +0       |                   | +0       |
 |    +p    |                   |    -q    |
 |       +q |   if and only if  |       -p |
 |    -p    |                   |    -q    |

Theorem 19. Contrapositive.

 | +0          |                   | +0          |
 |    +p       |                   |    +p       |
 |       +q    |                   |       -r    |
 |          +r |   if and only if  |          -q |
 |       -q    |                   |       +r    |
 |    -p       |                   |    -p       |

Theorem 20.

 | +0          |                  
 |    +p       |                  
 |       +q    |                  
 |          +r | if and only if (+0 & +p & +q) ⇒ +r
 |       -q    |                  
 |    -p       |

Theorem 21. +□□p = +$$p & +p
Proof: +□□+p = +$(+$p&+p)&+$p &p. +□□+p = (+$$p & +$p & +$p & p) = (+$$p & +$p & p). $$p ⇒ $p.

Theorem 22. (+□+p|+□□+p) = +□+p.
Proof: (+□+p|+□□+p) = (($p&+p)|($$p&+p)) = ((+$p|+$$p)&+p) = (+$p&+p) = +□+p. Q.E.D.

Theorem 23. (+□+p & +□□+p) = +□□+p.
Proof: (+□+p&+□□+p) = (($p &+p)&($$p&+p)) = ($$p &$p&+p) = ($$p &+p) = +□□+p. Q.E.D.

Theorem 24. (+□+p | +□□-p) = (+□+p | +$$+p).
Proof: (+□+p|+□□-p) = ((+$p&+p)|(+$$p&-p)) = ((+$p|$$p)&(+$p|-p)&(+p|+$$p)&(+p|-p)) = (+$p&(+p|+$$p)) = ((+$p&+p)|(+$p&+$$p)) = ((+$p&+p)|+$$p) = (+□+p|+$$p). Q.E.D.

Theorem 25. (+□+p&+□□-p)=Ø.
Proof: (+□+p&+□□-p) = ((+$p&+p)&(+$$p&-p)) = (+$p&+p&+$$p&-p) = Ø. Q.E.D.

Theorem 26.
Proof:

Theorem 27.
Proof:

Theorem 28.
Proof:

Theorem 29.
Proof:

Theorem 30.
Proof:

Theorem 31.
Proof:

Theorem 32.
Proof:

Theorem 33.
Proof:

Theorem 34.
Proof:

Theorem 35.
Proof:

Theorem 36.
Proof:

Theorem 37.
Proof:

Theorem 38.
Proof:

Theorem 39.
Proof:

SCREEN 37. METHOD OF PROOF:
LIVE PROOF OF COROLLARY 1.

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Proof: 1.1. If. ((+$$p ⇒ +$p) & (+$$p &+$p &+p)) ⇒ (+$$p & +p).
The corresponding nandsets are:

{-$$p, +$$p, +$p, +p, -$$p},
{-$$p, +$$p, +$p, +p, -p},
{+$p, +$$p, +$p, +p, -$$p}, and
{+$p, +$$p, +$p, +p, -p}.

Proof: 1.2. Only If. ((+$$p ⇒ +$p) & (+$$p &+p)) ⇒ (+$$p & +$p & +p) = +□□+p.
The corresponding nandsets are:

{-$$p, +$$p, +p, -$$p},
{-$$p, +$$p, +p, -$p},
{-$$p, +$$p, +p, -p},
{+$p, +$$p, +p, -$$p},
{+$p, +$$p, +p, -$p}, and
{+$p, +$$p, +p, -p}.

Live Proof:

Live Proof:

0.1. Example: (+p ⇒ +q) ⇒ (+p ⇒ +p).
Proof: Nandsets {-p,+p,-p} and {+q,+p,-p}. are vacuous.
Live Proof:

SCREEN 38. METHOD OF PROOF:
TWO CLASSES OF PROPOSITIONS:
DATA AND MEDICAL ENTITIES.

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SCREEN 44. METHOD OF PROOF:
EMPTY DATASET SATISFIES OCCAM'S RAZOR.

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(Occam, William of Ockham, 1285-1349, English logician and Franciscan friar).

SCREEN 45. ZERMELO-FRANKEL SET THEORY (ZFST).

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1. Zermelo-Frankel Set Theory (ZFST) is ordinary set theory (Ernst Zermelo, 1871-1953, German mathematician; Abraham Fraenkel, 1891-1965, German mathematician) (Lewis, 1932; Suppes, 1960; Halmos, 1960; Moore et al, 1968).

2. Undefined concepts of ZFST: is-a-member-of or belongs-to ∈; null-set or empty-set, Ø or {}.

3. Set is defined exactly by its members, arbitrary order.

4. Set-of-x not equal x; no repeat elements in a set.

5. Roster (extensional, list) notation: set O = {heart, lung, liver, pancreas, ...}.

6. Raster (intensional) notation: O = {x|x is a major-body-organ}.

7. Fuzzy Set Theory (FST) ( Zadeh, 1965; Zadeh, 1968; Zadeh, 1969; Zadeh, 1972; Zadeh, 1973; Zadeh, 1978; Zadeh, 1982; Zadeh, 1983; Zadeh, 1984; Zadeh, 1985; Zadeh, 1986; Zadeh, 1996; Zadeh, 2001; ........... ). Partial membership. FUZZY DEFINITION 1: For every ω ∈ Ω such that (+$^zω ∧ +ω) is true at the Jth data-collection-step, μ_J(+ω) =(1 - 2^-1-z) and μ_J(-ω) = 2^-1-z, where z=0 if -$ω is true at the Jth data-collection-step.

The nandset version for FUZZY DEFINITION 1 is: For every ω ∈ Ω such that {-$^zω}, {-ω} ∈ ∫(S_J ∪O_J), μ_J(+ω) =(1 - 2^-1-z) and μ_J(-ω) = 2^-1-z, where z=0 if {+$^zω} ∈ ∫(S_J ∪O_J).

SCREEN 46. ZERMELO-FRANKEL SET THEORY.

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0. Ernst Zermelo, 1871-1953, German mathematician; Abraham Fraenkel, 1891-1965, German mathematician.

1. SUBSET: X ⊆ Y if and only if for every x ∈ X, x ∈ Y.

2. EQUALITY: X = Y if and only if X ⊆ Y and Y ⊆ X.

3. UNION: X ∪ Y is the set of all x such that x ∈ X or x ∈ Y or both.

4. INTERSECTION: X ∪ Y is the set of all x such that x ∈ X and x ∈ Y.

5. SUBTRACTION: X - Y is the set of all x such that x ∈ X and x ~∈ Y.

SCREEN 47. NO PARADOX OF SELF REFERENCE.

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1. Epimenides the Cretan: All Cretans are liars.

2. St. Paul's Letter to Titus: 1:12. "One of themselves, even a prophet of their own, said, The Cretans are always liars, evil beasts, slow bellies...." [100].

3. Barber paradox: The Barber of Seville (Opera by Rossini) shaves everyone who doesn't shave himself. Who shaves the Barber of Seville?

4. Russell's Paradox (Letter to Frege): Set of all sets [101]. (Gottlob Frege, 1848-1925, German mathematician; Bertrand Russell, 1872-1970, British philosopher).

5. G. G. Berry's Paradox: "The smallest positive integer not nameable in under eleven words." (Berry, 2004; Hofstadter, 1979; Hofstadter, 2007).

6. Baltimore VAMC patient states: All Baltimore VAMC patients are liars. Do you believe the medical history or not?

SCREEN 48. BASIC CONCEPTS OF THE THEORY.

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1. Atomset, Ω, set of distinct, atomic statements (atoms, Ω), each with a definite true-false status.

2. Each atom is either a datum or a medical entity: (D ∪ E) = Ω.

3. Data include complaints, history, physical findings, laboratory values, statements of consent, etc.

4. Medical entities include cancer, inflammation, necrosis, etc.

5. No datum is an entity and no entity is a datum: (D ∪ E) = Ø.

6. To each atom, there exists known-to-the-ω $^kω ∈ $Ω, for every integer k, up to a maximum, M.

7. To each datum, there exists value-to-know-d, #d ∈ #D, and pay-to-know-d, !d ∈ !D.

THEOREM §6.1. CONSISTENCY OF RDF CLASSES.

is consistent.
Live Proof:
Solution: Theorem is non-vacuous.

THEOREM §6.2. IDENTITY.

Class p implies class p.


 +p
    +p

Nandset: {+p, -p}.
Live Proof:
Solution: Theorem is vacuous.

THEOREM §6.3. OR-EXPANSION.


 +p                      +p
    +q         ⇒           +q
                            +q
                            +q
                            ...

Nandsets: {+p,-p,+q,+q,+q....} and {-q,-p,+q,+q,+q....}.
Live Proof:
Solution: Theorem is vacuous.

THEOREM §6.4. TELESCOPING.


 +p                      +p
    +q         ⇒            +u
       +r                      
          +s                   
             +t                 
                 +u

Nandsets: {+p,+p,-p,+r}, {+p,+q,-p,+r}, {+p,-r,-p,+r}, {-q,+p,-p,+r}, {-q,+q,-p,+r}, and {-q,-r,-p,+r}.
Live Proof:
Solution: Theorem is vacuous.

THEOREM §6.5. CONTEXTUALIZATION.


 +p                      +p
    +p         ⇒            +q
       +q                      +r
    +p                         +s
       +r
       +s

Nandsets: {+p,+p,-p,-q,+r,+s}, {+p,-r,-p,-q,+r,+s}, {+p,-s,-p,-q,+r,+s}, {-q,+p,-p,-q,+r,+s}, {-q,-r,-p,-q,+r,+s}, and {-q,-s,-p,-q,+r,+s}.
Live Proof:

Solution: Theorem is vacuous.

THEOREM §6.6. INTERCALATION.

Procedure for inserting (intercalating) a new subhierarchy into the hierarchy, while not disturbing the remaining hierarchy.


 +p                      +p
    +p                      +q
       +q         ⇒         +r
       +r
    +p
       +s
       +t

Nandsets: {+p,+p,-p,+q,+r}, {+p,-s,-p,+q,+r}, {+p,-t,-p,+q,+r}, {-q,+p,-p,+q,+r}, {-q,-s,-p,+q,+r}, {-q,-t,-p,+q,+r}, {-r,+p,-p,+q,+r}, {-r,-s,-p,+q,+r}, and {-r,-t,-p,+q,+r}.
Live Proof:

6.6.    : +0^
 6.6.1.  :    +0^
         :       +p^
         :       +p^
         :       -p^
         :       +q^
         :       +r^
 6.6.2.  :    +0^
         :       +p^
         :       -s^
         :       -p^
         :       +q^
         :       +r^
 6.6.3.  :    +0^
         :       +p^
         :       -t^
         :       -p^
         :       +q^
         :       +r^
 6.6.3.  :    +0^
         :       -q^
         :       +p^
         :       -p^
         :       +q^
         :       +r^
 6.6.4.  :    +0^
         :       -q^
         :       -s^
         :       -p^
         :       +q^
         :       +r^
 6.6.5.  :    +0^
         :       -q^
         :       -t^
         :       -p^
         :       +q^
         :       +r^
 6.6.6.  :    +0^
         :       -r^
         :       +p^
         :       -p^
         :       +q^
         :       +r^
 6.6.7.  :    +0^
         :       -r^
         :       -s^
         :       -p^
         :       +q^
         :       +r^
 6.6.8.  :    +0^
         :       -r^
         :       -t^
         :       -p^
         :       +q^
         :       +r^

Solution: Theorem is vacuous.

THEOREM §6.7. RETIREMENT.

Procedure for removing a subhierarchy (obsolete concept), without disturbing the remainder of the hierarchy.


 +p                      +p
    +p            ⇒         +q
       +q
       +r
    +p
       -r

Nandsets: {+p,+p,-p,+q}, {+p,+r,-p,+q}, {-q,+p,-p,+q}, {-q,+r,-p,+q}, {-r,+p,-p,+q}, and {-r,+r,-p,+q}.
Live Proof:
Solution: Theorem is vacuous.

SCREEN 49. COMPLEMENTIZERS:
DICITUR HOMERUM CAECUM ESSE.

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1. DICITUR HOMERUM CAECUM ESSE. (Latin: It is said that Homer was blind. Homer, 8th century BC, Greek poet). This famous paradigm of Latin pedagogy contains two assertions: a factual assertion (here, medical assertion), namely, Homer was blind, and a modal assertion, namely, It is said that.... In the present, evidence-based model of medicine, no assertion is made without qualifying its source: certainty, payment, and value. In linguistics, the connector, that, is called a complementizer. In this report, there are three complementizers: know-whether/certainty ($), value-to-know-whether/value (#), and pay-to-know-whether (!). In this report, the complementizers absorb negations. Thus, if we know whether Homer was blind, then we know whether Homer was not-blind; if we pay-to-know whether Homer was blind, then we pay-to-know whether Homer was not-blind; if we value-to-know whether Homer was blind, then we value-to-know whether Homer was not-blind.

2. Modal part: DICITUR... It is said that...
Medical part: HOMERUM CAECUM ESSE. .. Homer was blind.

3. Modal part: DICITUR SIVE... It is said whether...
Medical part: HOMERUM CAECUM ESSE (...SIVE HOMERUM NON CAECUM ESSE). .. Homer was blind (or Homer was not blind).

4. Modal part: COGNITUR SIVE... It is known whether...
Medical part: HOMERUM CAECUM ESSE.... .. Homer was blind.

5. Modal part: QUAERITUR SIVE... It is sought-to-know whether...
Medical part: HOMERUM CAECUM ESSE.... .. Homer was blind.

6. Modal part: CONATUR SIVE... It is tried-to-know whether...
Medical part: HOMERUM CAECUM ESSE.... .. Homer was blind.

7. It is known/valued-to-know/paid-to-know whether the patient's serum prostatic specific antigen is elevated.

8. It is known whether the patient has prostate cancer, +$prostatecancer.

SCREEN 50. MODAL/FUZZY LOGIC AND COMPLEMENTIZERS.

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1. Modal/fuzzy/multi-valued logic discusses the strength of a truth [4,5,6,7,11,80,81].

2. COGNITIVE ($): It is certain whether...

3. QUISITIVE (#): It is valued-to-know whether...

4. CONATIVE (!): It is paid-to-know whether...

5. VENN DIAGRAM:

SCREEN 51: MODAL/FUZZY LOGIC:
ST PETER'S RULE.

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1. Modal logic involving necessarily (□) and possibly (◇) operators has a rich history in Western philosophy and mathematics. Aristotle denounced the idea (Aristotle, 384-322 BC, Greek philosopher). Łukasiewicz (Jan Łukasiewicz, 1848-1956, Polish logician) embraced the idea and it was later modernized and generalized by Zadeh and coworkers, as FUZZY SETS. I am particularly fond of the New Testament reference, that is engraved in 2-meter-high golden letters in Latin and Greek on the western ceiling of the Sistine Chapel in Vatican City.

2. "...Thou art Peter, and upon this rock... and whatsoever thou shalt bind (□) on earth shall be bound (□) in heaven; and whatsoever thou shalt loose (◇) on earth shall be loosed (◇) in heaven...." [103].

3. □a = (a ∧ $a).

4. ◇a = (a ∨ -$a).

5. □a = -◇-a; ◇a = -□-a.

6. □^ka = (a ∧ $^ka).

7. ◇^ka = (a ∨ -$^ka).

SCREEN 52: SUTTON'S LAW.

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Willie Sutton, 1901-1980, American Bank Robber, nicknamed "Slick Willie".

1. Reporter: Willie, why to you always rob banks?
Willie Sutton: Because that's where the money is. [3,104].

2. Fever of Undermined Origin [105].

3. In the event of uncertainty, go where the money (i.e., the most likely result) is.

4. In the event of fever in a patient with cough, rusty sputum, shortness of breath, lobar pneumonia, go for streptococcal pneumonia, i.e., the most likely result, while waiting for culture results.

5. For data δ.. and entity e, □^kΔ..⇒ (□^ke|□^k+1-e),

6. Another version of Sutton's Law is: if you hear hoofbeats in the street, think of horses not zebras. At least in North America, horses are much more likely than zebras. Continuining this metaphor, a rare medical case is called a ZEBRA, and a tertiary-care hospital that specializes in rare medical cases, such as the University of Maryland Medical System or The Johns Hopkins Medical Institutions, is called a ZEBRA FARM.

SCREEN 53. BASIC DEFINITIONS.

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1. CARDINALITY OF SET X, ñX, is number of elements in X.

2. M >1 is MAXIMUM KNOWLEDGE, for $¹a, $²a,..., $^Ma.

3. Data are collected sequentially in steps 0, 1, 2,..., H, MAXIMUM DATABASE, to comprise the KNOWLEDGE/DATABASE, denoted B₀, B₁, B₂,..., B_H.

4. G is the number of elements in the knowledge/database, B_H, i.e., G = ñB_H.

5. ATOMSET, A = {+a,-a,...}, where for every +a ∈ A, -a ∈ A, -a ~= a, ++a = +a, and --a = +a.
D = {+d,-d,...} is the set of DATA, where for every d ∈ D, -d ∈ D.
E = {+e,-e,...} is the set of ENTITIES, where for every e ∈ E, -e ∈ E.
(D ∪ E) = A and (D ∪ E) = Ø.

5. COMPLEMENTIZERS: $^k, #, !, where for every 1 < k < M, and for every a ∈ A, and d ∈ D, a=$^ka = $^k-a, #d=#-d, and !d=!-d, where: COGNITIVE, $^ka: known-to-the-k whether a ....
QUISITIVE, #d: value-to-know whether d ....
CONATIVE, !d: pay-to-know whether d ....

6. FULLSET, F = {+f,-f,...}, where f ∈ F if and only if: f ∈ A; or for some a ∈ A and 1 < k < M, f=$^ka or f=-$^ka, or for some d ∈ D, f=#d, f=-#d, f=!d, or f=-!d.

7. WORLD, W, is the set of all w ∈ W where w ⊆ F, i.e., W is the powerset of F, denoted ∏F.

8. The SET OF ALL POSSIBLE PATIENTS, or the POSSIBLE WORLDS, or the TRUTH TABLE, T⊆W [5], is the set of all t ∈ T such that for every f ∈ F, either f ∈ t or -f ∈ t, but not both.

9. NANDSET/NULLITY[3,4,106-110]: It is true that (x₁ | x₂ | x₃ |...) for X if and only if {-x₁,-x₂,-x₃,...} ∈ X. NANDSETS have the property that if Y ⊆ Z, then Y implies Z.

10. For any X ⊆ W, the CONSEQUENCES OF X, ÇX, ÇX is the set of all y ∈ ÇX such that for every t ∈ T, y ⊆ t if and only if there exists an x ∈ X such that x ⊆ t.

Claim: ÇX is computable after cG⁴ steps, for some constant, c.

SCREEN 54. RULE 1. DOUBLE-NEGATIVE=POSITIVE.
COMPLEMENTIZERS ABSORB NEGATIVES.

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0. Double-negative = positive. Complementizer-negative = complementizer-positive.

1. A = {+a,-a,...} is the ATOMSET.

2. For every +a ∈ A, -a ∈ A, -a ~= a, ++a = +a, and --a = +a.

3. For every +a ∈ A, $^ka = $^ka;

4. For every +d ∈ D, #+d = #-d; !+d = !-d.

SCREEN 55. RULE 2. KNOWLEDGE-LADDER.

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0. Know-more implies know-less.

1. ($^k+1a⇒$^ka)@B₀.

2. NANDSET DEFINITION: {-$^ka, +$^k+1a} ∈ B₀, for every k, 1 < k < M-1 and a ∈ A.

3. VENN DIAGRAMS:

SCREEN 56. RULE 3. DATA-ABSOLUTE.

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0. You either know a datum or not.

1. ($d⇒$^Md)@B₀.

2. NANDSET DEFINITION: {+$d,-$^Md} ∈ B₀, for every d ∈ D.

3. VENN DIAGRAMS:

SCREEN 57. RULE 4. d-HIPPOCRATIC.

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0. Hippocrates. First do no harm. (Hippocrates, 460-370 BC, Greek physician, father of medicine).

1. (-#d⇒-!d)@B₀ [99].

2. NANDSET DEFINITION: {-#d,+!d} ∈ B₀, for d ∈ D.

3. VENN DIAGRAMS:

SCREEN 58. RULE 5. d-CONATIVE.

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0. Not-know-datum and value-datum implies payment-datum.

1. ((-$d&#d)⇒!d)@B₀.

2. NANDSET DEFINITION: {-$d,+#d,-!d} ∈ B₀, for d ∈ D.

3. VENN DIAGRAMS:

SCREEN 59. RULE 6. keδ..d-VEXATIVE.

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1. (□^ke&□^kδ, ...,&-$d)⇒(#d| □^k+1-e) @ B₀.

2. NANDSET DEFINITION: {+$^ke,e,+$^kδ,δ,-$d,-#d, -$^k+1e} ∈ B₀, for 1 < k < M-2, δ∈ D, and e ∈ E.

3. The keδ..d-vexative definition supports a VOBIS-DIFFICILE CONDITION (Latin: Difficult-thing for you).

4. A condition that is easy for some patients but difficult for others.

SCREEN 60. RULE 7. kδ...e-ONTOLOGIC.

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1. Ontology: Platonic description of essential reality [111-115] (Plato, 424-348 BC, Greek philosopher).

2. Contrast: what one can see (observation, accident); what one can know (epistemology); what one can believe (doxology); other aspects of perceiving reality (St Thomas Aquinas, 1225-1274, Roman Catholic theologian).

3. Metaphysical commitments or presuppositions embodied in natural sciences.

4. Example: belief that a cancer can metastasize.

5. In medical informatics, ontology is a structured list of concepts and relations among concepts.

6. Eventually, an ontology should be prepared by an expert or panel of experts. For example, the AJCC/UICC Tumor Staging Manual, Sixth Edition, is an ontology of tumor prognosis. The bigger the tumor, the worse the prognosis.

7. (□^kδ..)⇒ (□^ke|□^k+1-e) @ B₀, 1<k<M-2.

8. What is □^Me? Or more generally, what is □^∞e? Consider this German rhyme:

"Alle Kunst
Ist umsunst
Wenn der Engel
Auf dem Zundloch brunst."

All artifice is in vain when the angel urinates on your musket.

Quoted by Prof. Rüdiger Breitnaecker, MD, in his lecture on forensic pathology to The Johns Hopkins Medical School second-year pathology students, February, 1977.

That is, □^∞e is "the angel" (der Engel), the devil, the Adversary (Hebrew: שתן ), Robin Goodfellow (Shakespeare: Midsummer Night's Dream), Prince of Darkness, Lord of the Flies, etc., who reverses the established order and experience of medical science.

In straight poker, □^∞e is like SHOW.

8. VENN DIAGRAMS:

9. NANDSET DEFINITION: {+$^kδ,δ,-e,-$^k+1e} ∈ B₀ and {+$^kδ,δ,-$^ke} ∈ B₀ for 1 < k < M-2, d ∈ D, δ ⊆ (D - {+d,-d}).

SCREEN 61. RULE 8. ETHICAL-DATIVE.

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0. If d is d-Hippocratic, then there exists at most one I, 1 < I < H, such that:
1. (POS-DATA): +$d, +d, +!d true for B_I, xor
2. (NEG-DATA): +$d, -d, +!d true for B_I, xor
3. (FAIL-DATA): -$d, +!d true for B_I, xor
4. (NOPAY-DATA): -$d, +$d, -#d, +#d, -!d, +!d not true for B_I.

9. NANDSET DEFINITION:
1. (POS-DATA): {-$d}, {-d}, {-!d} ∈ B_I, xor
2. (NEG-DATA): {-$d}, {+d}, {-!d} ∈ B_I, xor
3. (FAIL-DATA): {+$d}, {-!d} ∈ B_I, xor
4. (NOPAY-DATA): {+$d}, {-$d}, {+#d}, {-#d}, {+!d}, {-!d} ~∈ B_I.

SCREEN 62. RULE 9. COVER.

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1. It is true that -$^ka @ C_I if and only if it is not true that +$^ka @ ÇB_I

2. NANDSET DEFINITION: {+$^ka} ∈ C_I if and only if {-$^ka} ~ ∈ ÇB_I, for 1 < I < H, 1 < k < M, and a ∈ A.

3. In straight poker, COVER is like CALL.
SCREEN 63. THEOREM 1a. THEOREM 1. CONSISTENCY OF B₀

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1. B₀ IS CONSISTENT.

2. NANDSET DEFINITION: Ø ~∈ ÇB₀.

SCREEN 64. THEOREM 1a. STYLE OF PROOF.

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To demonstrate that Ø ~∈ ÇB₀, it suffices to construct a possible-patient / truth-table-element, t' that is NOT A SUPERSET of any member of B₀. For if every t' were a superset of some member of B₀, since every t' is a superset of Ø, it would follow that Ø ∈ ÇB₀, so that B₀ would be inconsistent.

For this demonstration, construct t' such that every modal member of t' is negative. That is: t' is a superset of {-$^kd, -$^k-1d, -$d, -#d, -!d,... -$^ke, -$^k-1e...}, for every k, d, e. (The (non-modal) values of d, e do not matter.) Then:

B₀ element	Nandset Definition	Possible Patient	Range
Rule 2. KnowledgeOrdinal,$^kd	{-$^kd,+$^k+1d}	-$^k+1d...	1<k<M-1
Rule 2. KnowledgeOrdinal$^ke	{-$^ke,+$^k+1e}	...-$^k+1e...	1<k<M-1
Rule 3. DataAbsolute	{+$d,-$^Md}	...-$d ...	.
Rule 4. d-Hippocratic	{-#d,+!d}	... -!d...	.
Rule 5. d-Conative	{-$d,+#d,-!d}	...-#d...	.
Rule 6. keδ..d-Vexative	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...-$^ke...	1<k<M-2
Rule 7. kδ..e-Ontologic	{+$^kδ,+δ,-e,-$^k+1e}	...-$^kδ...	1<k<M-2
Rule 7. kδ..e-Ontologic	{+$^kδ,+δ, -$^ke}	...-$^kδ...	1<k<M-2

Therefore, the possible patient, t', is not a superset of any B₀ element specified by Rules 2-7, so that Ø ~∈ ÇB₀.

SCREEN 65. THEOREM 1b,c,d. OCCAM'S RAZOR.

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(Occam, William of Ockham, 1285-1349, English logician and Franciscan friar).

Theorem. 1b. No $d is true for ÇB₀. Occam's Razor: No data are implied without data.
Theorem. 1c. No $e is true for ÇB₀ Occam's Razor: No entities are implied without data.
Theorem. 1d. No #d is true for ÇB₀ Occam's Razor: No data are needed without other data.

SCREEN 66. COMPUTATIONAL COMPLEXITY.

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1. Computational complexity is the quantity of computer resources necessary to complete a particular computer algorithm, involving G data elements [116,117,118].

2. An algorithm is LINEAR COMPLETE if one can successfully complete the algorithm after c×G steps, for constant c. Example: finding and fetching a single element in an unsorted list.

3. An algorithm is LOG COMPLETE if one can successfully complete the algorithm after c×log_bG steps, where typically b=2, i.e., complete after c×log₂G steps. Example: finding and fetching a single element in a sorted list, using the heapsort or quicksort method.

4. An algorithm is LOG-LINEAR COMPLETE if one can successfully complete the algorithm after c×nlog₂G steps. Example: creating a sorted list, using the heapsort or quicksort method.

5. An algorithm is said to be QUADRATIC COMPLETE if one can successfully complete the algorithm after c×G² steps;

6. An algorithm is CUBIC COMPLETE if one can successfully complete the algorithm after c×G³ steps.

7. An algorithm is QUARTIC COMPLETE if one can successfully complete the algorithm after c×G⁴ steps.

8. In general, an algorithm is POLYNOMIAL COMPLETE if one can successfully complete the algorithm after c×G⁴ steps, for some integer constant, k.

9. An algorithm is EXPONENTIAL COMPLETE, if one can successfully complete the algorithm after c&×2^G steps. An exponential-complete algorithm is essentially hopeless for most practical computing problems.

10. An algorithm is FORMALLY INCOMPLETE (German: formal unentscheidbar) if one cannot successfully complete the algorithm after any number of steps, so-called Gödel-undecidability [116,119,120,121]. (Kurt Gödel (1906-1978), Czech/Austrian logician).

11. A very famous class of computer algorithms is NON-POLYNOMIAL COMPLETE (NP-COMPLETE), i.e., at worst exponential complete, but for which it is unknown whether a polynomial complete algorithm exists.

12. In this report, we claim that the algorithm for solving the consequences of B_H is quartic-complete, i.e, soluble after cG⁴ steps, where G = ñB_H

13. TRICK: G could be very large, say, possibly up to 2^(ñA). The assumption is that physician ontologies are not that intricate.

14. THEOREM 10: G The number of calculations to obtain ÇB_H is equal to c×G⁴, for some constant c.

SCREEN 68. TOKEN SWAP METHOD REVISITED.

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The TOKEN SWAP TEST (TST) is a statistical test for analyzing data in a 2×2 CONTINGENCY TABLE (2×2CT). The 2×2CT is the backbone of hypothesis-testing in clinicopathologic (case series) research. For example, if there is an entity, e, predicted by data, δ..., then a clinicopathologic patient series might yield the results: □e - + ------------------ - | a | b | v □δ ------------------ + | c | d | w ------------------ | x | y | z

.	~	+	.
~	a	b	v
+	c	d	w
.	x	y	z

where □-δ are the patients for which data are negative;
□+δ are the patients for which data are positive;
□-g are the patients for which the entity is negative; and
□+g are the patients for which the entity is positive.
Values a, b, c, d comprise the CELL TOTALS, where: a is the number of patients with
□-δ & □-g, i. e., necessarily not-δ and necessarily not-g;
b is the number of patients with
□-δ & □+e, i. e., necessarily not-δ and necessarily e;
c is the number of patients with □+δ & □-e, i. e., necessarily not-δ and necessarily not-e;
and d is the number of patients with □+δ & □+e, i. e., necessarily not-δ and necessarily e;
Values v, w, x, y comprise the MARGINAL TOTALS, where v = a + b; w = c + d; x = a + c; y = b + d.
Value z is the GRAND TOTAL, where z = v + w = x + y = a + b + c + d.

The token swap test examines the assertion that □+δ⇒□+e and □-δ⇒□-e, or more precisely, □^k+δ⇒(□^k+e|□^k+1-e) and □^k-δ⇒(□^k-e|□^k+1+e).

SCREEN 69. LOOSE ENDS.

1. Computer Translation [122-130]: How does Marked Generalized Atherosclerosis get translated into: {C0205082,C0205046,C0205246}.

2. Zipf's Law for Word Distributions [71,72,73,74]: f = (k/r), where f is the frequency of a particular word; and r is the rank of that word in the descending-order word distribution (of=rank-1, and=rank-2, the=rank-3, etc.).

3. Zipf's Law Part A: Common words are very common.
Zipf's Law Part B: Uncommon words are composites of uncommon words.

4. Zipf's Law for Phrase Distributions.

5. Zipf's Law for Grammar Distributions.

SCREEN 60. SUMMARY.

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1. Pathology studies the etiology and pathogenesis of disease.

2. Any data-mining program must incorporate the fundamental constraints on data acquisition in routine medical practice, including value, payment, and levels-of-certainty.

3. Some data are unnecessary, uneconomic, technically unfeasible, or unethical to collect.

4. Mathematically consistent theory of clinicopathologic inference.

5. Modal/fuzzy concepts of certainty/know-whether ($), value-to-know-whether (#), and payy-to-know-whether (!).

6. Occam's Razor: no entities are known without data. (Occam, William of Ockham, 1285-1349, English logician and Franciscan friar).

7. d-Hippocratic, d-conative, keδ..d-vexative, and kδe-ontologic properties: consistent if data are entered consensually, consecutively, and consistently. (Hippocrates, 460-370 BC, Greek physician, father of medicine).

8. Computer algorithm concludes within polynomial time.

9. Theory is completely general.

10. Definitions of patient injury include possible death, morbidity, inconvenience, financial constraints, or loss-of-privacy.

11. Definitions of payment-to-know may differ among observers: patient, physician, insurer, national health policy, research protocol.

12. There are, for example, numerous patients in computerized systems (the 172 Veterans Affairs hospitals, serving five million honorably-discharged veteran patients, for example) which could employ a systematic mechanism for alerting providers to necessary upcoming events, such as an annual hemoglobin a1c and podiatry examination for diabetic patients.

13. Such a computer mechanism amounts to moving points from the clear space in the Screen #27 Venn Diagram into the blue area (i.e., developing a concept space); and from the blue area into the central gray area (i.e., seeing the patients).

14. Mathematical theories can organize medical knowledge, and improve the scheduling and effectiveness of data collection and surveillance.

SCREEN 72. THEOREMS.₀

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SCREEN 71. THEOREMS.₀

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SCREEN 73. THEOREM 1. CONSISTENCY OF B₀

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Definition 0. ÇX denotes the set of logical consequences of X.
Theorem 0. Subset Corollary. X is a subset of ÇX.
Theorem 1a. B₀ is consistent: Ø ~∈ÇB₀.
Theorem 1b. No $d is true for ÇB₀. Occam's Razor: No data are implied without data: {-$d} ~∈ÇB₀.
Theorem 1c. No $e is true for ÇB₀ Occam's Razor: No entities are implied without data: {-$e} ~∈ÇB₀.
Theorem 1d. No #d is true for ÇB₀ Occam's Razor: No data are needed without other data: {-#d} ~∈ÇB₀.
Proof: To demonstrate that Ø ~∈ ÇB₀, it suffices to construct any possible-patient / truth-table-element, t' that is NOT A SUPERSET of any member of B₀. For if every t were a superset of some member of B₀, since every t is a superset of Ø, it would follow that Ø ∈ ÇB₀, so that B₀ would be inconsistent.

For this demonstration, construct t' such that every modal member of t' is negative. That is: t' = {-$^kd, -$^k-1d, -$d, -#d, -!d, ... -$^ke, -$^k-1e...}, for every k, d, e. t' belongs to the outside (uncolored) space in the Venn diagram, above. The (non-modal) values of d, e do not matter in the proof. Then:

B₀ element	Nandset Definition	Possible Patient	Range
Rule 2. KnowledgeOrdinal,$^kd	{-$^kd,+$^k+1d}	-$^k+1d...	1<k<M-1
Rule 2. KnowledgeOrdinal$^ke	{-$^ke,+$^k+1e}	...-$^k+1e...	1<k<M-1
Rule 3. DataAbsolute	{+$d,-$^Md}	... -$d ...	.
Rule 4. d-Hippocratic	{-#d,+!d}	... -!d ...	.
Rule 5. d-Conative	{-$d,+#d,-!d}	... -#d ...	.
Rule 6. keδ..d-Vexative	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...-$^ke...	1<k<M-2.
Rule 7. kδ..e-Ontologic	{+$^kδ,+δ,-e,-$^k+1e}	...-$^kδ...	1<k<M-2.
Rule 7. kδ..e-Ontologic	{+$^kδ,+δ, -$^ke}	...-$^kδ...	1<k<M-2.

Part (a). Thus, Ø ~∈ÇB₀, because Ø ⊆ t'.
Part (b). By Definition of C₀, {-$d} ~∈ÇB₀, because {-$d} ⊆ t'. Thus, {$d} ∈ C₀, by Definition of Cover.
Part (c). By Definition of C₀, {-$e} ~∈ÇB₀, because {-$e} ⊆ t'. Thus, {$e} ∈ C₀, by Definition of Cover.
Part (d). By Definition of C₀, {-#d} ~∈ÇB₀, because {-#d} ⊆ t'.

SCREEN 74. THEOREM 2.

THEOREM 2. Ø ~∈ÇB_H
Proof: Construct t' as follows. For each e, {-$^Me,+$^M-1e,...,±e} ⊆ t'. For each d, if d is:
notry, then let {-$^Md,-$^M-1d,...,-#d,-!d,±d} ⊆ t';
failed, then let {-$^Md,-$^M-1d,...,+#d,+!d,±d} ⊆ t';
positive, then let {+$^Md,+$^M-1d,...,+#d,+!d,+d} ⊆ t';
negative, then let {+$^Md,+$^M-1d,...,+#d,+!d,-d} ⊆ t'.
Then t'~∈ B_H, as follows:

B₀ element	Nandset Definition	Possible Patient	Range
Rule 2. KwnlOrd$kd/notry	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/fail	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/pos	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KwnlOrd$kd/neg	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KnwlOrd$Me	{-$^M-1e,+$^Me}	...-$^Me...	.
Rule 2. KnwlOrd$ke	{-$^ke,+$^k+1e}	...+$^ke...	1<k<M-1
Rule 3. DataAbs$d/notry	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/fail	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/pos	{+$d,-$^Md}	... +$^Md ...	.
Rule 3. DataAbs$d/neg	{+$d,-$^Md}	... +$^Md ...	.
Rule 4. d-Hippocr/notry	{-#d,+!d}	... -!d ...	.
Rule 4. d-Hippocr/fail	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/pos	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/neg	{-#d,+!d}	... +#d ...	.
Rule 5. d-Conativ/notry	{-$d,+#d,-!d}	... -#d ...	.
Rule 5. d-Conativ/fail	{-$d,+#d,-!d}	... +!d ...	.
Rule 5. d-Conativ/pos	{-$d,+#d,-!d}	... +$d ...	.
Rule 5. d-Conativ/neg	{-$d,+#d,-!d}	... +$d ...	.
Rule 6. keδ..d-Vex	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-e,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-$^ke}	...+$^ke...	1<k<M-2.
Rule 8. pos	{-$^Md},{-d},{-!d}	...+$^Md ...+!d,...+d...	.
Rule 8. neg	{-$^Md},{+d},{-!d}	...+$^Md ...+!d,...-d...	.
Rule 8. fail	{$d},{-!d}	...-$d,...+!d,...	.

SCREEN 75. THEOREM 3.

THEOREM 3. For every k, 1< k<M, and for every d ∈ D:
{+$d} ∈ C_I if and only if {+d} ~∈ B_I and {-d} ~∈ B_I.
Proof: If. If {+d} ∈ B_I or {-d} ∈ B_I, then by Rule 8, {-$d} ∈ B_I. By the subset corollary, {-$d} ∈ ÇB_I. By Rule 9, {+$d} &126;∈ C_I.
Only If. Construct t' as follows. For each d ∈ D, if d is:
notry, then let {-$^Md,-$^M-1d,...,-#d,-!d,±d} ⊆ t';
failed, then let {-$^Md,-$^M-1d,...,+#d,+!d,±d} ⊆ t';
positive, then let {+$^Md,+$^M-1d,...,+#d,+!d,+d} ⊆ t';
negative, then let {+$^Md,+$^M-1d,...,+#d,+!d,-d} ⊆ t'.
For each e ∈ E, pick the k'<M-2 at which {+$^k'+1e} ∈ ÇB_IC_I and {-$^k'e} ∈ ÇB_IC_I, and let {...-$^k'+1e,+$^k'e,...,±e} ⊆ t'.
Then t'~∈ B_I, as follows:

B_I element	Nandset Definition	Possible Patient	Range
Rule 2. KwnlOrd$kd/notry	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/fail	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/pos	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KwnlOrd$kd/neg	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KnwlOrd$Me	{-$^M-1e,+$^Me}	...-$^Me...	.
Rule 2. KnwlOrd$ke	{-$^ke,+$^ke}	...+$^k+1e...	1<k<M-1
Rule 3. DataAbs$d/notry	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/fail	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/pos	{+$d,-$^Md}	... +$^Md ...	.
Rule 3. DataAbs$d/neg	{+$d,-$^Md}	... +$^Md ...	.
Rule 4. d-Hippocr/notry	{-#d,+!d}	... -!d ...	.
Rule 4. d-Hippocr/fail	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/pos	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/neg	{-#d,+!d}	... +#d ...	.
Rule 5. d-Conativ/notry	{-$d,+#d,-!d}	... -#d ...	.
Rule 5. d-Conativ/fail	{-$d,+#d,-!d}	... +!d ...	.
Rule 5. d-Conativ/pos	{-$d,+#d,-!d}	... +$d ...	.
Rule 5. d-Conativ/neg	{-$d,+#d,-!d}	... +$d ...	.
Rule 6. keδ..d-Vex	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-e,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-$^ke}	...+$^ke...	1<k<M-2.
Rule 8. pos	{-$^Md},{-d},{-!d}	...+$^Md ...+!d,...+d...	.
Rule 8. Negative	{-$^Md},{+d},{-!d}	...+$^Md ...+!d,...-d...	.
Rule 8. Fail	{$d},{-!d}	...-$d,...+!d,...	.

SCREEN 76. THEOREM 4.

THEOREM 4. For every k, 1< k<M, and for every e ∈ E:
if {-$e} ~ ∈ ÇB_IC_I, then {+e} ~∈ ÇB_IC_I and {-e} ~∈ ÇB_IC_I.
Proof. Let {-$e} ~∈ ÇB_IC_I, and without loss of generality, suppose that {-e} ∈ ÇB_IC_I. By Definition of Cover, {$e} ∈ C_I. Construct truth-table-element, t', such that {-e, -$e, -$²e} ⊆ t', where it must be true that t' ∈ ÇB_IC_I. The only way that this could be true is if Rule 7 contains {-e, -$e, -$²e}, whence it must be true that Rule 7 contains

{-e, +$e, -$²e};
{-e, -$e, -$²e}; and
{-e, -$e, +$²e}.....

Then ÇB_IC_I contains {-$e}. Contradiction. It is notable that the converse of the theorem is not necessarily true.

SCREEN 77. THEOREM 5.

THEOREM 5. CONSISTENCY OF B_IC_I. Ø ~∈ ÇC_IB_I
Proof: Construct t' ~∈ B_I, same as in Theorem 3, except, for each e, pick the k'<M-2 at which {+$^k'+1e} ∈ ÇB_IC_I and {-$^k'e} ∈ ÇB_IC_I, and let {...-$^k'+1e,+$^k'e,...,±e} ⊆ t'. Then:

B_I element	Nandset Definition	Possible Patient	Range
Rule 2. KwnlOrd$kd/notry	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/fail	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/pos	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KwnlOrd$kd/neg	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KnwlOrd$ke	{-$^ke,+$^k+1e}	...-$^k'+1e...	0<k<k'
Rule 2. KnwlOrd$ke	{-$^ke,+$^k+1e}	...+$^ke...	k'<k<M-2
Rule 3. DataAbs$d/notry	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/fail	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/pos	{+$d,-$^Md}	... +$^Md ...	.
Rule 3. DataAbs$d/neg	{+$d,-$^Md}	... +$^Md ...	.
Rule 4. d-Hippocr/notry	{-#d,+!d}	... -!d ...	.
Rule 4. d-Hippocr/fail	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/positive	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/negative	{-#d,+!d}	... +#d ...	.
Rule 5. d-Conativ/notry	{-$d,+#d,-!d}	... -#d ...	.
Rule 5. d-Conativ/fail	{-$d,+#d,-!d}	... +!d ...	.
Rule 5. d-Conativ/pos	{-$d,+#d,-!d}	... +$d ...	.
Rule 5. d-Conativ/neg	{-$d,+#d,-!d}	... +$d ...	.
Rule 6. keδ..d-Vex	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-e,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-$^ke}	...+$^ke...	1<k<M-2.
Rule 8. positive	{-$^Md},{-d},{-!d}	...+$^Md ...+!d,...+d...	.
Rule 8. negative	{-$^Md},{+d},{-!d}	...+$^Md ...+!d,...-d...	.
Rule 8. Fail	{$d},{-!d}	...-$d,...+!d,...	.
Rule 9. $k'+1e	{+$^k'+1e}	...-$^k'+1e...	1<k'<M-2
Rule 9. $k'e	{-$^k'e}	...+$^k'e...	1<k'<M-2

SCREEN 78. THEOREM 6.

THEOREM 6. ÇB_IC_I is d-Hippocratic if and only if B₀ is d-Hippocratic.
Proof: If. If B₀ is d-Hippocratic, then by Rule 4, {-#d,+!d} ∈ B₀. By the Subset corollary, {-#d,+!d} ∈ B₀ ⊆ B_I ⊆ ÇB_IC_I.
Only if: Construct t' ~∈ B_I, same as in Theorem 3, except, for each e, pick the k'<M-2 at which {$^k'+1e} ∈ Ç B_I C_I and {-$^k'e} ∈ Ç B_IC_I, and let {-$^k'+1e,+$^k'e,...,±e} ⊆ t'. Then:

B_I element	Nandset Definition	Possible Patient	Range
Rule 2. KwnlOrd$kd/notry	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/fail	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/pos	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KwnlOrd$kd/neg	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KnwlOrd$Me	{-$^M-1e,+$^Me}	...-$^Me...	1<k'<M-2
Rule 2. KnwlOrd$ke	{-$^ke,+$^k+1e}	...+$^ke...	1<k'<M-2
Rule 3. DataAbs$d/notry	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/fail	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/pos	{+$d,-$^Md}	... +$^Md ...	.
Rule 3. DataAbs$d/neg	{+$d,-$^Md}	... +$^Md ...	.
Rule 4. d-Hippocr/notry	{-#d,+!d}	... -!d ...	.
Rule 4. d-Hippocr/fail	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/pos	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/neg	{-#d,+!d}	... +#d ...	.
Rule 5. d-Conativ/notry	{-$d,+#d,-!d}	... -#d ...	.
Rule 5. d-Conativ/fail	{-$d,+#d,-!d}	... +!d ...	.
Rule 5. d-Conativ/pos	{-$d,+#d,-!d}	... +$d ...	.
Rule 5. d-Conativ/neg	{-$d,+#d,-!d}	... +$d ...	.
Rule 6. keδ..d-Vex	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-e,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-$^ke}	...+$^ke...	. 1<k<M-2.
Rule 8. Positive	{-$^Md},{-d},{-!d}	...+$^Md ...+!d,...+d...	.
Rule 8. Negative	{-$^Md},{+d},{-!d}	...+$^Md ...+!d,...-d...	.
Rule 8. Fail	{$d},{-!d}	...-$d,...+!d,...	.
Rule 9. $k'+1e	{+$^k'+1e}	...-$^k'+1e...	1<k'<M-2
Rule 9. $k'e	{-$^k'e}	...+$^k'e...	1<k'<M-2

SCREEN 79. THEOREM 7.

THEOREM 7. ÇB_IC_I is d-conative if and only if B₀ is d-conative.
Proof: If. If B₀ is d-conative, then by Rule 5, {-$d,+#d,-!d} ∈ B₀. By the Subset Corollary, {-$d,+#d,-!d} ∈ B₀ ⊆ B_I ⊆ ÇB_IC_I.
Only if: Construct t' ~∈ B_I, same as in Theorem 3, except, for each e, pick the k'<M-2 at which {$^k'+1e} ∈ ÇB_IC_I and {-$^k'e} ∈ ÇB_IC_I, and let {-$^k'+1e,+$^k'e,...,±e} ⊆ t'. Then:

B_I element	Nandset Definition	Possible Patient	Range
Rule 2. KwnlOrd$kd/notry	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/fail	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/pos	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KwnlOrd$kd/neg	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KnwlOrd$Me	{-$^M-1e,+$^Me}	...-$^Me...	.
Rule 2. KnwlOrd$ke	{-$^ke,+$^k+1e}	...+$^ke...	1<k<M-1
Rule 3. DataAbs$d/notry	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/fail	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/pos	{+$d,-$^Md}	... +$^Md ...	.
Rule 3. DataAbs$d/neg	{+$d,-$^Md}	... +$^Md ...	.
Rule 4. d-Hippocr/notry	{-#d,+!d}	... -!d ...	.
Rule 4. d-Hippocr/fail	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/pos	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/neg	{-#d,+!d}	... +#d ...	.
Rule 5. d-Conativ/notry	{-$d,+#d,-!d}	... -#d ...	.
Rule 5. d-Conativ/fail	{-$d,+#d,-!d}	... +!d ...	.
Rule 5. d-Conativ/pos	{-$d,+#d,-!d}	... +$d ...	.
Rule 5. d-Conativ/neg	{-$d,+#d,-!d}	... +$d ...	.
Rule 6. keδ..d-Vex	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-e,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-$^ke}	...+$^ke...	1<k<M-2.
Rule 8. pos	{-$^Md},{-d},{-!d}	...+$^Md ...+!d,...+d...	.
Rule 8. neg	{-$^Md},{+d},{-!d}	...+$^Md ...+!d,...-d...	.
Rule 8. fail	{$d},{-!d}	...-$d,...+!d,...	.
Rule 9. $k'+1e	{+$^k'+1e}	...-$^k'+1e...	1<k'<M-2
Rule 9. $k'e	{-$^k'e}	...+$^k'e...	1<k'<M-2

SCREEN 80. THEOREM 8.

THEOREM 8. ÇB_IC_I is keδd-vexative if and only if B₀ is keδd-vexative.
Proof: If. By Subset Corollary.
Only if. Construct t' ~∈ B_I, same as in Theorem 3, except, for each e, pick the k'<M-2 at which {$^k'+1e} ∈ Ç B_I C_I and {-$^k'e} ∈ Ç B_I C_I, and let {-$^k'+1e,+$^k'e,...,±e} ⊆ t'. Then:

B_I element	Nandset Definition	Possible Patient	Range
Rule 2. KwnlOrd$kd/notry	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/fail	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/pos	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KwnlOrd$kd/neg	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KnwlOrd$Me	{-$^M-1e,+$^Me}	...-$^Me...	.
Rule 2. KnwlOrd$ke	{-$^ke,+$^k+1e}	...+$^ke...	1<k<M-1
Rule 3. DataAbs$d/notry	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/fail	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/pos	{+$d,-$^Md}	... +$^Md ...	.
Rule 3. DataAbs$d/neg	{+$d,-$^Md}	... +$^Md ...	.
Rule 4. d-Hippocr/notry	{-#d,+!d}	... -!d ...	.
Rule 4. d-Hippocr/fail	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/pos	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/neg	{-#d,+!d}	... +#d ...	.
Rule 5. d-Conativ/notry	{-$d,+#d,-!d}	... -#d ...	.
Rule 5. d-Conativ/fail	{-$d,+#d,-!d}	... +!d ...	.
Rule 5. d-Conativ/pos	{-$d,+#d,-!d}	... +$d ...	.
Rule 5. d-Conativ/neg	{-$d,+#d,-!d}	... +$d ...	.
Rule 6. keδ..d-Vex	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-e,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-$^ke}	...+$^ke...	1<k<M-2.
Rule 8. pos	{-$^Md},{-d},{-!d}	...+$^Md ...+!d,...+d...	.
Rule 8. neg	{-$^Md},{+d},{-!d}	...+$^Md ...+!d,...-d...	.
Rule 8. fail	{$d},{-!d}	...-$d,...+!d,...	.
Rule 9. $k'+1e	{+$^k'+1e}	...-$^k'+1e...	1<k'<M-2
Rule 9. $k'e	{-$^k'e}	...+$^k'e...	1<k'<M-2

SCREEN 81. THEOREM 9.

THEOREM 9. ÇB_IC_I is kδe-ontologic if and only if B₀ is kδe-ontologic.
Proof: If. By Subset Corollary.
Only if. Construct t' ~∈ B_I, same as in Theorem 3, except, for each e, pick the k'<M-2 at which {$^k'+1e} ∈ Ç B_I C_I and {-$^k'e} ∈ Ç B_I C_I, and let {-$^k'+1e,+$^k'e,...,±e} ⊆ t'. Then:

B_H element	Nandset Definition	Possible Patient	Range
Rule 2. KwnlOrd$kd/notry	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/notry	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/fail	{-$^kd,+$^k+1d}	...-$^k+1d...	1<k<M-1
Rule 2. KwnlOrd$kd/pos	{-$^kd,+$^k+1d}	...+$^kd...	1<k<M-1
Rule 2. KwnlOrd$kd/neg	{-$^kd,+$^k+1d}	...+$^kd...	. 1<k<M-1
Rule 2. KnwlOrd$Me	{-$^M-1e,+$^Me}	...-$^Me...	.
Rule 2. KnwlOrd$ke	{-$^ke,+$^k+1e}	...+$^ke...	1<k<M-1
Rule 3. DataAbs$d/notry	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/fail	{+$d,-$^Md}	... -$d ...	.
Rule 3. DataAbs$d/pos	{+$d,-$^Md}	... +$^Md ...	.
Rule 3. DataAbs$d/neg	{+$d,-$^Md}	... +$^Md ...	.
Rule 4. d-Hippocr/notry	{-#d,+!d}	... -!d ...	.
Rule 4. d-Hippocr/fail	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/pos	{-#d,+!d}	... +#d ...	.
Rule 4. d-Hippocr/neg	{-#d,+!d}	... +#d ...	.
Rule 5. d-Conativ/notry	{-$d,+#d,-!d}	... -#d ...	.
Rule 5. d-Conativ/fail	{-$d,+#d,-!d}	... +!d ...	.
Rule 5. d-Conativ/pos	{-$d,+#d,-!d}	... +$d ...	.
Rule 5. d-Conativ/neg	{-$d,+#d,-!d}	... +$d ...	.
Rule 6. keδ..d-Vex	{+$^ke,e,+$^kδ,+δ,-$d,-#d,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-e,-$^k+1e}	...+$^k+1e...	1<k<M-2.
Rule 7. kδ..e-Ontol	{+$^kδ,+δ,-$^ke}	...+$^ke...	1<k<M-2.
Rule 8. pos	{-$^Md},{-d},{-!d}	...+$^Md ...+!d,...+d...	.
Rule 8. neg	{-$^Md},{+d},{-!d}	...+$^Md ...+!d,...-d...	.
Rule 8. fail	{$d},{-!d}	...-$d,...+!d,...	.
Rule 9. $k'+1e	{+$^k'+1e}	...-$^k'+1e...	1<k'<M-2
Rule 9. $k'e	{-$^k'e}	...+$^k'e...	1<k'<M-2

SCREEN 82. THEOREM 10ff.

THEOREM 10. ñ%ÇB_IC_I is quartic-complete.
Proof: 1. G > ~F/2 = ~t, for every t ∈ T; G > H.
2. Sort B_I in ascending order, G×log₂G steps; index each element in the sorted B_I list in F×log₂F steps.
3. Climb along B_I match to F elements, in F×log₂F steps.
4. Perform #3, H times. Total of (G×log₂G)³ steps, less than G⁴ steps, for G>1000.

T13. THEOREM: COMMUTATIVE &. & is COMMUTATIVE, i.e., for every x,y ∈ W, (x & y) = (y & x) ∈ W.
Proof: Deferred.

T14. THEOREM: COMMUTATIVE |. | is COMMUTATIVE, i.e., for every x,y ∈ W, (x | y) = (y | x) ∈ W.
Proof: Deferred.

T15. THEOREM: ASSOCIATIVE &. & is ASSOCIATIVE, i.e., for every x,y,z ∈ W, ((x & y) & z) = (x & (y & z)) ∈ W.
Proof: Deferred.

T16. THEOREM: ASSOCIATIVE |. | is ASSOCIATIVE, i.e., for every x,y,z ∈ W, ((x | y) | z) = (x | (y | z)) ∈ W.
Proof: Deferred.

T17. THEOREM: DEMORGAN -&. & is DEMORGAN, i.e., (x & y) = -(-x | -y).

T18. THEOREM: DEMORGAN -|;. | is DEMORGAN, i.e., (x | y) = -(-x & -y).
Proof: (x | y)
= (-(-x) | -(-y)) ; [Double negative, Brouwer].
= (-(-x) & -(-y)) ; [DeMorgan &].

D16: DEFINITION: DISTRIBUTIVE $&. $ is DISTRIBUTIVE OVER & if and only if $(x & y) = ($x & $y).

T19. THEOREM: DISTRIBUTIVE $|. $ is DISTRIBUTIVE OVER |, i.e., $(x | y) = ($x & $y).
Proof: $(x | y)
= $(-(-x & -y)) ; [DeMorgan | T08 ].
= $(-x & -y) ; [Rule 1].
= $-x & $-y ; [Definition $& D16 ].
= $x & $y ; [QED, Rule 1 ].

T20. THEOREM: □x = -◇-x.
Proof: □x
= (x &$x) ; [Defn of □ D18].
= -(-x | -$x) ; [DeMorgan -& T07].
= -(-x | -$-x) ; [Rule 1].
= -◇-x . [Defn of ◇ D19].

T21. THEOREM: ◇x = -□-x.
Proof: ◇x
= (x | -$x) ; [Defn of ◇ D18].
= (x | -$-x) ; [Rule 1].
= -(x & -$-x) ; [DeMorgan -| D16].
= -□-x . [Defn of □ D19].

T24. COROLLARY: DISTRIBUTIVE □&. □ is DISTRIBUTIVE OVER & if and only if □(x & y) = (□x & □$y).
Proof: □(x & y)
= ((x & $x) & (y & $y)) ; [Defn of □].
= ((x & y) & ($x & $y)) ; [Commutative &].
= □(□x & □y) ; [Defn of □].

T25. COROLLARY: DISTRIBUTIVE □|.

T26. COROLLARY: DISTRIBUTIVE ◇&.

T27. COROLLARY: DISTRIBUTIVE ◇|.

T28. THEOREM: ◇□x = ◇◇x.
Proof: ◇□x
= ◇(x & $x) ; [Definition □].
= ((x & $x) | -$(x & $x)) ; [Definition ◇ ].
= ((x & $x) | -($x & $$x)) ; [Distributive $& ].
= ((x & $x) | -(-$x | $$x)) ; [DeMorgan -& ].
= ((x & $x) | -$$x) ; [Rule 2].
= ((x | -$$x) & ($x | -$$x)) ;
= (x | -$$x) = ◇²x ; [ Theorem ◇² ] .

T29. THEOREM: □◇x = □□x.
Proof: □◇(x & $x)
= ß(x | -$x) ; [Definition ◇].
= ((x | -$x) & -$(x | -$x)) ; [Definition □ ].
= ((x | -$x) & -$x & $-$x ; [Distributive $| ].
= ((x | -$x) & -$x & $$x ; [Rule 1].
= ((x & -$x) & $$x) ; [Rule 2].
= (x & $$x) | (-$x & $$x) ; [Distributive &| ].
= (x | $$x) = □²x ; [ Theorem □² ] .

D17. DEFINITION: COMPLEMENTIZER FUNCTION, ¢. ¢() is a COMPLEMENTIZER FUNCTION if and only if for every x ∈ U, ¢(-x) = ¢(x). The complementizer functions are: $x, #x, !x.

D18. DEFINITION: BIND FUNCTION, □. □() is the bind function, if and only if for every x ∈ U, □(x) = $(x) & x.
Note: The Bind Function, □(), is akin to the NECESSARILY FUNCTION, ¤(), in modal logic. The necessarily function is also called BEWEISBAR (German: provable), and is used in some modal-logic proofs of Gödel's Theorem (Kurt Gödel (1906-1978), Czech/Austrian logician).

D19. DEFINITION: LOOSE FUNCTION, ◇. ◇() is the loose function, if and only if for every x ∈ U, ◇(x) = -$(x) | x.
Note: The Loose Function, ◇(), is akin to the Possibly Function, <>(), in modal logic.

T30. TELESCOPE "THEOREM": ◇²x = (x | $²x). THIS "THEOREM" FALSE!!!

T31. TELESCOPE "THEOREM": ◇ⁿx = (x | $ⁿx). THIS "THEOREM" FALSE!!!

T32. THEOREM: □²x = (x&$²x).
Proof: □²x
= □(x&$x) ; [Defn of □].
= (x&$x)&$(x&$x) ; [Defn of □].
= (x&$x)&($x&$²x) ; [Distrib &].
= x&$x&$²x ; [Associative &].
= x&$²x ; [Cascade &, &>].

T33. TELESCOPE THEOREM: □ⁿx = (x & $ⁿx).

SCREEN 82. REFERENCES.

Return to Table of Contents.

1. Berman J.
Resource page.
http://www.julesberman.info
Last tested: 4/27/2008.

2. Berman J.
A Practical Approach to Ethics for Biomedical Informaticians. Chapter 16. pp. 331-356.
In: Berman JJ. Biomedical Informatics.
Boston: Jones and Bartlett Publishers. 2007;:.
ISBN-13: 978-0-7637-4135-8, 459 pages.
ISBN-10: 0-7637-4135-3, 459 pages.
A masterful book, that covers all the major areas of Biomedical Informatics.

3. Brewka G, Dix J, Konolige K.
Nonmonotonic Reasoning. An Overview. CSLI Lecture Notes 73.
Stanford, CA: Center for the Study of Language and Information. 1997;:.
ISBN 1-8881526-83-6, 179 pages.

4. Harrison JH, Stewart J.
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5. Harrison JH.
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6. Hawking S.
Black Holes and Baby Universes and Other Essays.
New York: Bantam Books. 1993;:. Pages 44-45.
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7. Hippocrates. (Hippocrates of Cos, `Iπποκρατης, 460-370 BC, Greek physician, ethicist, father of medicine.)
Hippocrates. Volume I.
Jones WHS, transl. Loeb Classical Library. Cambridge, MA: Harvard University Press. 1923.
ISBN 0-674-99162-1, 361 pages.
Includes Hippocrates' Oath, with explanatory notes.
According to http://www.geocities.com/everwild7/noharm.html:
"'First, do no harm' is not in the Hippocratic Oath It is a widely held misconception that the familiar dictum 'First, do no harm' comes from the Hippocratic Oath, an oath many physicians take when they enter medical practice.
"However, the Hippocratic Oath does not and never did contain those words (nor was it actually written by Hippocrates, according to many sources). It expresses a similar idea, but never employs the words 'First, do no harm.'
"It is the opinion of many scholars that Hippocrates did, in fact, originate the phrase, but did so in his Epidemics, Bk. I, Sect. XI. One translation reads: 'Declare the past, diagnose the present, foretell the future; practice these acts. As to diseases, make a habit of two things: to help, or at least to do no harm.'
"The Greek 'First, do no harm' becomes 'Primum non nocere' in Latin. A translation of the original perhaps, but some sources attribute 'Primum non nocere' to the Roman physician, Galen.
"Today there is no single oath that all physicians take upon entering practice. Depending on where they earn their medical degrees, they may take any one of many pledges, but all embody the ethics and ideals of Hippocrates, the acknowledged father of modern medicine.
"The exact wording of the original oath has been subject to dispute, as translations and interpretations of the original Greek have varied. Complicating the picture are the many modernizations of the oath which take into account changes in language, social mores, and medicine itself over the centuries."
This note supplied by Harris G. Yfantis, MD.

8. Sutton W, Linn E.
Where the Money Was. The Memoirs of the World's Greatest Bank Robber.
New York: Ballantine Books. 1976;:.
ISBN 0-345-25371-X-195, 422 pages.
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9. Petersdorf RG, Beeson PB.
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Medicine. 1961;40:1-30.
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10. Upton G, Cook I.
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Oxford, UK: Oxford University Press. 2006;:.
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(Karl Pearson, 1857-1936, British statistician).

11. Pearson K.
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(Karl Pearson, 1857-1936, British statistician).

12. Groopman J.
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New York: Houghton Mifflin Company. 2007 Mar 19;:.
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ISBN-13: 978-0618610037, 320 pages.
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13. Moore GW, Berman JJ.
Anatomic Pathology Data Mining. Chapter 4.
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Medical Data Mining and Knowledge Discovery.
2001. XVIII, 502 pp. 98 figs., 98 tabs. Hardcover.
ISBN: 3-7908-1340-0, 502 pages.

14. Moore GW, Boitnott JK, Miller RE, Eggleston JC, Hutchins, GM.
Integrated anatomic pathology reporting system using natural language diagnoses.
Modern Pathol. 1988;1:44-50.

15. Moore GW, Hutchins GM.
Symbolic logic analysis of congenital heart disease.
Pathol Res Pract. 1981 Mar;171(1):59-85.

16. Moore GW, Hutchins GM.
A Hintikka possible worlds model for certainty levels in medical decision making.
Synthese. 48:87-119, 1981.

17. Moore GW, Hutchins GM, Bulkley BH.
Certainty levels in the nullity method of symbolic logic: application to the pathogenesis of congenital heart malformations.
J Theor Biol. 1979 Jan 7;76(1):53-81.

17. Moore GW, Hutchins GM.
Consistency versus completeness in medical decision-making: Exemplar of 155 patients autopsied after coronary artery bypass graft surgery.
Med Inform (Lond). 1983 Jul-Sep;8(3):197-207.

18. Lewis CI, Langford CH.
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19. Suppes P.
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ISBN not stated, 265 pages.

20. Halmos PR.
Naive Set Theory.
Princeton, NJ: D. Van Nostrand Company, Inc. 1960;:. The University Series in Mathematics.
ISBN not stated, 104 pages.

21. Moore GW, Goodman M.
A set theoretical approach to immunotaxonomy: Analysis of species comparisons in modified Ouchterlony plates.
Bull Math Biophys. 1968 Jun;30(2):279-289.

22. Zadeh LA.
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23. Zadeh LA.
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24. Zadeh LA.
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25. Zadeh LA.
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26. Zadeh LA.
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27. Zadeh LA.
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28. Zadeh LA.
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66. Zadeh LA.
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29. Zadeh LA.
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Memorandum No. UCB/ERL M83/41, University of California, Berkeley. 1983;:.

30. Zadeh LA.
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31. Zadeh LA.
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IEEE Spectrum. 1984;8:26-32.

32. Zadeh LA.
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IEEE Trans Systems, Man, Cybernetics. 1985;SMC-15:754-763.

33. Zadeh LA.
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34. Zadeh LA.
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35. Zadeh LA.
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Ann N Y Acad Sci. 2001 Apr;929:221-252. Review.
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36. Dubois D, Lang J, Prade H.
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37. Goguen JA.
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38. Hurdle JF.
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39. Kanal LN, Lemmer JF, eds.
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40. Kern SE, Johnson JO, Westenskow DR.
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Artif Intell Med. 1997;11:9-31.

41. Kovalerchuk B, Triantaphyllou E, Ruiz JF, Clayton J.
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42. Maddox J.
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43. Martin JF.
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44. Shastri L, ed.
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45. Yager RR.
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46. Brulé JF.
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49. Bandler W, Kohout LJ. Semantics of implication operators and fuzzy relational products.
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50. Eschbach M, Cunningham J.
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51. Esragh F, Mamdani EH.
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52. Fox J.
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53. Haack S.
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55. Lejewski C.
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62. Osherson DN, Smith EE.
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63. Roth EM, Mervis CB.
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65. Bezdek J, ed.
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58. Jain R.
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78. Sugeno M, ed.
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84. Dorsey DW, Coovert MD.
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87. Łukasiewicz J.
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90. Łukasiewicz J.
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91. Garson J.
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93. U. S. National Library of Medicine, Unified Medical Language System.
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94. Sinard JH, Moore GW.
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95. Moore GW, Brenner DS, Berman JJ.
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96. U. S. Code of Federal Regulations. 1995. 45 CFR Subtitle A (10-1-95 Edition), part 46.101 (b) (4). U. S. Department of Health and Human Services. Office of the Secretary.
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97. The University of Mississippi has published its Multiple Project Assurance Document at URL:
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98. National Cancer Institute's Confidentiality Brochure, at URL:
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99. U. S. Code of Federal Regulations. 1999. 45 CFR Parts 160 - 164. Standards for Privacy of Individually Identifiable Health Information; Proposed Rule. Department of Health and Human Services. Office of the Secretary.
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100. U. S. Health Insurance Portability and Accountability Act. 1996. (HIPAA, Kennedy-Kassebaum Bill, H.R. 3103 of 104th U. S. Congress). U. S. Government Documents at URL:
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101. U. S. National Bioethics Advisory Commission (NBAC). 1995.
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105. Parfrey NA, Moore GW, Hutchins GM.
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106. Moore GW, Hutchins GM, Miller RE.
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112. Berry paradox.
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139. Moore GW, Hutchins GM, Miller RE.
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360. Miettinen M.
Immunohistochemistry of Soft Tissue Tumors.
In: Miettinen M, Diagnostic Soft Tissue Pathology. New York: Churchill Livingstone. 2003;:. ISBN 0-443-006611-6, 593 pages.
pp. 73-74:
"The bcl2 gene product is a 25-kd protein in the mitochondrial, microsomal, and some inner membranes. It has an apoptosis preventing function and has complex interactions with other apoptosis-modulating proteins (Hockenberry, 1995). This gene for bcl2 was originally known from follicular lymphoma, where it is overexpressed as a result as a result of the t(14;18) translocation, which causes juxtaposition of the bcl2 gene with the promoter of the immunoglobulin heavy chain gene (Tsujimoto, 1986). Bcl2 is constitutively expressed in many long-lived cell types, such as neurons (Lebrun, 1993).

"Of soft tissue tumors, bcl2 has been widely expressed in the tested tumors. Strongly positive are Kaposi sarcoma, GISTs, solitary fibrous tumor, synovial sarcoma (especially spindle cell components), whereas nodular fasciitis and desmoid and GI leiomyomas are negative. These findings may be of some differential diagnostic value (Suster, 1998, Miettinen, 1998).

"Although there are indications for the use of bcl2 as a prognostic/biologic potential marker for breast and some other carcinomas, no such applications have been validated for soft tissue tumors."

361. Hockenberry DM.
bcl-2, a novel regulator of cell death.
Bioessays. 1995;17:631-638.
(cited in: Miettinen M, Diagnostic Soft Tissue Pathology.)

362. Tsujimoto Y, Croce CM.
Analysis of the structure, transcripts, and protein products of bcl-2, the gene involved in human follicular lymphoma.
Proc Natl Acad Sci USA. 1986;83:5214-5218.
(cited in: Miettinen M, Diagnostic Soft Tissue Pathology.)

363. LeBrun DP, Warnke RA, Cleary ML.
Expression of bcl-2 in fetal tissues suggests a role in morphogenesis.
Am J Pathol 1993;142:743-753.
(cited in: Miettinen M, Diagnostic Soft Tissue Pathology.)

364. Suster S, Fisher C, Moran CA.
Expression of bcl-2 oncoprotein in benign and malignant spindle cell tumors of soft tissue, skin, serosal surfaces, and gastrointestinal tract.
Am J Surg Pathol. 1998;22:863-872.
(cited in: Miettinen M, Diagnostic Soft Tissue Pathology.)

365. Miettinen M, Sarlomo-Rikala M, Kovatich AJ.
Cell-type and tumor-type related bcl-2 reactivity in mesenchymal cells and soft tissue tumors.
Virchows Arch. 1998;433-255-260.
(cited in: Miettinen M, Diagnostic Soft Tissue Pathology.)

366. U. S. National Cancer Institute. U. S. National Institutes of Health.
Cancer Topics.
http://www.nci.nih.gov/cancertopics/wyntk/skin

367. Berman JJ, Moore GW.
Spontaneous regression of residual tumour burden: prediction by Monte Carlo simulation.
Anal Cell Pathol. 1992 Sep;4(5):359-368.
PMID: 1445794; UI: 93075631.
Full Text of Article

368. Moore GW, Berman JJ.
Cell growth simulations predicting polyclonal origins for 'monoclonal' tumors.
Cancer Lett. 1991 Nov;60(2):113-119.
PMID: 1933835; UI: 92034658.
Full Text of Article

369. Wilcox HJ, Myers DL.
An Introduction to Lebesgue Integration and Fourier Series.
New York: Dover Publications, Inc. 1994;:.
ISBN 0-486-68293-5, 155 pages.

370. Seife C.
Zero. The Biography of a Dangerous Idea.
London: Penguin Books. 2000.
ISBN: 0-670-88457-X, 248 pages.
This book includes an account of the execution of Hippasus of Metapontum, a member of the Pythagorean cult, who had dared to reveal the existence of irrational numbers to persons outside the cult.

371. Maor E.
e: The Story of a Number.
Princeton, NJ: Princeton University Press. 1998;:.
ISBN: 0691058547, 232 pages.
"Rarely in the history of science has an abstract mathematical idea been received more enthusiastically by the entire scientific community than the invention of logarithms..."

372. Apostol T.
Mathematical Analysis.
Reading, MA: Addison-Wesley, 1957;:.

373. Asplund E, Bungart L.
First Course in Integration.
New York: Holt, Rinehart, and Winston. 1966;:.

374. Bartle R.
The Elements of Integration.
New York: John Wiley and Sons. 1966;:.

375. Burkill J.
The Lebesgue Integral. Cambridge Tracts No. 40.
New York: Cambridge University Press. 1961;:.

376. Goldberg R.
Methods of Real Analysis.
Waltham, MA: Blaisdell, 1964;:.

377. Halmos P.
Measure Theory.
Princeton, NJ: D. Van Nostrand, 1950;:.

378. Hewitt E, Stromberg K.
Real and Abstract Analysis.
New York: Springer Verlag, 1965;:.

379. Lebesgue H.
Measure and the Integral.
San Francisco: Holden-Day, 1966;:.

380. Munroe M.
Introduction to Measure and Integration.
Reading, MA: Addison Wesley, 1953;:.

381. Royden H.
Real Analysis. Second edition.
New York: Macmillan, 1968;:.

382. Rudin W.
Principles of Mathematical Analysis.
New York: McGraw-Hill: 1953;:.

383. Scanlon J.
Advanced Calculus.
Boston, MA: Heath. 1967;:.

384. Sprecher D.
Elements of Real Analysis.
New York: Academic Press. 1970;:.

385. Temple G.
The Structure of Lebesgue Integration Theory.
Oxford: Clarendon Press, 1971;:.

386. Williamson J.
Lebesgue Integration.
New York: Holt, Rinehart and Winston, 1962;:.

387. Moore GW, Brenner DS, Berman JJ.
Automatic Indexing of a Pathology Image Archive using UMLS. (Abstract).
Arch Pathol Lab Med. 2000 Jun;124:809.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_1.html
http://www.netautopsy.org/apep99im.htm

388. Moore GW, Vardar E, Erozan YS, Durmusoglu F.
Turkish Language Annotation of an Internet Pathology Image Archive. (Abstract).
Arch Pathol Lab Med. 2000 Jun;124:820.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_5.html
http://www.netautopsy.org/apep99tk.htm

389. Kao GF, Moore GW.
Dermatopathology False Negative Terms in UMLS. (Abstract).
Arch Pathol Lab Med. 2000 Jun;124:809.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_2.html
http://www.netautopsy.org/apep99dr.htm

390. Baumann RP, Moore GW.
Evaluation of 530,000 Siagnoses Encoded in SNOMED II.
Arch Pathol Lab Med. 2000 Jun;124:809.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_3.html

391. Nonaka D, Moore GW, Satomura Y.
Japanese Language Annotation of an Internet Pathology Image Archive. (Abstract).
Arch Pathol Lab Med. 2000 Jun;124:820.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_4.html
http://www.netautopsy.org/apep99jp.htm

392. Moore GW, Brown LA, Miller RE.
Set Theory Definition and Algorithm for Medical De-Identification. (Abstract).
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_2.html
http://www.netautopsy.org/apep00st.htm
Comment: This Kosher Kitchen Principle (כשר) for Medical De-identification might be summarized as follows: The patient should not be able to recognize his/her own medical record on the internet, and thus be embarrassed or otherwise injured by this recognition. This is a very ancient sensibility, and should not be ignored. The prohibition in Jewish kosher laws against mixing meat and dairy is based upon the sensibility of a mother goat's milk comixing with the flesh of its offspring: "Thou shalt not seethe a kid in his mother's milk" (Exodus 23:19). Two mechanisms against violating this sensibility are either to obliterate any distinctive (i.e., unique, or involving only a few patients) part of a report; or to create model (fictitious) reports.

393. Miller RE, Boitnott JK, Moore GW.
Web-based Free-Text Query System for Surgical Pathology Reports with Automatic Case De-Identification. (Abstract).
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_5.html
http://www.netautopsy.org/apep00wb.htm

394. Alonsozana GLG, Moore GW, Hutchins GM.
UMLS Concordance for Human Embryology. (Abstract).
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_3.html
http://www.netautopsy.org/apep00em.htm

395. Sinard JH, Moore GW.
UMLS Concordance for a Comprehensive Pathology Text.
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_4.html
http://www.netautopsy.org/apep00cn.htm

396. Moore GW, Miller RE.
Linguistic Inventory of the Johns Hopkins Surgical Pathology Database. (Abstract).
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_1.html
http://www.netautopsy.org/apep00li.htm

397. Moore GW, Brown LA, Miller RE.
Goedelization of a Pathology Database: Re-identification by Inference. (Abstract).
Arch Pathol Lab Med. 2002 Jun;126:.
http://apiii.upmc.edu/abstracts/posterarchive/2001/moore.html
http://www.netautopsy.org/apep01go.htm

398. Giere W, Moore GW.
Goethe University Autopsy Register: Anonymized Bilingual Database. (Abstract).
Arch Pathol Lab Med. 2002 Jun;126:.
http://apiii.upmc.edu/abstracts/posterarchive/2001/giere.html
http://www.netautopsy.org/apep01gu.htm

399. Moore GW, Brown LA, Burger RH, Hutchins GM, Miller RE.
Modal Logic Theory for Pathology Inference. (Abstract).
Arch Pathol Lab Med. 2004 Jun;128:.
http://apiii.upmc.edu/abstracts/posterarchive/2003/moore.html
http://www.netautopsy.org/modlthry.htm

400. Moore GW, Brown LA, Burger RH, Kao GF, Hutchins GM, Miller RE.
Spreadsheet Order Logic for Pathology Inference. (Abstract).
Arch Pathol Lab Med. 2005 Jun;129:.
http://apiii.upmc.edu/abstracts/display.cfm?id=262
http://www.netautopsy.org/ordrlogc.htm

401. Moore GW, Struble RA, Brown LA, Kao GF, Hutchins GM.
Infinite Papilloma: Model for Unbounded Tumor Growth. (Abstract).
Arch Pathol Lab Med. 2006 Jun;130:898.
http://apiii.upmc.edu/abstracts/posterarchive/2005/moore.html
http://www.netautopsy.org/infnpapl.htm

402. Moore GW, Struble RA, Brown LA, Kao GF, Hutchins GM.
Cell Surface Tessellation: Model for Malignant Growth. (Abstract).
Arch Pathol Lab Med. 2007 Jun;131:.
http://apiii.upmc.edu/abstracts/posterarchive/2006/eposter/moore.html
http://www.netautopsy.org/celltess.htm

403. Moore GW, Struble RA, Brown LA, Kao GF, Hutchins GM.
Triple-spiked Zones in Cell Surface Tessellations: Model for Malignant Growth. (Abstract).
Arch Pathol Lab Med. 2008 Jun;132:. in press.
Scientific Presentation. September 10, 2007.
Advancing Practice, Instruction and Innovation through Informatics.
Pittsburgh Marriott City Center, Pittsburgh, PA
http://apiii.upmc.edu/abstracts/display_07.cfm?id=376
http://www.netautopsy.org/triplspk.htm

404. Moore GW, Kao GF, Brown LA.
Resource Description Framework for Mucosal Surface Pathology. (Abstract).
Arch Pathol Lab Med. 2008 Jun;132: in press.
Scientific Presentation. September 10, 2007.
Advancing Practice, Instruction and Innovation through Informatics.
Pittsburgh Marriott City Center, Pittsburgh, PA
http://apiii.upmc.edu/abstracts/display_07.cfm?id=324
http://www.netautopsy.org/mucordfh.htm

405. Moore GW, Kao GF, Brown LA.
Resource Description Framework for Dermatopathology. (Abstract).
Scientific Poster. 44th Annual Meeting. October 18-21, 2007. The American Society of Dermatopathology (ASDP).
Baltimore Marriott Waterfront Hotel, Baltimore, MD
http://www.netautopsy.org/dermrdfh.htm

406. Moore GW, Hutchins GM.
The persistent importance of autopsies.
Mayo Clin Proc. 2000 Jun;75(6):557-558.

407. Book Review: Seife C.
Zero. The Biography of a Dangerous Idea.
London: Penguin Books. 2000.
ISBN: 0-670-88457-X, 248 pages.
Reviewed in: Neurocomputing. 2001 Jan;42(1):335.

408. Book Review: Stewart I.
Flatterland. Like Flatland. Only More So.
Cambridge, MA: Perseus Publishing. 2001.
ISBN 0-7382-0442-0, 301 pages.
Reviewed in: Neurocomputing. 2001 Jan;42(1):337.
http://www.medparse.com/rvflatte.htm

409. Book Review: Casti JL, DePauli W.
Gödel. A Life of Logic.
Cambridge, MA: Perseus Publishing. 2000.
ISBN 0-7382-0274-6, 210 pages.
Reviewed in: Neurocomputing. 2001 Jan;42(1):331.
http://www.medparse.com/rvgodell.htm
(Kurt Gödel (1906-1978), Czech/Austrian logician).

410. Book Review: Aleksandr I, Morton H.
An Introduction to Neural Computing. Second Edition.
London: International Thomson Computer Press. 1995.
ISBN 1-85032-167-1, 284 pages.
Reviewed in: Neurocomputing. 2001;:. 2001 Jan;42(1):337.
http://www.medparse.com/rvneuroc.htm

411. Book Review: Scarborough D, Sternberg S.
Methods, Models, and Conceptual Issues. An Invitation to Cognitive Science. Volume 4.
Cambridge, MA: MIT Press. 1998.
ISBN 0-262-65946-0, 950 pages.
Reviewed in: Neurocomputing. 2001;:.
http://www.medparse.com/rvcognis.htm

412. Book Review: Changeux J-P, Connes A.
Conversations on Mind, Matter, and Mathematics
Ed & Transl: DeBevoise MB. Princeton, NJ: Princeton University Press. 1995.
ISBN 0-691-08759-8, 260 pages.
Reviewed in: Neurocomputing. 2001;:.

413. Book Chapter: Moore GW, Berman JJ.
Anatomic Pathology Data Mining.
Chapter 4. In: Cios KJ. Medical Data Mining and Knowledge Discovery. Berlin: Springer Verlag. 2000;4:61-107.
ISBN: 3-7908-1340-0, 502 pages.
Published within the series: "Studies in Fuzziness and Soft Computing", Physica-Verlag Heidelberg, a Springer-Verlag Company.
http://www.medparse.com/apdmchap.htm

414. Book Chapter: Cios KJ, Moore GW.
Medical Data Mining and Knowledge Discovery: Overview.
Chapter 1. In: Cios KJ. Medical Data Mining and Knowledge Discovery. Berlin: Springer Verlag. 2000;1:1-16.
ISBN: 3-7908-1340-0, 502 pages.
Published within the series: "Studies in Fuzziness and Soft Computing", Physica-Verlag Heidelberg, a Springer-Verlag Company.

415. Moore GW.
Internet pamphlet:
What is Pathology Informatics? http://www.netautopsy.org/whatpinf.htm

416. Moore GW.
Internet pamphlet:
What is Artificial Intelligence? http://www.netautopsy.org/whataiai.htm

417. Moore GW.
Internet pamphlet:
What is Calculus? http://www.netautopsy.org/whatcalc.htm

418. Moore GW.
Internet pamphlet:
What is Cryptography? http://www.netautopsy.org/whatcryp.htm

419. Moore GW.
Internet pamphlet:
What is the Internet? http://www.netautopsy.org/whatnett.htm

420. Moore GW.
Internet pamphlet:
What is Natural Language Processing? http://www.netautopsy.org/natlngpr.htm

421. Moore GW.
Internet pamphlet:
What is a Medical Parser? http://www.netautopsy.org/whatpars.htm

422. Moore GW.
Internet pamphlet:
What is the Barrier Word Method? http://www.netautopsy.org/whatbrwd.htm

423. Moore GW.
Internet pamphlet:
What is Ontology? http://www.netautopsy.org/whatonto.htm

424. Moore GW.
Internet pamphlet:
What is Perl? http://www.netautopsy.org/whatperl.htm

425. Moore GW.
Internet pamphlet:

Book Translation: Sadegh-zadeh K.
When Humans Forgot How to Think: Emergence of Machina sapiens.
German: Als der Mensch das Denken verlernte: Die Entstehung der Machina sapiens.
Translated by: Moore GW.
Tecklenburg, Germany: Burgverlag. 2000;:.
ISBN 3-922506-99-2, 164 pages.
Volume 3 in the series, Machina Sapiens: ISSN 0179-7174.
Copies of this translation were distributed to participants in the October 26, 2006, meeting, National Institutes of Health (NIH), Biomedical Computing Interest Group (BCIG), 5:30-7:30 PM, NIH Clinical Center, Bethesda, MD.
Dr. Moore was the facilitator for this meeting.
The author, Prof. Kazem Sadegh-zadeh, Professor Emeritus, Münster University, Münster, Germany, participated by webcam.
http://www.altum.com/bcig/events/bookclub/2006/2006_10.htm
http://www.medparse.com/machinasapiens/

426. Award: Moore GW.
Acceptance Speech. Association for Pathology Informatics. Honorary Fellow, 2007.
Presented: 6:30 PM, September 11, 2007. Annual Awards Dinner, Advancing Practice, Instruction and Innovation through Informatics. Pittsburgh Marriott City Center, 112 Washington Place, Pittsburgh, Pennsylvania 15219.
http://www.medparse.com/apihonfl.htm
http://www.pathologyinformatics.org/2007APIAward

427. Berman JJ, Moore GW.
Implementing an RDF Schema for Pathology Images.
Presented: 7:30 AM, September 10, 2007. Advancing Practice, Instruction and Innovation through Informatics. Pittsburgh Marriott City Center, 112 Washington Place, Pittsburgh, Pennsylvania 15219.
http://apiii.upmc.edu/programs/workshops.html
http://www.julesberman.info/spec2img.htm
http://www.julesberman.info/img_sch.xml

428. Berman JJ. Doublet method for very fast autocoding.
BMC Med Inform Decis Mak. 2004 Sep 15;4:16.
PMID: 15369595
PubMed Entry

429. Berman JJ. Tumor classification: molecular analysis meets Aristotle. BMC Cancer. 2004 Mar 17;4:10. PMID: 15113444
PubMed Entry

430. Zipf GK.
Human Behavior and The Principle of Least Effort. An Introduction to Human Ecology.
Reading, MA: Addison-Wesley Press. 1949;:19-55.

431. Haack S.
Do we need fuzzy logic?
Intl J Man-Mach Stud. 1979:11:437-445.
Objections to fuzzy set theory in linguistics:
(1) speech itself is not fuzzy;
(2) there are no applications [sic!].
(Gottlob Frege, 1848-1925, German mathematician; Bertrand Russell, 1872-1970, British philosopher).

433. Łukasiewicz J.
Elementy Logiki Matematycznej.
Warsaw. 1929;:.
as cited in Zeman, 1973.
(Jan Łukasiewicz, 1848-1956, Polish logician).

434. Łukasiewicz J.
A system of Modal Logic.
The Journal of Computing Systems. 1953;1:111-149.
as cited in Zeman, 1973.

435. Łukasiewicz J.
Arithmetic and Modal Logic.
The Journal of Computing Systems. 1953;1:213-219.
as cited in Zeman, 1973.

536. Łukasiewicz J.
On a Controversial Problem of Aristotle's Modal Syllogistic.
Dominican Studies. 1954;7:114-123.
as cited in Zeman, 1973.

437. Heckering PS.
Token swap test revisited.
Comput Methods Programs Biomed. 2003 Mar;70(3):265-269.
PMID: 12581559.
PubMed Entry

439. Sutton W, Linn E.
Where the Money Was. The Memoirs of the World's Greatest Bank Robber.
New York: Ballantine Books. 1976;:.
ISBN 0-345-25371-X-195, 422 pages.
Part Two: Breaking Out. Sutton's Law, pp. 148-150.

440. Petersdorf RG, Beeson PB.
Fever of Unexplained Origin.
Medicine. 1961;40:1-30.
Remark about Sutton's Law on p. 27.

441. Quine WV.
Theory of Deduction.
Cambridge, MA: Harvard Cooperative Society. 1948;:65-81.

442. Hutchins WJ.
Machine Translation : Past, Present, Future .
Ellis Horwood/Wiley, Chichester/New York. 1986;:. Ellis Horwood Series in Computers and Their Applications. ASIN: 0135435218 .

443. Nagao M. Machine Translation.
In: Shapiro SC, ed. Encyclopedia of Artificial Intelligence. Volume 2. M-Z.
New York: Wiley-Interscience. 1992;:898-902.

444. Condon EU.
Statistics of vocabulary.
Science. 1928;67:300, 1928.

445. Steimann F.
Fuzzy Set Theory in Medicine. Editorial
Artif Intell Med. 1997;11:1-7.

446. Feinstein AR.
Clinical Judgment.
Huntington, NY: Krieger Publishing Co, Inc. 1976;:.

447. Sadegh-Zadeh K.
Family resemblance concepts fuzzified.
Artif Intell Med. 2001;22:.

448. Aristotle.
The Metaphysics. Books I-IX [Engl. Translation: Hugh Tredennick].
London: William Heinemann, 1961.

449. da Costa NCA.
On the theory of inconsistent formal systems.
Notre Dame J Formal Logic 1974;15:497-510.

456. Haack S.
Do we need "fuzzy logic"?
Int J Man-Machine Stud 1979;11:437-445.

457. Kalmanson D, Stegall HF.
Cardiovascular investigations and fuzzy set theory.
Am J Cardiol 1975;35:80-84.

468. Zadeh LA.
From computing with numbers to computing with words - from manipulation of measurements to manipulation of perceptions.
IEEE Trans Circuits System I: Fundam Theory Appl 1999;45:105-119.

469. Zadeh LA.
Fuzzy sets.
Information and Control. 1965;8:338-353.

470. Zadeh LA.
Fuzzy sets and systems.
In: J. Fox, ed. System Theory. Brooklyn, New York: Polytechnic Press. 1965;:29-39.

471. Zadeh LA.
Fuzzy Algorithms.
Information and Control. 1968;12:94-102.

472. Zadeh LA.
Towards a theory of fuzzy systems.
In: Kalman RE, DeClaris RN, eds. Aspects of Networks and Systems Theory. New York: Holt, Reinhart & Winston, 1971;:469-490.

473. Klir GJ, Yuan B.
Fuzzy Sets and Fuzzy Logic. Theory and Applications.
Upper Saddle River, NJ: Prentice Hall. 1995;:.

474. Struble RA.
Can one do serious mathematics with pictures and calculus?
Colloquium. Department of Mathematics. North Carolina State University, Raleigh, NC. Tuesday, April 17, 1984. 3:45 PM, Harrelson Room 307.
http://www.medparse.com/stru0409.htm

475. Struble RA.
Infinite products rescued.
http://www.medparse.com/struinfp.htm

476. Struble RA.
Infinite products and integration.
http://www.medparse.com/struitgr.htm

477. Struble RA.
Curriculum Vitae.
http://www.medparse.com/strublcv.htm

478. Derbyshire J.
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics.
New York: Plume Books. 2004 May 25;:.
ISBN: 0452285259, 448 pages.

479. Seife C.
Zero. The Biography of a Dangerous Idea.
London: Penguin Books. 2000.
ISBN: 0-670-88457-X, 248 pages.
This book includes an account of the execution of Hippasus of Metapontum, a member of the Pythagorean cult, who had dared to reveal the existence of irrational numbers to persons outside the cult.

480. Maor E.
e: The Story of a Number.
Princeton, NJ: Princeton University Press. 1998;:.
ISBN: 0691058547, 232 pages.
"Rarely in the history of science has an abstract mathematical idea been received more enthusiastically by the entire scientific community than the invention of logarithms..."

481. Fryxell PA, Koch SD.
Pavonia Ecostata (Malvaceae), a New Species from Jalisco, Mexico.
Brittonia. 1991 Jan-Mar;43(1):24-26.

482. Ruse ME.
Gregg's Paradox: A Proposed Revision to Buck and Hull's Solution.
Systematic Zoology. 1971 Jun;20(2):239-245.

483. MacKenna MC, Bell SK.
Classification of Mammals.

ISBN-10: 0231110138, 640 pages.
ISBN-13: 978-0231110136, 640 pages.
"Attempts to systematize organism come and go; none is permanent and there are many kinds (Huxley 1869:1;Gilmour 1940, 1951; Griffiths 1974; Bouquet 1996)...".
"Such redundant monotypy, often cited as exemplifying "Gregg's paradox," should not (but sometimes does) create confusion (Buck and Hull 1966; Farris 1967, 1968, 1976; Gregg 1967; Wiley 1979, 1980)."

484. Hawking S.
Black Holes and Baby Universes and Other Essays.
New York: Bantam Books. 1993;:. Pages 44-45.
ISBN 0-553-37411-7, 182 pages.
Here is Hawking's description of Schrödinger's cat:

"In my opinion, the unspoken belief in a model independent reality is the underlying reason for the difficulties philosophers of science have with quantum mechanics and the uncertainty principle. There is a famous thought experiment called Schrödinger's cat. A cat is placed in a sealed box. There is a gun pointing at it, and it will go off if a radioactive nucleus decays. The probability of this happening is fifty percent. (Today no one would dare propose such a thing, even purely as a thought experiment, but in Schrödinger's time they had not heard of animal liberation.)

"If one opens the box, one will find the cat either dead or alive. But before the box is opened, the quantum state of the cat will be a mixture of the dead cat state with a state in which the cat is alive. This some philosophers of science find very hard to accept. The cat can't be half shot and half not-shot, they claim, any more than one can be half pregnant. Their difficulty arises because they are implicitly using a classical concept of reality. In this view, an object has not just a single history but all possible histories. In most cases, the probability of having a particular history will cancel out with the probability of having a very slightly different history; but in certain cases, the probabilities of neighboring histories reinforce each other. It is one of these reinforced histories that we observe as the history of the object.

"In the case of Schrödinger's cat, there are two histories that are reinforced. In one the cat is shot, while in the other it remains alive. In quantum theory both possibilities can exist together. But some philosophers get themselves tied in knots because they implicitly assume that the cat can only have one history."

485. Taleb NN.
The Black Swan. The Impact of the Highly Improbable.
New York: Random House. 2007 Apr 17;:.
ISBN-13: 978-1400063512, 400 pages.
http://www.netautopsy.org/bcig/blckswan.htm
There are many, many forms of Sutton's Law, dating back to the ancient Greek philosophers Plato and Aristotle: the unwise Greek (as in: "All Greeks are wise; Socrates is a Greek..."); the white crow ("all crows are black..."); the white raven; the black swan; the bird that can't fly, etc.
(Aristotle, 384-322 BC, Greek philosopher).
(Plato, 424-348 BC, Greek philosopher).
(Socrates, 470-399 BC, Greek philosopher). To name a few more:

1. Impecunious banks (Sutton's Law).
2. Zebras in the street: "If you hear hoofbeats in the street, think of horses, not zebras."
3. Plato: Essence vs accident.
4. Aristotle: "Amicus Plato, sed magis amica veritas." "Plato is my friend, but Truth is more my friend."
(Aristotle, 384-322 BC, Greek philosopher).
(Plato, 424-348 BC, Greek philosopher).
(Socrates, 470-399 BC, Greek philosopher).
5. Avicenna (Ibn-Sina, 980-1037, Persian physician, philosopher): Temporal logic.
6. St Thomas Aquinas: Jesus' blood (essence) vs sacramental wine (accident). (St Thomas Aquinas, 1225-1274, Roman Catholic theologian).
7. Karl Pearson: Population vs sample (Karl Pearson, 1857-1936, British statistician).
8. Jan Łukasiewicz: Multi-valued logic. (Jan Łukasiewicz, 1848-1956, Polish logician).
9. C.I. Lewis: Modal logic. (C.I. Lewis, 1883-1964, American philosopher).
10. Lotfi A. Zadeh: Fuzzy logic. (Lotfi Zadeh, Iranian/American engineer, mathematician).
11. Susan Haack: Deviant logic.
12. Gerhard Brewka: Non-monotonic logic. An Overview.
13. Austrian folk poem: "Alle Kunst / Ist umsunst / Wenn der Engel / Auf dem Zundloch brunst." [All technology is in vain, if the Angel urinates on your musket."]
14. Kurt Gödel: Über unentscheidbare Sätze der Principia mathematica und verwandte Systeme. I. ["Regarding undecidable propositions of the Principia mathematica and related systems. I."] Monatsh Math Phys. 1931;38:173-198. (Kurt Gödel (1906-1978), Czech/Austrian logician).
15. "God is dead" --Nietsche; "Nietsche is Dead" -- God.
16. Isaac Asimov: "The Mule" in The Foundation Series.
17. DaCosta's Paraconsistency.
18. Boolos G: The Unprovability of Consistency. An Essay in Modal Logic. Cambridge: Cambridge University Press. 1979;:. ISBN 0-521-21879-9, 184 pages. (George S. Boolos, 1940-1996, American philosopher.)

19. Ronald W. Reagan (1911-2004, 40th President of the United States, 1981-1989): "Trust, but Verify" was a signature phrase of Ronald Reagan. He used it in public, although he was not the first person known to use it. When Reagan used this phrase, he was usually discussing relations with the Soviet Union, and he almost always presented it as a translation of the Russian proverb "doveryai, no proveryai" (доверяй но проверяй). At the signing of the INF Treaty, Reagan used the phrase again, and his counterpart Mikhail Gorbachev responded: "You repeat this phrase every time we meet." The phrase has also been attributed to U.S. journalist and fiction writer Damon Runyon (1884-1947).

20. Disinformation, fib, lie, mendacity, prevarication, ....

21. Talking Horse.

22. Zipf's Law.

23. Pareto's Principle.

486. Upton G, Cook I.
A Dictionary of Statistics. Second Edition.
Oxford, UK: Oxford University Press. 2006;:.
ISBN 0-19-861431-4, 490 pages.
ISBN 978-0-19-861431-9, 490 pages.
Contingency table (p. 96). "The term was first used by Karl Pearson in 1904...."

487. Klotz L.
Active surveillance for favorable risk prostate cancer: Rational, risks, and results. Seminar article.
Urologic Oncology: Seminars and Original Investigations. 25;2007:505-509.

488. Klotz L.
Point: Active surveillance for favorable risk prostate cancer:
J Natl Compr Canc Netw. 2007;5(7):693-698.

489. Kaplan R, Kaplan E.
Out of the Labyrinth. Setting Mathematics Free.
Oxford, UK: Oxford University Press. 2007;:.
ISBN-13: 978-0-19-514744-5, 244 pages.

490. Hellman H.
Great Feuds in Mathematics. Ten of the Liveliest Disputes Ever.
New York: John Wiley & Sons, Inc. 2006;:.
ISBN-13 978-0-471-64877-2, 256 pages.
ISBN-10 0-471-64877-9, 256 pages.
1. Tartaglia vs Cardano: Solving Cubic Equations, 7.
2. Descartes vs Fermat: Analytic Geometry and Optics, 26.
3. Newton vs Leibniz: Credit for the Calculus, 51.
4. Bernoulli vs Bernoulli: Sibling Rivalry of the Highest Order, 73.
5. Sylvester vs Huxley: Mathematics: Ivory Tower or Real World?, 94.
6. Kronecker vs Cantor: Mathematical Humbug, 116.
7. Borel vs Zermelo: The "Notorious Axiom", 142.
8. Poincaré vs Russell: The Logical Foundations of Mathematics, 156.
9. Hilbert versus Brouwer: Formalism vs Intuitionism, 179.
10. Absolutists/Platonists vs Fallibilitists/Constructivists: Are Mathematical Advances Discoveries or Inventions?, 200.

491. Hellman H.
Great Feuds in Medicine: Ten of the Liveliest Disputes Ever.
Publisher: Wiley; 1 edition (February 1, 2002)
ISBN-10: 0471208337, 256 pages.
ISBN-13: 978-0471208334, 256 pages.

492. Hellman H.
Great Feuds in Science: Ten of the Liveliest Disputes Ever (Hardcover)
Publisher: Wiley; 1 edition (August 20, 1999)
ISBN-10: 0471350664, 256 pages.
ISBN-13: 978-0471350668, 256 pages.

493. Hellman H.
Great Feuds in Technology: Ten of the Liveliest Disputes Ever.
ISBN-10: 0471208671, 256 pages.
ASIN: B000J3EGGM, 256 pages.

494. Hofstadter D.
Gödel, Escher, Bach.
Johann Sebastian Bach, 1685-1750, German composer.
M. C. Escher, 1898-1972, Dutch graphic artist.
Kurt Gödel (1906-1978), Czech/Austrian logician.

495. Hofstadter D.
I am a Strange Loop.
New York: Basic Books. 2007;:.
ISBN-13: 978-0-465-03078-1, 412 pages.
ISBN-10: 0-465-03078-5, 412 pages.

BCIG-NIH video link:

https://webmeeting.nih.gov/p84624254/

I haven't read Hofstadter and Dennett's The Mind's I, but I have seen summaries, and the Strange Loop book covers the same range of ideas. The present book is very personal, with a long discussion of the author's wife's untimely death, leaving behind two young children.

To be honest, the response by the BCIG book club to the book was lukewarm. For myself, it seemed like a lot of verbiage to cover a relatively limited amount of material.

I give credit to Hofstadter for one thing: he has popularized Gödel (Kurt Gödel (1906-1978), Czech/Austrian logician) (and to a lesser extent, Escher ) in a way that nobody else has. Before Hofstadter, only specialists in the USA had ever heard of Gödel.

While I agree with Dr. McLaughlin that Strange Loop shouldn't be mistaken for hard science, I also think that there is a place in the world for popularizers like Hofstadter. I have never seen such easy-to-read, yet fairly robust, explanations of Gödel's work as Hofstadter's writings. I was on a long busride to the airport a few years ago, sitting next to a medical malpractice lawyer, which could have been a fairly unpleasant two hours, but we fell into a conversation about Gödel-Escher-Bach, and it was a very good ride after all.

At the BCIG book club meeting (2/28/2008), there was a lively discussion of the book, which made the trip worthwhile. With quite a few biologists, biochemists, etc., we also agreed that Hofstadter had almost no insight about biomedicine. And, Sadegh-zadeh's book, Machina sapiens, came up for brief discussion. Machina sapiens has a much better coverage of the biomedical perspective.

Hofstadter had a lot of discussion of hierarchical self-recognizing systems (such as Sadegh-zadeh's Pe-Kawe), but it is not clear to me that Hofstadter is familiar with Sadegh-zadeh's work. Hofstadter takes most of his serious examples from physics, music, art, or his personal life. He has a very superficial knowledge of biomedicine. The book has a nice layman-level discussion of Gödel's proof, Whitehead-Russell Principia Mathematica, etc. That discussion alone makes the book worth reading.

496. Lukasiewicz J.
A system of Modal Logic.
J Comput Sys. 1953;1:111-149.
Jan Lukasiewicz (1883-1964), Polish logician.

497. Gödel K.
Über formal unentscheidbare Saetze der Principia Mathematica und verwandter Systeme. I.
Monatsh Math Phys. 1931;38:173-198.
Kurt Gödel (1906-1978), Czech/Austrian logician.

498. Haack S.
Do we need fuzzy logic?
Intl J Man-Mach Stud. 1979:11:437-445.
Objections to fuzzy set theory in linguistics:
(1) speech itself is not fuzzy;
(2) there are no applications [sic!].

499. Haack S.
Deviant Logic. Fuzzy Logic. Beyond the Formalism.
Chicago: University of Chicago Press. 1996;:.
ISBN 0-226-31133-3, 291 pages.
ISBN 0-226-31134-1, 291 pages.

500. Lewis CI, Langford CH.
Symbolic Logic. Second Edition.
New York: Dover Publications, Inc. 1932;:.
ISBN 0-486-60170-6, 518 pages.
C. I. Lewis (1883-1964), American philosopher.

501. Titus 1:12. The Holy Bible. King James Version.
St. Paul's restatement of the Paradox of Epimenides:
"One of themselves, even a prophet of their own, said, The Cretans are always liars, evil beasts, slow bellies. This witness is true. Wherefore rebuke them sharply, that they may be sound in the faith...."
It seems that St. Paul didn't quite "get it" at the deeper philosophical level.

502. Matthew 16:18-19. The Holy Bible. King James Version.
16:18. And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.
16:17. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.
"Keys of the Kingdom" may be regarded as a mathematical function, that is one-to-one and onto, between earth and heaven.
This Bible-verse, is written in 2-meter-high letters on the ceiling of the Sistine Chapel, Vatican City. These words of Jesus to St Peter (the first pope) is a justification for the supremacy of the Roman Catholic pope.

503. Irvine AD.
Russell's Paradox.
The Stanford Encyclopedia of Philosophy (Summer 2003 Edition).
http://plato.stanford.edu/archives/sum2003/entries/russell-paradox/
(Gottlob Frege, 1848-1925, German mathematician; Bertrand Russell, 1872-1970, British philosopher).

504. Moore GW, Hutchins GM.
Effort and demand logic in medical decision making.
Metamedicine. 1980;1:277-304.

505. Zeman J.
Modal Logic, The Lewis-Modal Systems.
Oxford: Oxford University Press. 1973;:.
ISBN not stated, 302 pages.

506. Garson J.
Modal Logic.
The Stanford Encyclopedia of Philosophy (Winter 2001 Edition)
Edward N. Zalta, ed.
http://plato.stanford.edu/archives/win2001/entries/logic-modal/
(Plato, 424-348 BC, Greek philosopher).

507. Berry paradox.
From Wikipedia, the free encyclopedia.
http://www.wikipedia.org/wiki/Berry_paradox

508. Sutton W, Linn E.
Where the Money Was. The Memoirs of the World's Greatest Bank Robber.
New York: Ballantine Books. 1976;:.
ISBN 0-345-25371-X-195, 422 pages.
Part Two: Breaking Out. Sutton's Law, pp. 148-150.
"Sutton's Law" is also known as the Zebra Rule.
Willie Sutton (1901-1980), American bank robber.

509. Petersdorf RG, Beeson PB.
Fever of Unexplained Origin.
Medicine. 1961;40:1-30.
Remark about Sutton's Law on p. 27.

510. Groopman J.
How Doctors Think.
New York: Houghton Mifflin Company. 2007 Mar 19;:.
ISBN-10: 0618610030, 320 pages.
ISBN-13: 978-0618610037, 320 pages.
Discussion of the Zebra Rule: "when you hear hoofbeats in the street, think of horses, not zebras."
BCIG Book Club selection, September 27, 2007.

511. Elster J.
Active and Passive Negation. An Essay in Ibanskian Sociology.
In: Watzlawick P. The Invented Reality: How Do We Know What We Believe We Know? (Contributions to Constructivism). 1984;:175-205.
New York: W. W. Norton & Company, Inc. (March 1, 1984).
ISBN-10: 0393333477, 352 pages.
ISBN-13: 978-0393333473, 352 pages.
Originally presented: Ninth World Congress of Political Science, Moscow, 12-18 August, 1979 (long before the end of the Cold War).
Book by Aleksander Zinoviev, The Yawning Heights, 1977.
Aleksander Zinoviev (b. 1922): Cold War Soviet dissident.
Paul Watzlawick (1921-2007): Austrian theoretician in Communication Theory and Radical Constructivism.

I was particularly interested in the points that Dr. McLaughlin made in the informal discussion afterwards, and I think that he is right on target. While it is possible to imagine realities beyond those that we occidentally-educated scientists all know and love, the great edifice of modern medicine, including the wonders of modern pharmacology, rest predominantly upon western concepts of reality (even though many Americans can't afford either). It is fun to play around with alternate realities, and essential to know that such realities are possible (i.e., the exception proves the rule, using “prove” in the sense of a philosophical trial-by-fire). However, it is rare that these alternate realities have a palpable, practical value; non-Euclidean geometry, and general relativity that lives in this geometry, being a notable exception. One could even make the argument that general relativity was little more than a toy for physicists thinking about massive bodies and fast-moving particles, until (as I have been told) the advent of global positioning systems, which are apparently dependent upon relativistic calculations. GPS is extremely practical for the ordinary person. I could never have driven to my nephew's wedding in central Michigan without it.

From the previous BCIG book club, I was fascinated by Bertrand Russell's (1872-1970, British philosopher). dismissal of Gödel's Theorem, (Kurt Gödel, 1906-1978, Czech/Austrian logician) on the grounds that nobody cares about self-referential proofs anyhow. I agree with Russell's dismissal (what, after all, has come from Gödel, besides a few oddities like the Axiom of Choice and the Generalized Continuum Hypothesis, of interest exclusively to mathematical theologians?). However, that's a pretty bold statement coming from a guy who made his early career by cleaning Gottlob Frege's (German mathematician, 1848-1925) clock, by showing the impossibility of the set of all sets. For me, the most stunning consequence Gödel's Theorem, is that you can't prove consistency for mathematics that includes a concept of infinity (i.e., non-constructivist mathematics). This fact means that the entire edifice of western mathematics rests upon the brain tissue of three thousand years of bright mathematicians, not upon any (demonstrable, Platonic) consistency (Boolos G: The Unprovability of Consistency. An Essay in Modal Logic. Cambridge: Cambridge University Press. 1979;:. ISBN 0-521-21879-9, 184 pages. George S. Boolos, 1940-1996, American philosopher.) This result, in turn, gives comfort to those of us in the softer sciences, such as biology and medicine, who have traditionally been relegated to the back seat by physicists and mathematicians.

512. Aristotle's Law of Excluded Middle.
Paraphrases Romans 8:31: "...If God be for us, who can be against us?"

513. Steiger I.
Radio Eriwan antwortet.
München: Lichtenberg-Verlag. 1984;:.
ISBN 3-7852-1086-8, pages.

514. Parth WW, Schiff M, Steiger I.
Neues von Radio Eriwan.
München: Lichtenberg-Verlag. 1984;:.
ISBN 3-596-21299-5, pages.

515. Bazarow B.
Im Prinzip Ja - Flüsterwitze vom Sender Eriwan.
München: Goldmann Verlag. 1970;:.
ISBN 3-442-02777-2, pages.

516. Schiff M.
Radio Eriwan antwortet.
Publisher: Kindler (1969).
ASIN: B0000BT4L3, 122 pages.

519. Croskerry P.
The importance of cognitive errors in diagnosis and strategies to minimize them.
Acad Med. 2003 Aug;78(8):775-780. Review.
PMID: 12915363.
PubMed Entry

520. Croskerry P.
Cognitive forcing strategies in clinical decisionmaking.
Ann Emerg Med. 2003 Jan;41(1):110-120.
PMID: 12514691.
PubMed Entry

521. Cosby KS, Croskerry P.
Patient safety: a curriculum for teaching patient safety in emergency medicine.
Acad Emerg Med. 2003 Jan;10(1):69-78. Review.
PMID: 12511320.
PubMed Entry

522. Croskerry P.
Achieving quality in clinical decision making: cognitive strategies and detection of bias.
Acad Emerg Med. 2002 Nov;9(11):1184-1204.
PMID: 12414468.
PubMed Entry
Description of "zebra retreat".
As cited in Groopman (2007).

523. Croskerry P, Chisholm C, Vinen J, Perina D.
Quality and education.
Acad Emerg Med. 2002 Nov;9(11):1108-1115.
PMID: 12414458.
PubMed Entry

524. Shapiro MJ, Croskerry P, Fisher S.
Profiles in patient safety: sidedness error.
Acad Emerg Med. 2002 Apr;9(4):326-329.
PMID: 11927462.
PubMed Entry

525. Croskerry P, Shapiro MJ.
"Profiles in patient safety": a new feature.
Acad Emerg Med. 2002 Apr;9(4):324.
PMID: 11927460.
PubMed Entry

526. Croskerry P.
The feedback sanction.
Acad Emerg Med. 2000 Nov;7(11):1232-1238. Review.
PMID: 11073471.
PubMed Entry

527. Croskerry P.
The cognitive imperative: thinking about how we think.
Acad Emerg Med. 2000 Nov;7(11):1223-31. Review.
PMID: 11073470.
PubMed Entry

528. Asimov I.
Foundation.
Publisher: Spectra; Revised edition (October 1, 1991)
ISBN-10: 0553293354, 320 pages.
ISBN-13: 978-0553293357, 320 pages.

529. Asimov I.
Foundation and Empire.
Publisher: Spectra (June 1, 2004)
ISBN-10: 0553803727, 256 pages.
ISBN-13: 978-0553803723, 256 pages.

530. Asimov I.
Second Foundation.
Publisher: Spectra (June 1, 2004)
ISBN-10: 0553803735, 256 pages.
ISBN-13: 978-0553803730, 256 pages.

531. Asimov I.
The Complete Stories. Volume 1.
Publisher: Spectra (June 1, 2004)
ISBN-10: 0553803735, 256 pages
ISBN-13: 978-0553803730, 256 pages
The first short story in this volume, "The Dead Past", is a paradigm for the installation of comprehensive new software in a medical institution. As soon as you copy in the records from the past (as you must; there is no tabula rasa [Latin: blank tablet] in medicine), you find old records that you wish you hadn't found.

The short story gives an account of a history professor (Asimov's dream job, according to his autobiography), delving into why an expensive, government-sponsored project, to develop a look-back technology for historical events, has been fruitless for over twenty years. According to government propaganda, the results of this project would be the opportunity to witness Julius Caesar's assassination, Suliemann's assault on Vienna, Napoleon's surrender at Waterloo, etc.

What the history professor discovers is that the technology only supports accurate, short-term lookbacks, such as the argument you had with your boss or your spouse a few weeks ago, in which all the principals have made up and moved onward. Horrors! We are now all living in a fishbowl; all privacy is gone, etc.

Comment: Internet and email have created some of this privacy vacuum that Asimov writes about.

532. 6102 webpage:
http://vaww.va.gov/6102/

533. Register webpage:
http://vaww.va.gov/webregistry

534. VA Websearch webpage:
http://vaww.va.gov/vawebsearch/

535. Privacy webpage:
http://vaww.va.gov/privacy/

536. No-Fear Act webpage:
http://vaww1.va.gov/ohrm/EmployeeRelations/grievance.htm

537. Department of Veterans Affairs Homepage.
http://vaww.va.gov/

538. Department of Veterans Affairs. Website Search:
http://vaww.va.gov/search/

539. Department of Veterans Affairs. Facilities Site Location:
http://vaww.va.gov/sta/guide/home.asp

540. Department of Veterans Affairs. VA Accessibility Information:
http://vaww.va.gov/accessible

542. Department of Veterans Affairs. Privacy & Security Statement:
http://vaww.va.gov/privacy

543. Department of Veterans Affairs. Disclaimers of liability and endorsement:
http://vaww.va.gov/disclaim.htm

544. U. S. Freedom of Information Act:
http://vaww.va.gov/foia/

551. Gamble M, Wilson I.
The Hematoxylins and Eosin. Chapter 8, pp. 125-138.
In: Bancroft JD, Gamble M.
Theory and Practice of Histological Techniques. Fifth Edition.
Edinburgh: Churchill Livingstone. 2002;:125-138.
ISBN 0-443-06435-0, 796 pages.

552. Carazzi D.
Eine neue Hämatoxylinlösung. [German: A new hematoxylin solution].
Z f wissenschaftl Mikroskopie u mikroskop Technik. 1911;28:273.

553. Ehrlich P.
Fragekasten. [German: Query box.]
Z f wissenschaftl Mikroskopie u mikroskop Technik. 1886;3:150.

554. Gill GW, Frost JK, Miller KA.
A new formula for half-oxidized hematoxylin solution that neither overstains nor requires differentiation.
Acta Cytol. 1974;18:300.

555. Harris HF.
On the rapid conversion of hematoxylin into hematein in staining reactions.
J Appl Microsc Lab Methods. 1900;3;777.

556. Heidenhain M.
Noch einmal über die Darstellung der Centralkörper durch Eisenhämatoxylin nebst einigen allgemeinen Bemerkungen über die Hämatoxylinfarben. [German: Once again regarding the demonstration of nuclear bodies through staining with hematoxylin].
Z f wissenschaftl Mikroskopie u mikroskop Technik. 1896;13:186.

557. Lillie RD, Fulmer HM.
Histopathologic Technic and Practical Histochemistry. Fourth Edition.
New York: McGraw-Hill. 1976;:.

558. Mayer P.
Über Schleimfärbung. [German: On staining mucus].
Mitteil zoolog Station zu Neapel. 1896; 12:303.

559. Mayer P.
Notiz über Hämatin und Hämalaun. [German: Note regarding Hematin and Hemalaun].
Z f wissenschaftl Mikroskopie u mikroskop Technik. 1903;20:409.

560. Mallory FB.
On certain improvements in histological technique.
J Exptl Med. 1897;2:529.

561. Mallory FB.
A contribution to staining methods.
J Exptl Med. 1900;5:15.

562. McManus JFA.
Histological demonstration of mucin after periodic acid.
Nature (Lond). 1946;158:202.

563. McManus JFA.
Histological demonstration of mucin after periodic acid.
Nature (Lond). 1946;158:202.

564. McManus JFA, Mowry RW
Staining Methods, Histologic and Histochemical.
London: Harper & Row. 1964;:268.

565. Verhoeff FH.
Some new staining methods of wide applicability. Including a rapid differential stain for elastic tissue.
JAMA. 1908;50:876.

566. Weigert K.
Eine kleine Verbesserung der Hämatoxylin van-Gieson-methode. [German: A small improvement in the hematoxylin van-Gieson method].
Z f wissenschaftl Mikroskopie u mikroskop Technik. 1904;21:1.

567. Leong AS, ed.
Principles and Practice of Medical Laboratory Science. Volume 1: Basic Histotechnology. First Edition.
Philadelphia: W.B. Saunders Company. 1996;:.
ISBN: 0443053693, 171 pages.

568. Prophet EB, Mills B, Arrington JB, Sobin LH.
Laboratory Methods in Histotechnology.
Washington, DC: American Registry of Pathology. 1992;:53-58.
ISBN: 1-881041-00-X 1992.

569. Brown GG.
An introduction to histotechnology: A manual for the student, practicing technologist, and resident-in-pathology.
New York: Appleton-Century-Crofts. 1978;:.
ISBN: 0838543405, 453 pages.

570. Prophet EB, Mills B, Arrington JB, Sobin LH, eds.
Laboratory Methods in Histotechnology.
Washington, DC: Armed Forces Institute of Pathology. 1992;:.
ISBN 1-881041-00-X, 278 pages.

571. Mikel UV, ed.
Advanced Laboratory Methods in Histology and Pathology.
Washington, DC: Armed Forces Institute of Pathology. 1994;:.
ISBN 1-881041-13-1, 254 pages.

601. Freedman D, Pisani R, Purves R.
Statistics. Third Edition.
New York: W.W. Norton & Company. 1998.
ISBN 0-393-97083-3, 578 pages.

602. Livio M.
The Golden Ratio. The Story of Phi, the World's Most Astonishing Number.
New York: Broadway Books. 2003.
ISBN 0-7679-0816-3, 290 pages.

603. Huntley HE.
The Divine Proportion. A Study of Mathematical Beauty.
New York: Dover Publications, Inc. 1970.
ISBN 486-22254-3, 186 pages.

604. Singh S.
Fermat's Enigma. The Epic Quest to solve the World's Greatest Mathematical Problem.
New York: Anchor Books. A Divsion of Random House, Inc. 1997.
ISBN 0-385-49362-2, 315 pages.

605. Croxton FE.
Elementary Statistics with Applications. in Medicine and the Biological Sciences.
New York: Dover Publications, Inc. 1953.

606. Murphy EA.
A Companion to Medical Statistics.
Baltimore: The Johns Hopkins University Press. 1985.

607. Edwards AL.
Statistical Analysis. Revised Edition.
New York: Rinehart & Company, Inc. 1946.

608. Afifi AA, Azen SP.
Statistical Analysis. A Computer Oriented Approach. Second Edition.
New York: Academic Press. 1979.

609. Lombard OM.
Biostatistics for the Health Professions.
New York: Appleton-Century-Crofts. 1975.

610. Hines WW, Montgomery DC.
Probability and Statistics. In Engineering and Management Science.
New York: The Ronald Press Company. 1972.

611. Downing D, Clark J.
Statistics. The Easy Way.
New York: Barron's Educational Series, Inc. 1989.

612. Fogiel M.
The Statistics Problem Solver. A Complete Solution Guide to Any Textbook.
Piscataway, NJ: Research and Education Association. 1994.

613. Mood AM, Graybill FA.
Introduction to the Theory of Statistics. Second Edition.
New York: McGraw-Hill Book Company. 1963.

614. Lilienfeld DE, Stolley PD.
Foundations of Epidemiology. Fifth Edition.
New York: Oxford University Press. 1994.

615. MacMahon B, Dimitrios T.
Epidemiology. Principles and Methods. Second Edition.
New York: Little, Brown and Co. 1996.

616. Barker DJP, Cooper C, Rose G.
Epidemiology in Medical Practice. Fifth Edition.
New York: Churchill Livingstone. 1998.

617. Gordis L.
Epidemiology.
Philadelphia: W. B. Saunders Co. 1996.

618. Farmer R, Miller D, Lawrenson R.
Lecture Notes on Epidemiology and Public Health Medicine. Fourth Edition. Oxford: Blackwell Science. 1996.

619. Moore GW, Boitnott JK, Miller RE, Eggleston JC, Hutchins GM.
Integrated pathology reporting, indexing, and retrieval system using natural language diagnoses.
Mod Pathol. 1988 Jan;1(1):44-50.
PMID: 3070549

620. Moore GW, Berman JJ.
Anatomic Pathology Data Mining.
Chapter 4. In: Cios KJ. Medical Data Mining and Knowledge Discovery. Berlin: Springer Verlag. 2000;4:61-107.
ISBN: 3-7908-1340-0, 502 pages.
Published within the series: "Studies in Fuzziness and Soft Computing", Physica-Verlag Heidelberg, a Springer-Verlag Company.
http://www.netautopsy.org/apdmchap.htm

621. Cios KJ, Moore GW.
Medical Data Mining and Knowledge Discovery: Overview.
Chapter 1. In: Cios KJ. Medical Data Mining and Knowledge Discovery. Berlin: Springer Verlag. 2000;4:61-107.
ISBN: 3-7908-1340-0, 502 pages.
Published within the series: "Studies in Fuzziness and Soft Computing", Physica-Verlag Heidelberg, a Springer-Verlag Company.

622. Brown DG, Brown G, Goldstein M.
Introduction to CCS MUMPS.
COMP Computing, Inc. 1601 Westheimer, Suite 201, Houston, Texas 77006, pp. 1-99, 1985

623. DataTree, Inc.
DataTree MUMPS-PC System Overview, v. 4.2.
DataTree, Inc., 300 Fifth Ave, Waltham, MA 02154 1-617-890-1620, 1991, pp. 10-13

624. DataTree, Inc.
DataTree MUMPS Language Reference, v. 4.2.
DataTree, Inc., 300 Fifth Ave, Waltham, MA 02154 1-617-890-1620, 1991, pp. 16-17.

625. Walters RF, Bowie J, Wilcox JC.
Mumps Primer. M Technology Association,
1738 Elton Road, Suite 205, Silver Spring, MD 20903-1725.

626. Kirsten W.
Von ANS MUMPS zu ISO/M.
epsilon Verlag, Darmstadt Hochheim. 1993, pp. 47-84.

625. Simpson A.
HTML Publishing Bible. Windows 95 Edition.
IDG Books Worldwide, Inc. 1996.

626. Smith RD, Benson ES, Anderson RE.
Some characteristics of the community practice of pathology in the United States.
Arch Pathol Lab Med. 1989;113:1335-1342.

627. The World Wide Web Consortium. Extensible Markup Language.
http://www.w3.org/xml/

628. Sokolowski R, Dudek J.
XML and its impact on content and structure in electronic health care documents.
Proc AMIA Symp 1999; :147-151.

629. Kahn CE Jr, de la Cruz NB.
Extensible markup language (XML) in health care: integration of structured reporting and decision support.
Proc AMIA Symp 1998, 725-729.

630. The HL7 Organization.
http://www.hl7.org/

631. Dolin RH, et al.
HL7 document patient record architecture: an XML document architecture based on a shared information model.
Proc AMIA Symp 1999; :52-56.

632. The World Wide Web Consortium.
XML Schema.
http://www.w3.org/XML/Schema.html

633. Health Level Seven. Draft HL7 Reference Information Model.
http://www.hl7.org/library/data-model/RIM/C30096/rim0096h.htm.

634. Carter KJ, et al.
Quality assurance in anatomic pathology: automated SNOMED coding.
J Am Med Informatics Assoc 1996;3:270-272, 1996.

635. Friedman C, Hripcsak GW.
Evaluating natural language processors in the clinical domain.
Meth Inform Med 1998;37:334-344.

636. The World Wide Web Consortium.
Extensible Markup Language.
http://www.w3.org/xml/

637. Sokolowski R, Dudek J.
XML and its impact on content and structure in electronic health care documents.
Proc AMIA Symp 1999, 147-151.

638. Friedman C, et al.
Representing information in patient reports using natural language processing and the Extensible Markup Language.
J Am Med Informatics Assoc 6:76-87, 1999.

639. Kahn CE Jr, de la Cruz NB.
Extensible markup language (XML) in health care: integration of structured reporting and decision support.
Proc AMIA Symp 1998, 725-729.

640. The HL7 Organization.
http://www.hl7.org/

641. Dolin RH, et al.
HL7 document patient record architecture: an XML document architecture based on a shared information model.
Proc AMIA Symp 1999, 52-56.

642. The World Wide Web Consortium.
XML Schema.
http://www.w3.org/XML/Schema.html

643. Health Level Seven.
Draft HL7 Reference Information Model.
http://www.hl7.org/library/data-model/RIM/C30096/rim0096h.htm

644. SQL Server Magazine, SQL Server Magazine: The XML files.
http://msdn.microsoft.com/library/default.asp?url=/library/en-us/dnsqlmag2k/html/TheXMLFiles.asp
2000;:.

645. Tang Z, Kim P.
Building Data Mining Solutions with SQL Server 2000.
DM Review, White Paper Library.
a href="http://www.dmreview.com/whitepaper/wid292.pdf"> http://www.dmreview.com/whitepaper/wid292.pdf 2001;:.

646. XML and Access2002, Exploring XML and Access 2002.
http://msdn.microsoft.com/library/default.asp?url=/library/en-us/dnacc2k2/html/odc_acxmllnk.asp
2001;:.

651. Freedman D, Pisani R, Purves R.
Statistics. Third Edition.
New York: W.W. Norton & Company. 1998.
ISBN 0-393-97083-3, 578 pages.

652. Livio M.
The Golden Ratio. The Story of Phi, the World's Most Astonishing Number.
New York: Broadway Books. 2003.
ISBN 0-7679-0816-3, 290 pages.

653. Huntley HE.
The Divine Proportion. A Study of Mathematical Beauty.
New York: Dover Publications, Inc. 1970.
ISBN 486-22254-3, 186 pages.

654. Brown D.
The Da Vinci Code.
New York: Doubleday. 2003.
ISBN 0-385-50420-9, 454 pages.
A best-seller murder mystery.
p. 91, ch 20. Nice discussion of the Golden Ratio (1.618....) and the Fibonacci Sequence. Repeats the legend that the ratio of the height to the umbilicus-to-ground-height of a beautiful woman is the Golden Ratio, phi.
p. 199, ch. 45. Mention of cryptographers Bruce Schneier and Philip K. Zimmerman.

655. Singh S.
Fermat's Enigma. The Epic Quest to solve the World's Greatest Mathematical Problem.
New York: Anchor Books. A Divsion of Random House, Inc. 1997.
ISBN 0-385-49362-2, 315 pages.
p. 62. "Cuius rei damonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet." Latin: I have a sanely miraculous demonstration of this thing, which the tightness of this margin of text might not capture."
p. 52. Photograph, Frontispiece of Claude Gaspar Bachet's French translation of Diophantus's Arithemetica (originally in Latin). Published 1621. Found in Fermat's literary estate.
"Diophanti Alexandrini Arithmeticorum Libri Sex. Et de Numeris Multangulis Liber Unus."
Latin: Six Books of Arithemetic by Diophantus of Alexandria. Book One of multangular numbers. Six books extant from a total of thirteen books. Other seven books lost in the tragic burning of the Library of Alexandria in 389 CE, by order of Emperor Theodosius, certainly one of the least distinguished Roman Emperors in an altogether very undistinguished line of rulers.

656. Bühler WK.
Gauss : A Biographical Study .
Berlin: Springer Verlag; ISBN: 0387106626. Hardcover (April, 1981) .

657. Croxton FE.
Elementary Statistics with Applications. in Medicine and the Biological Sciences.
New York: Dover Publications, Inc. 1953.

658. Murphy EA.
A Companion to Medical Statistics.
Baltimore: The Johns Hopkins University Press. 1985.

659. Edwards AL.
Statistical Analysis. Revised Edition.
New York: Rinehart & Company, Inc. 1946.

660. Afifi AA, Azen SP.
Statistical Analysis. A Computer Oriented Approach. Second Edition.
New York: Academic Press. 1979.

661. Lombard OM.
Biostatistics for the Health Professions.
New York: Appleton-Century-Crofts. 1975.

662. Hines WW, Montgomery DC.
Probability and Statistics. In Engineering and Management Science.
New York: The Ronald Press Company. 1972.
ISBN not stated, 509 pages.

663. Downing D, Clark J.
Statistics. The Easy Way.
New York: Barron's Educational Series, Inc. 1989.
ISBN 0-8120-4196-8, 330 pages.

664. Staff of Research and Education Association, Fogiel M, director.
The Statistics Problem Solver®. A Complete Solution Guide to Any Textbook.
Piscataway, NJ: Research and Education Association. 1994;:.
ISBN 0-87891-515-X, 1045 pages.

665. Mood AM, Graybill FA.
Introduction to the Theory of Statistics. Second Edition.
New York: McGraw-Hill Book Company. 1963.

666. Lilienfeld DE, Stolley PD.
Foundations of Epidemiology. Fifth Edition.
New York: Oxford University Press. 1994.

667. MacMahon B, Dimitrios T.
Epidemiology. Principles and Methods. Second Edition.
New York: Little, Brown and Co. 1996.

668. Barker DJP, Cooper C, Rose G.
Epidemiology in Medical Practice. Fifth Edition.
New York: Churchill Livingstone. 1998.

669. Gordis L.
Epidemiology.
Philadelphia: W. B. Saunders Co. 1996.

670. Farmer R, Miller D, Lawrenson R.
Lecture Notes on Epidemiology and Public Health Medicine. Fourth Edition.
Oxford: Blackwell Science. 1996.

671. Moore GW, Boitnott JK, Miller RE, Eggleston JC, Hutchins GM.
Integrated pathology reporting, indexing, and retrieval system using natural language diagnoses.
Mod Pathol. 1988 Jan;1(1):44-50.
PMID: 3070549; UI: 89184449.

672. Pascal B.
Traité du Triangle Arithmétique. 1653.
As cited in: Huntley HE. The Divine Proportion. A Study of Mathematical Beauty.
Discussion of Pascal's Triangle, first discovered by the 13th c. Chinese. chap 10, pp. 131-140.

673. Kendall MG.
Rank Correlation Methods. Third Edition.
New York: Hafner Publishing Co. 1962.
ISBN not stated, 199 pages.

674. Johnson RR.
Elementary Statistics. Second Edition.
North Scituate, MA: Duxbury Press. 1976;:.
ISBN 0-87872-102-9, 550 pages.

675. Bernstein PL.
Against the Gods. The Remarkable Story of Risk.
New York: John Wiley & Sons, Inc. 1996.
ISBN 0-471-29563-9, 383 pages.
A fantastic excursion through the history of probability and chance, starting with the ancient Egyptians and ending with modern worldwide business practices. Probability was originally studied in order to INCREASE BENEFITS, as in winning at gambling or staying alive longer. Now, probability has its most important applications

676. DeCew JW.
In Pursuit of Privacy. Law, Ethics, and the Rise of Technology.
Ithaca, NY: Cornell University Press. 1997.
ISBN 0-8014-3380-0, 199 pages.

677. Sandritter W.
Histopathologie. Lehrbuch und Atlas fuer Studierende und Aerzte. Sechste, verbesserte Auflage.
Stuttgart: F. K. Schattauer Verlag. 1975.
ISBN 3-7945-0454-2, 309 pages.

678. Asimov I.
Isaac Asimov: The Complete Stories.
New York: Doubleday.
ISBN 038541627X, pages.
Begins with a tale of time travel......

679. Sternberg SS, ed. Antonioli DA, Carter D, Eggleston JC, Mills SE, Oberman H, assoc eds.
Diagnostic Surgical Pathology.
New York: Raven Press. 1989;:.
ISBN 0-88167-442-7, 1776 pages, 2 vols.
Surgical pathology with a strong emphasis on diagnosis and differential diagnosis from clinical and morphologic findings. Rich in differential diagnosis tables and photographs.

680. Lever W, Schaumburg-Lever G.
Histopathology of the Skin. Seventh edition.
Philadelphia: J.B.Lippincott Company. 1990;:.
ISBN 0-397-50868-9, 940 pages.
The seventh edition is a vast improvement on previous editions, which lacked many diseases commonly seen in dermatopathologic practice. An eighth edition is now available.

681. Enzinger FM, Weiss SW.
Soft Tissue Tumors. Second Edition.
St Louis: C.V.Mosby Company. 1988;:.
ISBN 0-8016-1902-5, 989 pages.
The definitive text on soft tissue tumors.

682. Lemay L, Tyler D.
SAMS Teach Yourself Web Publishing with HTML4 in 21 Days.
Indianapolis, IN: SAMS. A division of Macmillan Computer Publishing. 1998;:.
ISBN 0-672-31345-6, 795 pages.

683. Owen DA, Kelly JK.
Atlas of Gastrointestinal Pathology.
Philadelphia: W.B.Saunders Company. A division of Harcourt Brace & Company. 1994;:.
ISBN 0-7216-6730-9, 258 pages.

684. Percy C, Van Holten V, Muir C.
International Classification of Diseases for Oncology. Second Edition.
Geneva: World Health Organization. 1990;:.
ISBN 92-4-154414-7, 144 pages.

685. Rothwell DJ, Coté RA, Brochu L.
The systematized Nomenclature of Human and Veterinary Medicine. SNOMED International. Microglossary for Pathology.
Northfield, IL: College of American Pathologists. 1993;:.
ISBN not stated, 475 pages.
"Arguments for not making the switch to SNOMED International are principally familiarity with the old system and the cost of conversion. Although many of the current systems have been extended and modified to meet individual user needs, they lack the standardization and depth of SNOMED and are unsuitable for data exchange between individual institutions or individual units.
"Specific guidelines must be established by each institution to define how an entity with more than one possible SNOMED code will be coded.... The recommendation is to establish a convention for your own institution and adhere to it." p. 8.
GWM's note: This is a remarkable statement, considering that SNOMED is first recommended for inter-institutional data exchange, and then each institution is advised to use its own local standards for coding!!

686. von Neumann J.
The Computer and the Brain.
New Haven: Yale University Press. 1958;:.
ISBN not stated, 82 pages.

687. Zalman JF.
Biostatistics. Experimental Design and Statistical Inference.
New York: Oxford University Press. 1993;:.
ISBN 0-19-507810-1, 343 pages.

688. Walker EA.
Introduction to Abstract Algebra.
New York: Random House. The Random House/Birkhaeuser Mathematics Series. 1987;:.
ISBN 0-394-35611-X, 355 pages.

689. Collins KA, Hutchins GM, eds. Tursky CL, CAP editor and designer.
Autopsy Performance & Reporting. Second Edition.
Northfield, IL: College of American Pathologists (CAP). 2003:;.
ISBN 0-930304-78-0, 397 pages.

690. Hutchins GM, Berman JJ, Moore GW, Hanzlick RL, Collins KA, Members of the Autopsy Committee of the College of American Pathologists.
Autopsy Reporting. Chapter 28.
in: Collins KA, Hutchins GM, eds. Tursky CL, CAP editor and designer. Autopsy Performance & Reporting. Second Edition.
Northfield, IL: College of American Pathologists (CAP). 2003:;265-274.
ISBN 0-930304-78-0, 397 pages.

691. Moore GW.
Computer-based Indexing. Chapter 32.
in: Collins KA, Hutchins GM, eds. Tursky CL, CAP editor and designer. Autopsy Performance & Reporting. Second Edition.
Northfield, IL: College of American Pathologists (CAP). 2003:;313-323.
ISBN 0-930304-78-0, 397 pages.

692. McWhirter ND, McWhirter AR.
Guinness Book of World Records.
Toronto: Bantam Books. 1984;:.
ISBN 0-533-23900-2, 702 pages.

693. Arabie P, Carroll JD, DeSarbo WS.
Three-way scaling and clustering. Quantitative Applications in the Social Sciences.
A Sage University Paper. 07-065. Newbury Park, CA: Sage Publications. 1987;:.
ISBN 0-8039-3068-2, 92 pages.

694. Kleene SC.
Mathematical Logic.
Mineola, NY: Dover Publications, Inc. 1967;:.
ISBN 0-486-42533-9, 398 pages.

695. Kirsten W, Klar R, eds.
Dokumentation und Informationsaufbereitung für den Arzt. Beiträge zur Medizinischen Informatik der Wolfgang Giere.
Darmstadt: epsilon Verlag. 1996;:.
ISBN 3-9803214-7-9, 437 pages.

696. Moore GW, Wakai I, Satomura Y, Giere W.
TRANSOFT: Medical translation expert system.
In: Kirsten W, Klar R, eds. Dokumentation und Informationsaufbereitung für den Arzt. Beiträge zur Medizinischen Informatik der Wolfgang Giere. Darmstadt: epsilon Verlag. 1996;:.
ISBN 3-9803214-7-9, 437 pages. pp. 161-178.
Reprinted from: Artificial Intelligence in Medicine 1989;1:

697. Giere W, Wakai I.
Transpro: natural language to Prolog translation.
In: Kirsten W, Klar R, eds. Dokumentation und Informationsaufbereitung für den Arzt. Beiträge zur Medizinischen Informatik der Wolfgang Giere. Darmstadt: epsilon Verlag. 1996;:.
ISBN 3-9803214-7-9, 437 pages. pp. 179-
Reprinted from: Artificial Intelligence in Medicine 1991;3:

698. Angermeyer J, Fahringer R, Jaeger K, Shafer D, The Waite Group.
Tricks of the MS-DOS® Masters.
Indianapolis, IN: Howard W. Sams & Company. 1987;:.
ISBN 0-672-22525-5, 542 pages.

699. Lewkowicz J.
The Complete MUMPS. An Introduction and Reference Manual for the MUMPS Programming Language.
Englewood Cliffs, NJ: Prentice Hall. 1989;:.
ISBN 0-13-162125-4, 404 pages.

700. Hayslett HT jr.
Statistics Made Simple.
New York: Doubleday. 1968;:.
ISBN 0-385-02355-3, 192 pages.

701. Mendenhall W, Ott L.
Understanding Statistics. Second Edition.
Belmont, CA: Duxbury Press. A Division of Wadsworth Publishing Company. 1976;:.
ISBN 0-87872-101-0, 387 pages.

702. Noether GE.
Introduction to Statistics. A Nonparametric Approach. Second Edition.
Boston, MA: Houghton Mifflin Company. 1976;:.
ISBN 0-395-18578-5, 292 pages.

703. Hill B.
Principles of Medical Statistics. Fifth Edition.
New York: Oxford University Press. 1952;:.
ISBN not stated, 282 pages.

704. Arkin H, Colton RR.
Statistical Methods. With Lists of Formulae and Symbols; Tables.
New York: Barnes & Noble Books. A Division of Harper & Row, Publishers. 1970;:.
ISBN 389-00119-8, 344 pages.

705. Steen LA, ed.
Mathematics Today. Twelve Informal Essays.
New York: Springer Verlag. 1978;:.
ISBN 0-387-90305-4, 367 pages.

706. Valenstein PN, Wang E, O'Donohue T.
Productivity of Veterans Health Administration Laboratories. A College of American Pathologists Laboratory Management Index Program (LMIP) Study.
Arch Pathol Lab Med 2003;127:1557-1564.

707. Vestal KW, Fralicx RD, Spreier SW.
Organizational Culture: the critical line between strategy and results.
Hosp Health Serv Adm. 1997;42:339-365.

708. College of American Pathologists.
Laboratory Management Index Program Users Manual.
Northfield, IL: College of American Pathologists. 2002;:.

709. Mann HB, Whitney DR.
On a test of whether one of two random variables is stochastically larger than the other.
Ann Math Stat. 1947;18:50-60.

710. Kazis LE, Miller DR, Clak J, et al.
Health-related quality of life in patients served by the Department of Veterans Affairs: results from the Veterans Health Study.
Arch Intern Med. 1998;158:626-632.

711. Valenstein P, Praestgaard A, Lepoff R.
Six-year trends in productivity and utilization of 73 clinical laboratories.
Arch Pathol Lab Med. 2001;125:1153-1161.

712. Portugal B.
Benchmarking hospital laboratory financial performance.
Hosp Technol Serv. 1993;12:1-21.

713. Weir CR, Hurdle JF, Felgar MA, Hoffman JM, Roth B, Nebeker JR.
Direct text entry in electronic progress notes. An evaluation of input errors.
Methods Inf Med. 2003;42(1):61-7.
PMID: 12695797

714. Glassman PA, Simon B, Belperio P, Lanto A.
Improving recognition of drug interactions: benefits and barriers to using automated drug alerts.
Med Care. 2002 Dec;40(12):1161-1171.
PMID: 12458299

715. Brown SH, Hardenbrook S, Herrick L, St Onge J, Bailey K, Elkin PL.
Usability evaluation of the progress note construction set.
Proc AMIA Symp. 2001;:76-80.
PMID: 11825158

716. Murff HJ, Kannry J.
Physician satisfaction with two order entry systems.
J Am Med Inform Assoc. 2001 Sep-Oct;8(5):499-509.
PMID: 11522770

717. Weir CR, Crockett R, Gohlinghorst S, McCarthy C.
Does user satisfaction relate to adoption behavior?: an exploratory analysis using CPRS implementation.
Proc AMIA Symp. 2000;:913-917.
PMID: 11080017

718. Weir C, McCarthy C, Gohlinghorst S, Crockett R.
Assessing the implementation process.
Proc AMIA Symp. 2000;:908-912.
PMID: 11080016

719. Lovis C, Payne TH.
Extending the VA CPRS electronic patient record order entry system using natural language processing techniques.
Proc AMIA Symp. 2000;:517-521.
PMID: 11079937

720. Brown SH.
No free lunch: institutional preparations for computer-based patient records.
Proc AMIA Symp. 1999;:486-90.
PMID: 10566406

721. Meldrum K, Volpp B, Vertigan R.
Department of Veterans Affairs' Computerized Patient Record System.
Proc AMIA Annu Fall Symp. 1999;(1-2):1214.
PMID: 10558831

722. Payne TH, Savarino J.
Development of a clinical event monitor for use with the Veterans Affairs Computerized Patient Record System and other data sources.
Proc AMIA Symp. 1998;:145-149.
PMID: 9929199

723. Bulmer MG.
Principles of Statistics. Second Edition.
New York: Dover Publications, Inc. 1979;:.
ISBN 0-486-63760-3, 252 pages.

724. Boolos G.
The unprovability of consistency. An essay in modal logic.
Cambridge: Cambridge University Press. 1979;:.
ISBN 0-521-21879-9, 184 pages.

725. Aldenderfer MS, Blashfield RK.
Cluster Analysis.
A Sage University Paper. 07-044. Newbury Park, CA: Sage Publications. 1984;:.
ISBN 0-8039-2376-7, 87 pages.

726. Freund J.
Introduction to Probability.
New York: Dover Publications, Inc. 1973;:.
ISBN 0-486-67549-1, 247 pages.

727. Suppes P.
Axiomatic Set Theory.
New York: Dover Publications, Inc. 1972;:.
ISBN 0-486-61630-4, 267 pages.

728. Ball WWR.
A Short Account of the History of Mathematics.
New York: Dover Publications, Inc. 1960;:.
ISBN 0-486-20630-0, 522 pages.

729. Murphy EA.
A Companion to Medical Statistics.
Baltimore: The Johns Hopkins University Press. 1985;:.
ISBN 0-8018-2612-8, 303 pages.

730. Reith EJ, Ross MH.
Atlas of Descriptive Histology. Second Edition.
New York: Harper & Row, Publishers. 1970;:.
ISBN not stated, 243 pages.

731. Arbib MA, Manes EG.
Arrows, Structures, and Functors. The Categorical Imperative.
New York: Academic Press, Inc. A Subsidiary of Harcourt Brace Jovanovich, Publishers. 1975;:.
ISBN 0-12-059060-3, 185 pages.

732. Kemeny JG, Snell LJ, Thompson GL.
Introduction to Finite Mathematics. Second Edition.
Englewood Cliffs, NJ: Prentice-Hall, Inc. 1966;:.
ISBN not stated, 465 pages.

733. Aho AH, Hopcroft JE, Ullman JD.
The Design and Analysis of Computer Algorithms.
Reading, MA: Addison-Wesley Publishing Company. 1974;:.
ISBN not stated, 470 pages.
Chapter 10. NP-Complete Problems. pp. 364-404.

734. Minsky M.
Computation: Finite and Infinite Machines.
Englewood Cliffs, NJ: Prentice-Hall, Inc. 1967;:.
ISBN not stated, 317 pages.

735. McCorduck P.
Machines Who Think. A Personal Inquiry into the History and Prospects of Artificial Intelligence.
New York: W. H. Freeman and Company. 1979;:.
ISBN 0-7167-1135-4, 375 pages.

736. Bernays P.
Axiomatic Set Theory.
New York: Dover Publications, Inc. 1968;:.
ISBN 0-486-66637-9, 227 pages.

737. Brewka G, Dix J, Konolige K.
Nonmonotonic Reasoning. An Overview. CSLI Lecture Notes 73.
Stanford, CA: Center for the Study of Language and Information. 1997;:.
ISBN 1-8881526-83-6, 179 pages.

738. Harrison JH, Stewart J.
Training in pathology informatics: implementation at the University of Pittsburgh.
Arch Pathol Lab Med 2003;127:1019-1025.

739. Harrison JH.
Pathology Informatics Questions and Answers from the University of Pittsburgh Pathology Residency Informatics Rotation.
Arch Pathol Lab Med 2004;128:71-83.

752. Langman J.
Medical Embryology. Human Development--Normal and Abnormal.
Baltimore: Williams & Wilkins. 1969;:.
ISBN not stated, 386 pages.

753. Sternberg SS, ed.
Histology for Pathologists.
New York: Raven Press. 1992;:.
ISBN 0-88167-621-7, 977 pages.

754. Moore GW, Berman JJ.
Anatomic Pathology Data Mining.
In: Cios KJ, ed. Medical Data Mining and Knowledge Discovery.
2001. XVIII, 502 pp. 98 figs., 98 tabs. Hardcover.
ISBN: 3-7908-1340-0.
Copyright Springer-Verlag: Berlin/Heidelberg 1999.
http://www.netautopsy.org/apdmchap.htm

755. Berman JJ.
Tumor classification: molecular analysis meets Aristotle.
BMC Cancer. 2004 Mar 17;4:10.
PMID: 15113444
PubMed Entry
Aristotle (384-322 BCE), Greek philosopher.
This article is among the all-time most-viewed articles in BMC Cancer, and, as of September 2008, has been downloaded about 15,000 times from BiomedCentral.

756. Berman JJ.
Tumor taxonomy for the developmental lineage classification of neoplasms.
BMC Cancer. 2004 Nov 30;4(1):88.

757. Berman JJ.
Modern classification of neoplasms: reconciling differences between morphologic and molecular approaches.
BMC Cancer 2005, 5:100.

758. Berman JJ.
Developmental Lineage Classification and Taxonomy of Neoplasms.
http://www.julesberman.info/devclass.htm

759. Berman JJ.
Doublet method for very fast autocoding.
BMC Med Inform Decis Mak. 2004 Sep 15;4:16.
PMID: 15369595
PubMed Entry

760. Berman JJ.
Resource page.
http://www.julesberman.info/resource.htm

761. Berman JJ.
Implementing an RDF schema for pathology images.
http://www.julesberman.info/spec2img.htm

762. Berman JJ.
Chronology of Earth.
http://www.julesberman.info/chronos.htm

763. Berman JJ.
Biomedical Informatics (Paperback)
Publisher: Jones & Bartlett Publishers; 1 edition (October 18, 2006)
ISBN-10: 0763741353, 459 pages.
ISBN-13: 978-0763741358, 459 pages.

764. Berman JJ.
Perl Programming for Medicine and Biology (Series in Biomedical Informatics).
Publisher: Jones & Bartlett Publishers; 1 edition (April 6, 2007)
ISBN-10: 076374333X, 407 pages.
ISBN-13: 978-0763743338, 407 pages.

765. Berman JJ.
Perl: The Programming Language.
Publisher: Jones & Bartlett Publishers. 2009;:.
ISBN: 9780763757588, 52 pages.

766. Berman JJ.
Ruby Programming for Medicine and Biology (Jones and Bartlett Series in Biomedical Informatics).
Publisher: Jones & Bartlett Pub; 1 edition (September 13, 2007)
ISBN-10: 0763750905, 378 pages.
ISBN-13: 978-0763750909, 378 pages.

767. Berman JJ.
Ruby: The Programming Language.
Publisher: Jones & Bartlett Publishers. 2009;:.
ISBN: 9780763757571, 46 pages.

768. Berman JJ.
Neoplasms: Principles of Development and Diversity.
Publisher: Jones & Bartlett Publishers. 2008 Oct 1.
ISBN: 9780763755706, 464 pages.

"Dr. Berman's book, "Neoplasms: Principles of Development and Diversity," has been published, and is available from the Publisher's web site.

http://www.jbpub.com/catalog/9780763755706/

"This book is the first "post-informatics" pathology textbook. The book owes its existence to pre-existing tools that were developed in the early years of pathology informatics (databases, nomenclatures, ontologies, public data resources, particularly PubMed and SEER, LISs, and so on). It uses these informatics resources to ask (and answer) a wide variety of questions about tumor biology, that could not have been answered if these resources were not in place. This is strictly analogous to the use of "genomic" and "post-genomic" to describe the era when alignment, sequencing, mapping, and and analytic tools were developed and the human genome was sequenced (i.e., the genomic age); and the era when these tools and data are put to use to understand the development of organisms in health and disease (i.e., the post-genomic age). No other textbook has been written that tackles common problems in pathology (such as the causes and developmental steps leading to the comprehensive collection of the clinically encountered morphologic types of tumors) with common informatics methods.

"The two fundamental questions discussed in Neoplasms are:

"1. Is cancer a single disease process that is manifested in many different types of tumors, or is cancer many different diseases, all related by excessive cell growth? If all cancer can be characterized by a single disease process, why haven't we isolated the process and cured cancer? If cancer is thousands of different diseases, how can we ever hope to cure all of the different kinds of cancer?

"2. If cancer is characterized by the progressive accumulation of genetic abnormalities, and if every tumor specimen is genetically unique and distinct from every other tumor specimen, why do tumors fit into precisely named types? Worded another way, why does every unique tumor fall into one of the diagnostic entities (e.g., Warthin tumor, melanoma, lobular carcinoma of breast, and so on) that pathologists are taught to recognize?

"Believe it or not, by thinking deeply about these two questions, it is possible to develop a practical strategy to eradicate cancer. Though there are thousands of distinct named neoplasms, all neoplasms can be sensibly grouped into biological classes, and these biological classes can be characterized by shared developmental pathways (including precancer/cancer transitions), shared functional pathways (including genetic and epigenetic features), and shared restraints (determined by the cell lineage of the neoplasm).

"The book is divided into three major parts. The first part, Speciation, covers the causes of cancer, and why we see the kinds of restricted cancers that occur in man and animals. The concept of tumor speciation is key to building a classification of cancer, and it has been a constant wonder to the author that the people who write cancer textbooks always accept the extant species of cancer as a "given" condition that does not require any deep thought or explanation. It is very important to understand why we see the species of tumors that we see. We cannot start thinking about how to classify cancers until we understand tumor speciation. The lack of any serious attention to the subject manifests itself in the popular classifications of cancer, which are basically just lists of tumors that occur in an anatomic region (e.g. tumors of head and neck).

"The second part of the book is Classification. This section describes the different ways that cancers can be classified. To write this section, I used a variety of informatics methods to build a classification of neoplasms. The classification can be downloaded by readers as an ontology (in RDF format), or as a plain-text file, or as an XML file. The supplementary materials are available at the following web site:

http://www.julesberman.info/devclass.htm

"None of this effort (i.e., understanding tumor speciation and constructing a neoplasm classification) has any value if it does not lead to the reduction of deaths from cancer. The last part of the book explains how a biologically relevant classification reduces the perceived complexity of cancer by assigning each tumor to one of several dozen classes of tumors that may be amenable to class-specific prevention, diagnosis, and treatment. This is the most important part of the book, because it suggests practical ways of eradicating cancer by applying pre-existing approaches (designed for individual cancers) to classes of cancer, using an available neoplasm classification.

"This book should have particular appeal to pathology informaticians, because it builds upon expertise in pathology and informatics that many specialists already possess. Even if you disagree with the observations and conclusions offered in the book, you will still benefit from the exercise. You will see how fundamental questions in biomedicine can now be approached using concepts taken from pathology informatics."

Web site: http://www.julesberman.info/

Blog site: http://julesberman.blogspot.com/

769. Asimov I.
Asimov's Chronology of Science and Discovery: Updated and Illustrated.
New York: Harper Collins. 1994;:.
New York: Harper Collins. 1994 Oct 7;:.
ISBN-10: 0062701134, 791 pages.
ISBN-13: 978-0062701138, 791 pages.

770. Longworth AR.
Alice Roosevelt Longworth Quotes. (American author and humorist, 1884-1865). The Quotations Page.
Granddaugher of twenth-sixty U. S. President (1901-1909) Theodore Roosevelt (1858-1919), and controversial Washington, DC, socialite.
"If you can't say anything good about someone, sit right here by me."
http://www.quotationspage.com/quotes/Alice_Roosevelt_Longworth/

771. Philosopher's stone (Latin: lapis philosophorum).
Legendary substance, supposedly capable of turning inexpensive metals into gold.
http://en.wikipedia.org/wiki/Philosopher's_stone

772. Presburger M.
Presburger arithmetic.
First-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who published it in 1929. It is not as powerful as Peano arithmetic because it omits multiplication.
http://en.wikipedia.org/wiki/Presburger_arithmetic

780. Moore GW.
Curriculum Vitae
http://www.medparse.com/gwmcv.htm

781. Moore GW, Hutchins GM, Berman JJ.
Object oriented programming system for autopsy retrieval. (Abstract)
Mod Pathol 5:100A, 1992; Lab Invest 66:100A, 1992.

782. Moore GW, Berman JJ, Sydnor DL.
Fractal dimension for pathology images, a repeatable and quantitative measurement of nuclear rim irregularity. (Abstract).
Am J Clin Pathol. 1994;102:538.
http://www.netautopsy.org/ascpfrac.htm

783. Moore GW, Berman JJ, Moore GW, Brown LA.
Software for image segmentation and analysis in pathology (ISAP): public domain image software and source code developed at the Baltimore VA Medical Center. (Abstract).
Am J Clin Pathol. 1994;102:538-539.
http://www.netautopsy.org/ascpisap.htm

784. Moore GW, Berman JJ, Sydnor DL.
Automated edge detection in image analysis: distinguishing the nucleus from the cytoplasm without a user's threshold estimate. (Abstract).
Am J Clin Pathol. 1994;102:539.
http://www.netautopsy.org/ascpedge.htm

785. Berman JJ, Moore GW, Donnelly WH, Massey JK, Craig B.
SNOMED analysis of 40,124 surgical pathology cases. (Abstract).
Am J Clin Pathol. 1994; 102:539-540.

786. Moore GW, Berman JJ, Sydnor DL.
Fractal Dimension for Pathology Images, a Repeatable and Quantitative Measurement of Nuclear Rim Irregularity. (Abstract).
Am J Clin Pathol. 1994;102:538.
http://www.netautopsy.org/ascpfrac.htm

787. Moore GW, Berman JJ, Moore GW, Brown LA.
Software for Image Segmentation and Analysis in Pathology (ISAP) (Abstract.)
Am J Clin Pathol. 1994; 102:538-539.
http://www.netautopsy.org/ascpisap.htm

788. Moore GW, Berman JJ, Sydnor, DL.
Automated Edge Detection in Image Analysis: Distinguishing the Nucleus from the Cytoplasm Without a User's Threshold Estimate. (Abstract.)
Am J Clin Pathol. 1994;102:539.
http://www.netautopsy.org/ascpedge.htm

789. Moore GW, Brenner DS, Berman JJ.
Automatic Indexing of a Pathology Image Archive using UMLS. (Abstract).
Arch Pathol Lab Med. 2000 Jun;124:809.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_1.html
http://www.netautopsy.org/apep99im.htm

790. Kao GF, Moore GW.
Dermatopathology False Negative Terms in UMLS. (Abstract).
Arch Pathol Lab Med. 2000 Jun;124:809.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_2.html
http://www.netautopsy.org/apep99dr.htm

791. Baumann RP, Moore GW.
Evaluation of 530,000 Siagnoses Encoded in SNOMED II.
Arch Pathol Lab Med. 2000 Jun;124:809.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_3.html

792. Nonaka D, Moore GW, Satomura Y.
Japanese Language Annotation of an Internet Pathology Image Archive. (Abstract).
Arch Pathol Lab Med. 2000 Jun;124:820.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_4.html
http://www.netautopsy.org/apep99jp.htm

793. Moore GW, Erozan YS, Vardar E.
Turkish Language Annotation of an Internet Pathology Image Archive. (Abstract).
Arch Pathol Lab Med. 2000 Jun;124:820.
http://apiii.upmc.edu/abstracts/posterarchive/1999/moore_5.html
http://www.netautopsy.org/apep99tk.htm

794. Moore GW, Brown LA, Miller RE.
Set Theory Definition and Algorithm for Medical De-Identification. (Abstract).
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_2.html
http://www.netautopsy.org/apep00st.htm
Comment: This Kosher Kitchen Principle (כשר) for Medical De-identification might be summarized as follows: The patient should not be able to recognize his/her own medical record on the internet, and thus be embarrassed or otherwise injured by this recognition. This is a very ancient sensibility, and should not be ignored. The prohibition in Jewish kosher laws against mixing meat and dairy is based upon the sensibility of a mother goat's milk comixing with the flesh of its offspring: "Thou shalt not seethe a kid in his mother's milk" (Exodus 23:19). Two mechanisms against violating this sensibility are either to obliterate any distinctive (i.e., unique, or involving only a few patients) part of a report; or to create model (fictitious) reports.

795. Miller RE, Boitnott JK, Moore GW.
Web-based Free-Text Query System for Surgical Pathology Reports with Automatic Case De-Identification. (Abstract).
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_5.html
http://www.netautopsy.org/apep00wb.htm

796. Sinard JH, Moore GW.
UMLS Concordance for a Comprehensive Pathology Text.
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_4.html
http://www.netautopsy.org/apep00cn.htm

797. Moore GW, Miller RE.
Linguistic Inventory of the Johns Hopkins Surgical Pathology Database. (Abstract).
Arch Pathol Lab Med. 2001 Jun;125:.
http://apiii.upmc.edu/abstracts/posterarchive/2000/moore_1.html
http://www.netautopsy.org/apep00li.htm

798. Moore GW, Brown LA, Miller RE.
Goedelization of a Pathology Database: Re-identification by Inference. (Abstract).
Arch Pathol Lab Med. 2002 Jun;126:.
http://apiii.upmc.edu/abstracts/posterarchive/2001/moore.html
http://www.netautopsy.org/apep01go.htm

799. Giere W, Moore GW.
Goethe University Autopsy Register: Anonymized Bilingual Database. (Abstract).
Arch Pathol Lab Med. 2002 Jun;126:.
http://apiii.upmc.edu/abstracts/posterarchive/2001/giere.html
http://www.netautopsy.org/apep01gu.htm

800. Moore GW, Brown LA, Burger RH, Hutchins GM, Miller RE.
Modal Logic Theory for Pathology Inference. (Abstract).
Arch Pathol Lab Med. 2004 Jun;128:.
http://apiii.upmc.edu/abstracts/posterarchive/2003/moore.html
http://www.netautopsy.org/modlthry.htm

801. Moore GW, Brown LA, Burger RH, Kao GF, Hutchins GM, Miller RE.
Spreadsheet Order Logic for Pathology Inference. (Abstract).
Arch Pathol Lab Med. 2005 Jun;129:.
http://apiii.upmc.edu/abstracts/display.cfm?id=262
http://www.netautopsy.org/ordrlogc.htm

802. Moore GW, Struble RA, Brown LA, Kao GF, Hutchins GM.
Infinite Papilloma: Model for Unbounded Tumor Growth. (Abstract).
Arch Pathol Lab Med. 2006 Jun;130:898.
http://apiii.upmc.edu/abstracts/posterarchive/2005/moore.html
http://www.netautopsy.org/infnpapl.htm

803. Moore GW, Struble RA, Brown LA, Kao GF, Hutchins GM.
Cell Surface Tessellation: Model for Malignant Growth. (Abstract).
Arch Pathol Lab Med. 2007 Jun;131:.
http://apiii.upmc.edu/abstracts/posterarchive/2006/eposter/moore.html
http://www.netautopsy.org/celltess.htm

804. Moore GW, Struble RA, Brown LA, Kao GF, Hutchins GM.
Triple-spiked Zones in Cell Surface Tessellations: Model for Malignant Growth. (Abstract).
Arch Pathol Lab Med. 2008 Jun;132:. in press.
Scientific Presentation. September 10, 2007.
Advancing Practice, Instruction and Innovation through Informatics.
Pittsburgh Marriott City Center, Pittsburgh, PA
http://apiii.upmc.edu/abstracts/display_07.cfm?id=376
http://www.netautopsy.org/triplspk.htm

805. Moore GW, Kao GF, Brown LA.
Resource Description Framework for Mucosal Surface Pathology. (Abstract).
Arch Pathol Lab Med. 2008 Jun;132: in press.
Scientific Presentation. September 10, 2007.
Advancing Practice, Instruction and Innovation through Informatics.
Pittsburgh Marriott City Center, Pittsburgh, PA
http://apiii.upmc.edu/abstracts/display_07.cfm?id=324
http://www.netautopsy.org/mucordfh.htm

806. Moore GW.
Book Review: Amos M. Genesis Machines.

807. Moore GW.
Book Review: The Black Swan.

808. Moore GW.
Book Review:

809. Moore GW.
Book Review:

810. Moore GW.
Medical Etymology.
http://www.netautopsy.org/medetymo.htm

811. Moore GW.
Book Review: Seife C.
Zero. The Biography of a Dangerous Idea.
London: Penguin Books. 2000.
ISBN: 0-670-88457-X, 248 pages.
Reviewed in: Neurocomputing. 2001 Jan;42(1):335.

812. Moore GW.
Book Review: Stewart I.
Flatterland. Like Flatland. Only More So.
Cambridge, MA: Perseus Publishing. 2001.
ISBN 0-7382-0442-0, 301 pages.
Reviewed in: Neurocomputing. 2001 Jan;42(1):337.
http://www.netautopsy.org/rvflatte.htm

813. Moore GW.
Book Review: Casti JL, DePauli W.
Gödel. A Life of Logic.
Cambridge, MA: Perseus Publishing. 2000.
ISBN 0-7382-0274-6, 210 pages.
Reviewed in: Neurocomputing. 2001 Jan;42(1):331.
http://www.netautopsy.org/rvgodell.htm

814. Moore GW.
Book Review: Aleksandr I, Morton H.
An Introduction to Neural Computing. Second Edition.
London: International Thomson Computer Press. 1995.
ISBN 1-85032-167-1, 284 pages.
Reviewed in: Neurocomputing. 2001;:. 2001 Jan;42(1):337.
http://www.netautopsy.org/rvneuroc.htm

815. Moore GW.
Book Review: Scarborough D, Sternberg S.
Methods, Models, and Conceptual Issues. An Invitation to Cognitive Science. Volume 4.
Cambridge, MA: MIT Press. 1998.
ISBN 0-262-65946-0, 950 pages.
Reviewed in: Neurocomputing. 2001;:.
http://www.netautopsy.org/rvcognis.htm

816. Moore GW.
Book Review: Changeux J-P, Connes A.
Conversations on Mind, Matter, and Mathematics
Ed & Transl: DeBevoise MB. Princeton, NJ: Princeton University Press. 1995.
ISBN 0-691-08759-8, 260 pages.
Reviewed in: Neurocomputing. 2001;:.

817. Moore GW.
Book Review: Steen, LA (ed.).
Mathematics Today: Twelve Informal Essays. Springer Verlag, 1979,
Reviewed in: Metamedicine 1:123, 1980.

818. Yu CC-Y, Moore GW, Unschuld PU.
Romanized Chinese respelling rules for an English medical word list.
Proc Annu Symp Comput Appl Med Care. 1987;11:. Washington DC, November 1-4, 1987.

819. Moore GW, Hutchins GM, Boitnott JK, Miller RE, Polacsek RA.
Word root translation of 45,564 autopsy reports into MeSH titles.
Proc Annu Symp Comput Appl Med Care. 1987;11:. Washington DC, November 1-4, 1987.

820. Moore GW, Miller RE, Hutchins GM.
Indexing by MeSH titles of natural language pathology phrases identified on first encounter using the barrier word method.
In, Scherrer JR, Côté RA, and Mandil SH, eds., Computerized Natural Medical Language Processing for Knowledge Representation. North-Holland, Amsterdam, 1989.

821. Tersmette KWF, Scott AF, Moore GW, Matheson NW, Miller RE.
Barrier word method for detecting molecular biology multiple word terms.
Proc Annu Symp Comput Appl Med Care. 1988;12:207-211. Washington DC, November 6-9, 1988.

822. Moore GW, Wilcock RA, Miller RE. TRANSOFT: MUMPS-based polyglot medical translator.
15th MUG-Japan, Nagoya, December 9-11, 1988.

823. Moore GW, Wilcock RA, Miller RE.
TRANSOFT: MUMPS-based polyglot medical translator.
Joint Conference on Medical informatics, Tokyo, Japan, December 14-15, 1988.

824. Moore GW.
Medical Expert System User Interface.
Artif Intell Med. 1991:15;.

825. Sorace JM, Berman JJ, Carnahan GE, Moore GW.
PRELOG: precedence logic inference software for blood donor deferral.
Proc Annu Symp Comput Appl Med Care. 1991;:976-977.
PMID: 1807774; UI: 92223911.
PubMed Entry

826. Berman JJ, Moore GW.
Object-oriented controlled-vocabulary translator using TRANSOFT + HyperPAD.
Proc Annu Symp Comput Appl Med Care. 1991;15:973-975.
PMID: 1807773; UI: 92223910.
PubMed Entry

827. Moore GW, Hutchins GM, Berman JJ.
Object-oriented retrieval system for the Johns Hopkins autopsy database.
MedInfo-92, Lun KC, Degoulet P, Piemme TW, Rienhoff, eds.
Amsterdam, NL: Elsevier, p. 1613.

828. Moore GW, Berman JJ.
Automatic SNOMED coding.
Proc Annu Symp Comput Appl Med Care. 1994;18:225-229.
PMID: 7949924; UI: 95037244.
PubMed Entry
Full Text of Article
http://www.netautopsy.org/autocode.htm

829. Berman JJ, Moore GW, Donnelly WH, Massey JK, Craig B.
A SNOMED analysis of three years accessioned cases (40,124) of a surgical pathology department: implications for pathology-based demographic studies.
J Amer Med Informatics Assn (JAMIA), Symposium Supplement, 1994, and Proceedings of the 18th Annual Symposium on Computer Applications in Medical Care 18:188-192, 1994.

830. Moore GW, Berman JJ, Hanzlick RL, Buchino JJ, Hutchins GM.
A prototype internet autopsy database: 1625 consecutive fetal and neonatal autopsy facesheets spanning twenty years.
Exhibit at College of American Pathologists (CAP) Conference on Restructuring Autopsy Practice for Health Care Reform, May 25-26, 1995, Washington, DC, Willard Inter-Continental Hotel.
Full Text of Article:
http://www.netautopsy.org/protoiad.htm

831. Berman JJ, Moore GW, Donnelly WH, Massey JK, Craig B.
A SNOMED analysis of three years' accessioned cases (40,124) of a surgical pathology department: implications for pathology-based demographic studies.
JAMIA (Suppl). 1994;:188-192.
Proc Annu Symp Comput Appl Med Care. 1994;:188-192.
PMID: 7949917.
PubMed Entry

832. Berman JJ, Moore GW, Hutchins GM.
Maintaining patient confidentiality in the public domain Internet Autopsy Database (IAD).
JAMIA (Suppl). 1996;20:328-332.
Proc AMIA Annu Fall Symp. 1996;20:328-332.
PMID: 8947682.
PubMed Entry
Full Text of Article:
http://www.netautopsy.org/confiden.htm

833. Berman JJ, Moore GW, Hutchins GM.
Internet autopsy database.
Hum Pathol. 1997 Apr;28(4):393-394.
PMID: 9104935.
PubMed Entry
Full Text of Article:
http://www.netautopsy.org/consent.htm

834. Moore GW, Berman JJ.
Automatic SNOMED Coding.
Journal of the American Medical Informatics Association (JAMIA), Symposium Supplement 1994 and the Proceedings of the 18th Annual Symposium for Computer Appllications in Medicine (SCAMC), pp 225-229, 1994

835. Moore GW, Berman JJ, Hanzlick RL, Buchino JJ, Hutchins GM.
A prototype national autopsy databank: 1,625 consecutive fetal and neonatal autopsy facesheets spanning twenty years.
Conference on Restructuring Autopsy Practice for Health Care Reform, May 25-26, 1995. Willard Inter-Continental Hotel, Washington, D.C.
Full Text of Article:
http://www.netautopsy.org/protoiad.htm

836. Moore GW, Hutchins GM.
The persistent importance of autopsies.
Mayo Clin Proc. 2000 Jun;75(6):557-558.

837. Moore GW, Berman JJ.
Anatomic Pathology Data Mining.
Chapter 4. In: Cios KJ. Medical Data Mining and Knowledge Discovery. Berlin: Springer Verlag. 2000;4:61-107.
ISBN: 3-7908-1340-0, 502 pages.
Published within the series: "Studies in Fuzziness and Soft Computing", Physica-Verlag Heidelberg, a Springer-Verlag Company.
http://www.netautopsy.org/apdmchap.htm

838. Cios KJ, Moore GW.
Medical Data Mining and Knowledge Discovery: Overview.
Chapter 1. In: Cios KJ. Medical Data Mining and Knowledge Discovery. Berlin: Springer Verlag. 2000;1:1-16.
ISBN: 3-7908-1340-0, 502 pages.
Published within the series: "Studies in Fuzziness and Soft Computing", Physica-Verlag Heidelberg, a Springer-Verlag Company.

839. Moore GW.
What is Pathology Informatics?
Internet pamplet.
http://www.netautopsy.org/whatpinf.htm

840. Moore GW.
What is Artificial Intelligence?
Internet pamplet.
http://www.netautopsy.org/whataiai.htm

841. Moore GW.
What is Calculus?
Internet pamplet.
http://www.netautopsy.org/whatcalc.htm

842. Moore GW.
What is Cryptography?
Internet pamplet.
http://www.netautopsy.org/whatcryp.htm

843. Moore GW.
What is the Internet?
Internet pamplet.
http://www.netautopsy.org/whatnett.htm

844. Moore GW.
What is Natural Language Processing?
Internet pamplet.
http://www.netautopsy.org/natlngpr.htm

845. Moore GW.
What is a Medical Parser?
Internet pamplet.
http://www.netautopsy.org/whatpars.htm

846. Moore GW.
What is the Barrier Word Method?
Internet pamplet.
http://www.netautopsy.org/whatbrwd.htm

847. Moore GW.
What is Ontology?
Internet pamplet.
http://www.netautopsy.org/whatonto.htm

848. Moore GW.
What is Perl?
Internet pamplet.
http://www.netautopsy.org/whatperl.htm

849. Moore GW.
Book Translation: Sadegh-zadeh K.
When Humans Forgot How to Think: Emergence of Machina sapiens.
German: Als der Mensch das Denken verlernte: Die Entstehung der Machina sapiens.
Translated by: Moore GW.
Tecklenburg, Germany: Burgverlag. 2000;:.
ISBN 3-922506-99-2, 164 pages.
Volume 3 in the series, Machina Sapiens: ISSN 0179-7174.
Copies of this translation were distributed to participants in the October 26, 2006, meeting, National Institutes of Health (NIH), Biomedical Computing Interest Group (BCIG), 5:30-7:30 PM, NIH Clinical Center, Bethesda, MD.
Dr. Moore was the facilitator for this meeting.
The author, Prof. Kazem Sadegh-zadeh, Professor Emeritus, Münster University, Münster, Germany, participated by webcam.
http://www.altum.com/bcig/events/bookclub/2006/2006_10.htm
http://www.netautopsy.org/machinasapiens/

850. Moore GW.
Acceptance Speech. Association for Pathology Informatics. Honorary Fellow, 2007.
Presented: 6:30 PM, September 11, 2007. Annual Awards Dinner, Advancing Practice, Instruction and Innovation through Informatics. Pittsburgh Marriott City Center, 112 Washington Place, Pittsburgh, Pennsylvania 15219.
http://www.netautopsy.org/apihonfl.htm
http://www.pathologyinformatics.org/2007APIAward

851. Berman JJ, Moore GW.
Implementing an RDF Schema for Pathology Images.
Presented: 7:30 AM, September 10, 2007. Advancing Practice, Instruction and Innovation through Informatics. Pittsburgh Marriott City Center, 112 Washington Place, Pittsburgh, Pennsylvania 15219.
http://apiii.upmc.edu/programs/workshops.html
http://www.julesberman.info/spec2img.htm
http://www.julesberman.info/img_sch.xml

SCREEN 83. MINIBIOGRAPHIES.

Note: Materials adapted from

Jules J. Berman's resource page: http://www.julesberman.info/chronos.htm ; Wikipedia: http://en.wikipedia.org/ ; and the list of Nobel Prize Winners: http://nobelprize.org/nobel_prizes/medicine/laureates/.

Sushruta (Indian anatomist, performed the first autopsy in 5000 BCE.
Pythagoras (Pythagoras of Samos (Ρυθαγορας), 580-490 BC, ancient Greek mathematician, philosopher, music theorist.
Zeno (Zeno of Elea. (Ζενο), 490-425 BC, Ancient Greek philosopher, mathematician.
Socrates (Socrates (Σωκρατης), 470-399 BC, Ancient Greek philosopher, teacher of Plato.
Hippocrates (Hippocrates of Kos `Iπποκρατης, 460-370 BC, Greek physician, ethicist, father of medicine.
Democritus Democritus (Δεμοκριτος), 460-370 BC, ancient Greek philosopher, atomic theory.
Plato Plato (Ρλατων), 427-347 BC, Ancient Greek philosopher, teacher of Aristotle.
Aristotle Aristotle (Αριστοτελης), 384-322 BC, Greek philosopher, encyclopedist, teacher of Alexander the Great.
Theophrastus Theophrastus (Θεοφραστος), 371-287 BC, ancient Greek biologist, physicist, ethicist, plant classification.
Euclid Euclid (Ευκλειδης), 325-275 BC, ancient Greek mathematician, summarized rules of geometry.
Ptolemy Ptolemy I, 323-283 BC, Egyptian pharoah.
Aristarchus Aristarchus of Samos (Aρισταρχος), 310-230 BC, ancient Greek astronomer, mathematician, heliocentric system.
Archimedes Archimedes (Αρχιμεδης) 287-212 BC, Ancient Greek mathematician, one of three greatest mathematicians of all time (Archimedes, Newton, Gauss). The Sand Reckoner: first discussion of large-number problems; elements of calculus; calculated π as 3.142
Eratosthenes Eratosthenes (Eρατοσθενης), 276-194 BC, ancient Greek mathematician, Sieve of Eratosthenes, prime number finder, basis of modern computer security methods; calculated size of the earth.
Hipparchus Hipparchus (`Iππαρχος), 190-120 BC, ancient Greek astronomer, geographer, mathematician, calculated distance to moon.
Dioscorides Dioscorides (Διοσκοριδης), 40-90, ancient Greek botanist, physician, pharmacologist, Materia Medica, botanical medicine.
Galen (Claudius Galenus, 129-200, Greco-Roman physician.
Diophantes Diophantes of Alexandria (Διοφαντης), 200-214, algebraic concepts, basis for Fermat's last theorem, with Al-Khawárizmi, father of algebra.
Sun Tse Sun-Tse. (孫子). Chinese mathematician, inventor of Chinese Remainder Theorem.
Brahmagupta (Brahmagupta, 589-668, Indian mathematician, astrophysicist, algebraist, inventor of zero.
Al Khawarizmi Abu Abdullah Muhammad bin Musa Al-Khawárizmi (أبو عبدالله محمد بن موسى الخوارزمي), 780-850, Uzbek-Persian mathematician; inventor of the algorithm for performing long-division; inventor of algebra, named after his book, Al-Jabr wa-al-Muqabilah. (Arabic: Integration and Equality).
Avicenna Avicenna (Ibn-Sina) (Abu `Ali al-Husayn ibn `Abd Allah ibn Sina al-Balkhi, Latinized as Avicenna), 980-1037, Persian-Muslim physician, philosopher, and polymath: physician, astronomer, alchemist, chemist, logician, mathematician, metaphysician, philosopher, physicist, poet, scientist, theologian, statesman, soldier, author of 450 books.
Maimonides (Moses Maimonides (משה דן מימון), 1135-1204, Jewish rabbi, physician, and philosopher.
Fibonacci (Fibonacci, Leonardo of Pisa, 1170-1250, Italian mathematician, who introduced Arabic numerals to Europe.
Al Nafis (Ibn al-Nafis, 1213-1288, Syrian physician, lawyer, writer, Muslim theologian. Heart-lung in circulation, aeration.
Aquinas (St Thomas Aquinas, 1225-1274, Roman Catholic priest, philosopher, and theologian.
Occam (Occam, William of Ockham, 1285-1349, English logician and Franciscan friar. Occam's Razor: Entia praeter necessitatem non sunt multiplicanda.
Brunelleschi (Filippo Brunelleschi, 1377-1446, Italian artist, invented perspective.
Gutenberg (Johannes zum Gutenberg, 1400-1468, goldsmith, printer, moveable type printing in Europe.
Trithemius (Johannes Trithemius, 1462-1516, Dutch monk, mathematician, mystic. Cryptography and steganography.
Copernicus (Nicolaus Copernicus (Mikolaj Kopernik) (1473-1543), Polish physicist, heliocentric theory. Polish monk, astrophysicist. Heliocentric theory.
Tartaglia (Niccolò Fontana Tartaglia, 1500-1557, Italian mathematician.
Cardano (Gerolamo Cardano, 1501-1576, Italian mathematician.
Pare (Ambroise Paré, 1510-1590, French physician, surgeon, modern surgical technique.
Vesalius (Andreas Vesalius, 1514-1564, Belgian physician, anatomist, De Humani Corporis Fabrica.
Kepler (Johannes Kepler, 1517-1630, German astronomer, mathematician. Planets move in ellipses.
Bombelli (Rafael Bombelli, 1526-1572, Italian mathematician, imaginary numbers.
Brahe (Tycho Brahe, 1546-1601, Danish astronomer, challenges belief in fixed universe.
Bruno (Giordano Bruno, 1548-1600, Italian philosopher, priest, philosopher, cosmologist, occultist. Burnt at the stake by Inquisition for espousing heliocentric theory.
Stevin (Simon Stevin, 1548-1620, Flemish mathematician, engineer, inventor of decimals.
Napier (John Napier, Laird of Merchiston, 1550-1617. Scottish nobleman, gentleman of leisure, inventor of logarithms, transformed multiplication problems into addition problems, division problems into subtraction problems.
Galilei (Galileo Galilei, 1564-1642. Italian physicist and astronomer, four moons of Jupiter, mathematical basis for heliocentric theory; discovery of Milky Way.
Janssen (Zaccharias Janssen, 1585-1632, Dutch spectacle maker, inventor of microscope.
Descartes (René Descartes, 1596-1650, French philosopher, mathematician, inventor of analytic geometry, an algebraic mirror Euclidean geometry.
Fermat (Pierre de Fermat, 1601-1665, French lawyer, mathematician. Fermat's Last Theorem.
Romer (Olaus Rømer, 1614-1710, Danish astronomer, speed of light.
Willis (Thomas Willis, 1621-1675, British physician, anatomist. Anatomy, pathology, neurophysiology of the brain. Circle of Willis.
Pascal (Blaise Pascal, 1623-1662, Swiss mathematician, philosopher. Co-inventor, Binomial Formula, with Sir Isaac Newton. Pascal's Wager: bet with the Lord God that He exists, using risk-benefit analysis.
Huygens (Christiaan Huygens, 1629-1695, Dutch mathematician, astrophysicist, pendulum clock.
Rudbeck (Olaus Rudbeck, 1630-1702, Swedish scientist, physician, anatomist, lymphatics.
Leeuwenhoek (Antonie van Leeuwenhoek, 1632-1723, Dutch tradesman, scientist, father of microbiology, microorganisms in pond water, human sperm.
Steno (Nicholas Steno, 1638-1686, Danish geologist, anatomist, fossils as petrified remains.
Newton (Sir Isaac Newton, 1642-1727, British physicist and mathematician, one of three greatest mathematicians of all time (Archimedes, Newton, Gauss). Inventor of Classical Physics. White light composed of different colors. Co-inventor, Binomial Formula, with Blaise Pascal. Co-inventor, differential and integral calculus, with Gottfried Leibniz.
Leibniz (Gottfried Leibniz, 1646-1716, German mathematician, philosopher. Co-inventor, differential and integral calculus, with Sir Isaac Newton.
Halley (Edmond Halley, 1656-1742, British astronomer, scientist, mathematician, meteorologist, physicist, charts Southern stars; mortality tables.
Bernoulli (Johann Bernoulli, 1667-1748, Swiss mathematician.
Morgagni (Giovanni Battista Morgagni, 1682-1771, Italian anatomist, father of modern anatomic pathology. De Sedibus et Causis Morborum. (Latin: On the seats and causes of diseases).
Bach (Johann Sebastian Bach, 1685-1750, German composer.
Goldbach (Christian Goldbach, 1690-1764, German mathematician, Goldbach's conjecture. Even numbers greater than 2 as sum of primes.
Bernoulli (Daniel Bernoulli, 1700-1782, Swiss mathematician.
Franklin (Benjamin Franklin (1706-1790), American printer, author, satirist, politician, inventor, scientist, statesman, diplomat; inventor of bifocal lenses.
Linnaeus (Carol Linnaeus, 1707-1778, Swedish botanist, physician, zoologist, Systema Naturae biological classification.
Euler (Leonhard Paul Euler, 1707-1783, Swiss mathematician, physicist, transcendental numbers.
Lind (James Lind, 1716-1794, British physician, naval surgeon, citrus prevents scurvy.
Bonnet (Charles Bonnet, 1720-1793, naturalist, philosopher, photosynthesis.
Spallanzani (Lazzaro Spallanzani (1729-1799), Italian biologist, refuted spontaneous generation.
Cavendish (Henry Cavendish (1731-1810), British scientist, discovery of hydrogen, gravitational constant, mass of the earth.
Wolff (Kaspar Friedrich Wolff (1733-1794), German physiologist, embryologist, theory of embryology. Eponym: Wolffian duct.
Withering (William Withering (1741-1799), British physician and surgeon, inventor of foxglove-digitalis.
Lavoisier (Antoine-Laurent Lavoisier (1743-1794), French chemist, biologist, economist; invented modern chemical nomenclature.
Laplace (Pierre-Simon Laplace (1749-1827), French mathematician, physicist, Laplace transform, central limit theorem.
Jenner (Edward Jenner (1749-1823), British physician, scientist, British physician, vaccination against smallpox.
Proust (Joseph-Louis Proust (1754-1826), French chemist, law of definite proportions for chemical compounds.
Dalton (John Dalton (1766-1844), British meteorologist, chemist, biologist, astronomer, writer, invented the modern atomic theory.
Bichat (Marie François Xavier Bichat (1771-1802), French physician and biologist, principles of histology.
Gauss (Johann Karl Friedrich Gauss, 1777-1855, German mathematician, one of the three greatest mathematicians of all time (Archimedes, Newton, Gauss); method of least squares in statistical theory; mathematical framework: arithmetic, classical physics.
Laennec (René Laennec, (1781-1826), French physician. Inventor of the stethoscope.
Prout (William Pickering Prout (1785-1850), British chemist, physician, theologian, stomach produces hydrochloric acid (proton pump), foods classified as carbohydrate, fat, or protein.
Fraunhofer (Joseph von Fraunhofer (1787-1826), German optician, spectral lines.
Morse (Samuel F. B. Morse, 1791-1872, American painter, inventor of telegraph, Morse code.
Babbage (Charles Babbage, 1791-1871, British mathematician, philospher, mechanical engineer, inventor of programmable computer.
Lobachevsky (Nikolai Ivanovich Lobachevsky, 1792-1856, Russian mathematician; co-inventor of non-Euclidean geometry, with János Bolyai.
Payen (Anselm Payen, 1795-1891, French chemist, discoverer of diastase.
Carnot (Nicolas Léonard Sadi Carnot, 1796-1832, French chemist, military engineer, heat engine, thermodynamics, physical limits of steam engine.
Wohler (Friedrich W&oum;hler, 1800-1882, German chemist, synthesis of urea.
Bolyai (János Bolyai, 1802-1860, Hungarian mathematician; co-inventor of non-Euclidean geometry, with Nikolai Ivanovich Lobachevsky.
Abel (Niels Henrik Abel, 1802-1829, Norwegian mathematician, impossibility of solving quintic equations.
Rokitansky (Karl Baron of Rokitansky, 1804-1878, Czech-Austrian pathologist. Father of modern autopsy pathology methods.
Saint Victor (Claude Félix Abel Niepce de Saint-Victor, 1805-1870, French chemist, photographer, radioactivity.
Darwin (Charles R. Darwin, 1809-1882, British physician, geologist, naturalist. The Origin of Species. The Descent of Man.
Snow (John Snow, 1813-1858, British physician, anesthesia, hygeine for cholera epidemic, London.
Paget (Sir James Paget, 1814-1899, British surgeon, pathologist.
Sylvester (James Joseph Sylvester, 1814-1897, English mathematician.
Boole (George Boole, 1815-1864, British logician.
Bismarck (Otto Eduard Leopold von Bismarck-Schönhausen, 1815-1898, German politician: The making of laws and sausages should not be witnessed by their consumers.
Semmelweis (Ignaz Philipp Semmelweiss, 1818-1865, Hungarian physician, reduction of puerperal fever by hand-washing.
Tyndall (John Tyndall, 1820-1893, British physicist, dimagnetism, greenhouse effect.
Chebyshev (Пафнътий Львович Чебышëв = Pafnytiih Lohvovich Chebyhshev = Pafnuty Lvovich Chebyshëv (1821-1894). Russian mathematician.
Virchow (Rudolph Ludwig Karl Virchow, 1821-1902, German pathologist; father of modern cellular pathology.
Mendel (Gregor Mendel, 1822-1884, Czech-German Augustinian monk, scientist, geneticist, principles of inheritance, law of recessive inheritance; law of segregation.
Pasteur (Louis Pasteur, 1822-1895, French chemist, microbiologist, pasteurization.
Hermite (Charles Hermite, 1822-1901, French mathematician e is transcendental number, i.e., not the solution of polynomial with integer coefficients.
Kronecker (Leopold Kronecker, 1823-1891, Jewish-German mathematician. "God made the integers."
Kirchoff (Gustav Kirchhoff, 1824-1887, German physicist, electrical circuits, spectral lines.
Lister (First Baron Joseph Lister, 1827-1912, British surgeon, phenol as antiseptic in surgery.
Maxwell (James Clerk Maxwell, 1831-1879, British mathematician, physicist, Maxwell's equations for electromagnetism.
Recklinghausen (Friedrich Daniel von Recklinghausen, 1833-1910, German pathologist.
Mendeleyev (Dmitri Ivanovich Mendeleyev, 1834-1907, Russian chemist, periodic table of chemical elements.
Sternberg (Brig. Gen. George Miller Sternberg, 1838-1915, American physician, bacteriologist, 18th U. S. Army Surgeon General, pneumococcus.
Kernig (Владимир Михайлович Керниг = Vladimir Mikhaihlovich Kernig = Vladimir Mikhailovich Kernig (1840-1917). Russian-German internist. Kernig sign.
Koch (Robert Koch, 1843-1910, German physician, Koch's postulates for disease.
Nietsche (Friedrich Nietsche, 1844-1900, German philosopher.
Metchnikoff (Илья Ильич Мечников = Ilya Ilych Mechnikoff (1845-1916), Nobel Medicine 1908, Russian biologist, immunologist.
Cantor (Georg Ferdinand Ludwig Philipp Cantor, 1845-1918, German mathematician.
Frege (Gottlob Frege, 1848-1925, German mathematician.
Osler (Sir William Osler, 1849-1919, Canadian-American physician.
Welch (William H. Welch, 1850-1934, American pathologist and microbiologist.
Halstead (William Stewart Halstead, 1852-1922, American surgeon, radical mastectomy.
Poincare (Henri Poincaré, 1854-1912, French physicist, mathematician.
Tesla (Nikola Tesla, 1856-1943, Croatian-American engineer.
Pearson (Karl Pearson, 1857-1936. British statistician, introduced correlation coefficient.
Koplik (Henry Koplik (1858-1927). American pediatrician.
Mall (Franklin P. Mall, 1862-1917, American anatomist.
Aschoff (Karl Albert Ludwig Aschoff, 1866-1942, German pathologist.
Warthin (Aldred Scott Warthin, 1866-1931, American pathologist.
Ewing (James Ewing, 1866-1943, American pathologist.
Landsteiner (Karl Landsteiner, 1868-1943, Nobel Medicine 1930, Austrian-American pathologist, blood groups.
Borel (Émile Borel, 1871-1956, French mathematician. Heine Borel Theorem.
Zermelo (Ernst Zermelo, 1871-1953, German mathematician. Zermelo-Fraenkel Set Theory.
Russell (Bertrand Russell, 1872-1970, British philosopher.
Gossett (William Sealey Gossett (Student), 1876-1937, British mathematician, statistician. Employee of Guinness Brewery, Dublin, Ireland, wrote the ground-breaking papers in the British journal, Nature, about the Student t test.
Student (William Sealey Gossett (Student), 1876-1937, British mathematician, statistician. Employee of Guinness Brewery, Dublin, Ireland, wrote the ground-breaking papers in the British journal, Nature, about the Student t test.
Einstein (Albert Einstein, 1879-1955, Nobel physics, 1921, Swiss-American Physicist, theory of relativity.
Fleming (Sir Alexander Fleming, 1881-1955, Nobel Medicine, 1945. Scottish physician, biologist, pharmacologist, discovery of penicillin as therapy in infectious diseases.
Papanicolaou (George N. Papanicolaou, 1883-1962, Greek-American physician, inventor of the gynecologic cytology screening test for cervical cancer.
Schrodinger (Erwin Schrödinger, 1887-1961, Nobel physics 1933, Austrian Physicist. Quantum mechanics.
Behcet (Hulusi Behçet (1889-1948), Turkish dermatologist;
Fisher (Sir Ronald Aylmer Fisher, 1890-1962, British statistician, statistical variance, experimental design.
Fraenkel (Abraham Adolf Fraenkel, 1891-1965, German mathematician. Zermelo-Fraenkel Set Theory.
Woodger (Joseph H. Woodger, 1894-1981, British biologist and logician.
Willis (Rupert Allan Willis, 1898-1980, Australian pathologist, embryologist.
Escher (M. C. Escher, 1898-1972, Dutch graphic artist.
Berkson (Joseph Berkson, 1899-1982, American statistician. Berkson's Paradox: if you don't die of one thing, you'll die of another.
Sutton (Willie Sutton, 1901-1980, American bank robber.
Dirac (Paul Adrien Maurice Dirac, 1902-1984, 1933 Nobel physics, British Physicist. Co-winner of 1933 Nobel Prize in physics, with Erwin Schrödinger. Quantum mechanics.
Kolmogorov (Андрей Николаевич Колмогоров = Andrey Nikolaevich Kolmogorov (1903-1987), Russian statistician, mathematician. Kolmogorov-Smirnov test.
Neumann (John von Neumann, 1903-1957, Hungarian-American mathematician, logician, designed the first digital computer, ENIAC. Early supporter of Gödel.
Gamow (George Gamow (1904-1968). Russian, American physicist.
Erdos (Pál Erdös, 1913-1996, Hungarian mathematician.
Sandritter (Walter Sandritter, 1920-1980, German pathologist.
Asimov (Isaac Asimov, 1920-1992, American biochemist, science fiction author.
Wied (George L. Wied, 1921-2004, American cytoopathologist.
Sadegh-zadeh (Kazem Sadegh-zadeh, Iranian-German analytic philosopher of medicine, promoter of fuzzy methods in medical informatics.
Ray's animal classification supersedes Pliny.

Miescher, Hoppe-Seyler,

von Lindemann, pi is transcendental number, i.e., not the solution of polynomial with integer coefficients.

Koch, tubercle bacillus.

Klebs, diphtherial bacteria.

Gram, Gram staining for bacteria.

Kitasato, bacterium for tetanus (Clostridium).

Eijkman, beri beri as nutritional disease.

Henri Becquerel, radioactivity.

Beijerinck, viruses.

Benda, mitochondria.

Herrick, Sickle cell anemia .

Peyton Rous, - , Nobel Medicine, 1966. American physician, Tumor-inducing viruses.

Werner Heisenberg, quantum mechanics.

Max Born, quantum mechanics.

Jordan, quantum mechanics.

Dournand, Dickinson, Cardiac catheterization.

Linus Pauling, gene for sickle cell anemia.

Chargoff, base complementarity in DNA.

Watson, Crick, DNA Double helix.

Nirenberg, Khorana, genetic code.

Paul Baran, internet.

Rachel Carson, Silent Spring.
Zadeh (Lotfi Asker Zadeh, Fuzzy set theory, cited over 15,000 times in peer-reviewed journals of mathematics.
Sadegh zadeh (Kazem Sadegh-zadeh, promoter of fuzzy methods in medical informatics.
Smithies (Oliver Smithies, - . Nobel, Medicine, 2007. gene modifications using embryonic stem cells.
Fire (Andrew Z. Fire, - , Nobel, Medicine, 2006. RNA interference, gene silencing, double-stranded RNA.
Mello (Craig C. Mello, - , Nobel, Medicine, 2006. RNA interference, gene silencing, double-stranded RNA.
Marshall (Barry J. Marshall, - , Nobel Medicine, 2005. Helicobacter pylori, role in gastritis, peptic ulcer disease.
Warren (J. Robin Warren, - , Nobel Medicine, 2005. Helicobacter pylori, role in gastritis, peptic ulcer disease.
Lauterbur (Paul C. Lauterbur, - , Nobel Medicine, 2003. magnetic resonance imaging.
Mansfield (Sir Peter Mansfield, - , Nobel Medicine, 2003. magnetic resonance imaging.
Brenner (Sydney Brenner, - , Nobel, Medicine, 2002. genetic regulation, organ development, programmed cell death.
Horvitz (H. Robert Horvitz - , Nobel, Medicine, 2002. genetic regulation, organ development, programmed cell death.
Hartwell (Leland H. Hartwell, - , Nobel Medicine, 2001. key regulators of the cell cycle.
Hunt (R. Timothy Hunt, - , Nobel Medicine, 2001. key regulators of the cell cycle.
Nurse (Paul M. Nurse, - , Nobel Medicine, 2001. key regulators of the cell cycle.
Carlsson (Arvid Carlsson, - , Nobel Medicine, 2000. signal transduction in nervous system.
Greengard (Paul Greengard, - , Nobel Medicine, 2000. signal transduction in nervous system.
Kandel (Eric Kandel, - , Nobel, Medicine, 2000. signal transduction in nervous system.
Blobel (Günter Blobel, - , Nobel, Medicine, 1999. proteins with intrinsic signals, governing transport and localization.
Furchtgott (Robert F. Furchgott, - , Nobel Medicine, 1998. nitric oxide as signalling molecule in cardiovascular system.
Ignarro (Louis J. Ignarro, - , Nobel Medicine, 1998. nitric oxide as signalling molecule in cardiovascular system.
Murad (Ferid Murad, - , Nobel Medicine, 1998. nitric oxide as signalling molecule in cardiovascular system.
Prusiner (Stanley B. Prusiner, - , Nobel Medicine, 1997. prions, new biological principle of infection.
Doherty (Peter C. Doherty, - , Nobel Medicine, 1996. cell mediated immune defense.
Zingernagel (Rolf M. Zinkernagel, - , Nobel Medicine, 1996. cell mediated immune defense.
Lewis (Edward B. Lewis, - , Nobel Medicine, 1995. genetic control of early embryonic development.
Nusslein Volhard (Christiane Nüsslein-Volhard, - , Nobel Medicine, 1995. genetic control of early embryonic development.
Wieschaus (Eric F. Wieschaus, - , Nobel Medicine, 1995. genetic control of early embryonic development.
Gilman (Alfred G. Gilman, - , Nobel Medicine, 1994. G-proteins in cellular signal transduction.
Rodbell (Martin Rodbell, - , Nobel Medicine, 1994. G-proteins in cellular signal transduction.
Roberts (Richard J. Roberts - , Nobel Medicine, 1993. discovery of split genes.
Sharp (Phillip S. Sharp - , Nobel Medicine, 1993. discovery of split genes.
Fischer (Edmond H. Fischer, - , Nobel Medicine, 1992. reversible protein phosphorylation as biological regulatory mechanism.
Krebs (Edwin G. Krebs, - , Nobel Medicine, 1992. reversible protein phosphorylation as biological regulatory mechanism.
Neher (Erwin Neher, - , Nobel Medicine, 1991. single ion channels in cells.
Sakmann (Bert Sakmann, - , Nobel Medicine, 1991. single ion channels in cells.
Murray (Joseph E. Murray, - , Nobel Medicine, 1990. organ and cell transplantation in treatment of human disease.
Thomas (E. Donnall Thomas, - , Nobel Medicine, 1990. organ and cell transplantation in treatment of human disease.
Bishop (J. Michael Bishop, - , Nobel Medicine, 1989. cellular origin of retroviral oncogenes.
Varmus (Harold E. Varmus, - , Nobel Medicine, 1989. cellular origin of retroviral oncogenes.
Black (Sir James W. Black, - , Nobel Medicine, 1988. principles for drug treatment of stomach ulcers.
Elion (Gertrude B. Elion, - , Nobel Medicine, 1988. principles for drug treatment of stomach ulcers.
Hitchings (George H. Hitchings, - , Nobel Medicine, 1988. principles for drug treatment of stomach ulcers.
Tonegawa (Susumu Tonegawa, - , Nobel Medicine, 1987. genetic principle for generation of antibody diversity.
Cohen (Stanley Cohen, - , Nobel Medicine, 1986. discoveries of growth factors.
Levi Montalcini (Rita Levi-Montalcini, - , Nobel Medicine, 1986. discoveries of growth factors.
Brown (Michael S. Brown, - , Nobel Medicine, 1985. regulation of cholesterol metabolism.
Goldstein (Joseph L. Goldstein, - , Nobel Medicine, 1985. regulation of cholesterol metabolism.
Jerne (Niels K. Jerne, - , Nobel Medicine, 1984. development and control of immune system, production of monoclonal antibodies.
Kohler (Georges J. F. Köhler, - , Nobel, Medicine, 1984. development and control of immune system, production of monoclonal antibodies.
Milstein (César Milstein, - , Nobel, Medicine, 1984. development and control of immune system, production of monoclonal antibodies.
McClintock (Barbara McClintock, - , Nobel Medicine, 1983. mobile genetic elements.
Bergstrom (Sune K. Bergström, - , Nobel, Medicine, 1982. prostaglandins and related biologically active substances.
Samuelsson (Bengt I. Samuelsson, - , Nobel Medicine, 1982. prostaglandins and related biologically active substances.
Vane (Sir John R. Vane, - , Nobel Medicine, 1982. prostaglandins and related biologically active substances.
Sperry (Roger W. Sperry, - , Nobel Medicine, 1981. functional specialization of cerebral hemispheres.
Hubel (David H. Hubel, - , Nobel Medicine, 1981. information processing in the visual system.
Wiesel Torsten N. Wiesel, - , Nobel Medicine, 1981. information processing in the visual system.
Benacerraf Baruj Benacerraf, - , Nobel Medicine, 1980. genetically determined structures on cell surface regulating immunologic reactions.
Dausset Jean Dausset, - , Nobel Medicine, 1980. genetically determined structures on cell surface regulating immunologic reactions.
Snell George D. Snell, - , Nobel Medicine, 1980. genetically determined structures on cell surface regulating immunologic reactions.
Cormack Alan M. Cormack, - , Nobel Medicine, 1979. computer assisted tomography.
Hounsfield Sir Godfrey N. Hounsfield, - , Nobel Medicine, 1979. computer assisted tomography.
Arber Werner Arber, - , Nobel Medicine, 1978. restriction enzymes, application to molecular genetics.
Nathans Daniel Nathans, - , Nobel Medicine, 1978. restriction enzymes, application to molecular genetics.
Smith Hamilton O. Smith, - , Nobel Medicine, 1978. restriction enzymes, application to molecular genetics.
Guillemin Roger Guillemin, - , Nobel Medicine, 1977. peptide hormone production of the brain.
Schally Andrew V. Schally, - , Nobel Medicine, 1977. peptide hormone production of the brain.
Yalow Rosalyn Yalow, - , Nobel Medicine, 1977. Radioimmunoassays of peptide hormones.
Blumberg Baruch S. Blumberg, - , Nobel Medicine, 1976. new mechanisms for the origin and dissemination of infectious diseases.
Gajdusek D. Carleton Gajdusek, - , Nobel Medicine, 1976. new mechanisms for the origin and dissemination of infectious diseases.
Baltimore David Baltimore, - , Nobel, Medicine, 1975. interaction between tumor viruses and the genetic material of the cell.
Dulbecco Renato Dulbecco, - , Nobel, Medicine, 1975. interaction between tumor viruses and the genetic material of the cell.
Temin Howard Martin Temin, - , Nobel Medicine, 1975. interaction between tumour viruses and the genetic material of the cell.
Claude Albert Claude, - , Nobel Medicine, 1974. structural and functional organization of the cell.
De Duve Christian de Duve, - , Nobel Medicine, 1974. structural and functional organization of the cell.
Palade George E. Palade, - , Nobel Medicine, 1974. structural and functional organization of the cell.
Frisch Karl von Frisch, - , Nobel Medicine, 1973. organization and elicitation of individual and social behaviour patterns.
Lorenz Konrad Lorenz, - , Nobel Medicine, 1973. organization and elicitation of individual and social behaviour patterns.
Tinbergen Nikolaas Tinbergen, - , Nobel Medicine, 1973. organization and elicitation of individual and social behaviour patterns.
Edelman Gerald M. Edelman, - , Nobel Medicine, 1972. chemical structure of antibodies.
Porter Rodney R. Porter, - , Nobel Medicine, 1972. chemical structure of antibodies.
Sutherland Earl W. Sutherland Jr., - , Nobel Medicine, 1971. mechanisms of the action of hormones.
Katz Sir Bernard Katz, - , Nobel Medicine, 1970. humoral transmitters in nerve terminals, storage, release, and inactivation.
Euler Ulf von Euler, - , Nobel Medicine, 1970. humoral transmitters in nerve terminals, storage, release, and inactivation.
Axelrod Julius Axelrod, - , Nobel Medicine, 1970. humoral transmitters in nerve terminals, storage, release, and inactivation.
Delbruck Max Delbrück, - , Nobel Medicine, 1969. replication mechanism and the gentic structure of viruses.
Hershey Alfred D. Hershey, - , Nobel Medicine, 1969. replication mechanism and the gentic structure of viruses.
Luria Salvador E. Luria, - , Nobel Medicine, 1969. replication mechanism and the gentic structure of viruses.

Robert W. Holley, - , Nobel Medicine, 1968. genetic code and its function in protein synthesis.

Har Gobind Khorana, - , Nobel Medicine, 1968. genetic code and its function in protein synthesis.

Marshall W. Nirenberg, - , Nobel Medicine, 1968. genetic code and its function in protein synthesis.

Ragnar Granit, - , Nobel Medicine, 1967. primary physiologic and chemical visual processes in the eye.

Haldan Keffer Hartline, - , Nobel Medicine, 1967. primary physiologic and chemical visual processes in the eye.

George Wald, - , Nobel Medicine, 1967. primary physiologic and chemical visual processes in the eye.

Peyton Rous, - , Nobel Medicine, 1966. American physician, Tumor-inducing viruses.

Charles Brenton Huggins, - , Nobel Medicine, 1966. hormonal treatment of prostatic cancer.

François Jacob, - , Nobel Medicine, 1965. genetic control of enzyme and virus synthesis.

André Lwoff, - , Nobel Medicine, 1965. genetic control of enzyme and virus synthesis.

Jacques Monod, - , Nobel Medicine, 1965. genetic control of enzyme and virus synthesis.

Konrad Bloch, - , Nobel Medicine, 1964. mechanism and regulation of the cholesterol and fatty acid metabolism.

Feodor Lynen, - , Nobel Medicine, 1964. mechanism and regulation of the cholesterol and fatty acid metabolism.

Sir John Carew Eccles, - , Nobel Medicine, 1963. ionic mechanisms in excitation and inhibition of peripheral and central portions of the nerve cell membrane.

Sir Alan Lloyd Hodgkin, - , Nobel Medicine, 1963. ionic mechanisms in excitation and inhibition of peripheral and central portions of the nerve cell membrane.

Sir Andrew Fielding Huxley, - , Nobel Medicine, 1963. ionic mechanisms in excitation and inhibition of peripheral and central portions of the nerve cell membrane.

Francis Harry Compton Crick, - , Nobel Medicine, 1962. molecular structure of nuclear acids for information transfer in living material.

James Dewey Watson, - , Nobel Medicine, 1962. molecular structure of nuclear acids for information transfer in living material.

Maurice Hugh Frederick Wilkins, - , Nobel Medicine, 1962. molecular structure of nuclear acids for information transfer in living material.

Sir Frank MacFarlane Burnet, - , Nobel Medicine, 1960. acquired immunological tolerance.

Sir Peter Brian Medawar, - , Nobel Medicine, 1960. acquired immunological tolerance.

Severo Ochoa, - , Nobel Medicine, 1959. mechanisms in biological synthesis of ribonucleic and deoxiribonucleic acids.

Arthur Kornberg, - , Nobel Medicine, 1959. mechanisms in biological synthesis of ribonucleic and deoxiribonucleic acids.

George Wells Beadle, - , Nobel Medicine, 1958. genes act by regulating definite chemical events

Edward Lawrie Tatum, - , Nobel Medicine, 1958. genes act by regulating definite chemical events

Joshua Lederberg, - , Nobel Medicine, 1958. genetic recombination and organization of bacterial genetic material.

Daniel Bovet, - , Nobel Medicine, 1957. synthetic compounds inhibiting action of body substances, especially on the vascular system and skeletal muscles.

André Frédéric Cournand, - , Nobel Medicine, 1956. heart catherization and pathologic changes in the circulatory system.

Werner Forssmann, - , Nobel Medicine, 1956. heart catherization and pathologic changes in the circulatory system.

Dickinson W. Richards, - , Nobel Medicine, 1956. heart catherization and pathologic changes in the circulatory system.

Axel Hugo Theodor Theorell, - , Nobel Medicine, 1955. nature and mode of action of oxidation enzymes.

John Franklin Enders, - , Nobel Medicine, 1954. ability of poliomyelitis viruses to grow in tissue cultures.

Thomas Huckle Weller, - , Nobel Medicine, 1954. ability of poliomyelitis viruses to grow in tissue cultures.

Frederick Chapman Robbins, - , Nobel Medicine, 1954. ability of poliomyelitis viruses to grow in tissue cultures.

Sir Hans Adolf Krebs, - , Nobel Medicine, 1953. citric acid cycle.

Fritz Albert Lipmann, - , Nobel Medicine, 1953. co-enzyme A in intermediary metabolism.

Selman Abraham Waksman, - , Nobel Medicine, 1952. streptomycin, first antibiotic effective against tuberculosis.

Max Theiler, - , Nobel Medicine, 1951. yellow fever and how to combat it.

Edward Calvin Kendall, - , Nobel Medicine, 1950. hormones of the adrenal cortex, their structure and biological effects.

Tadeus Reichstein, - , Nobel Medicine, 1950. hormones of the adrenal cortex, their structure and biological effects.

Philip Showalter Hench, - , Nobel Medicine, 1950. hormones of the adrenal cortex, their structure and biological effects.

Walter Rudolf Hess, - , Nobel Medicine, 1949. functional organization of the interbrain as coordinator of activities of the internal organs.

Paul Hermann Müller, - , Nobel Medicine, 1948. high efficiency of DDT as a contact poison against arthropods.

Carl Ferdinand Cori - , Nobel Medicine, 1947. catalytic conversion of glycogen

Gerty Theresa Cori née Radnitz - , Nobel Medicine, 1947. catalytic conversion of glycogen

Bernardo Alberto Houssay, - , Nobel Medicine, 1947. hormone of the anterior pituitary lobe in metabolism of sugar.

Hermann Joseph Muller, - , Nobel Medicine, 1946. mutations by x-ray irradiation.

Sir Alexander Fleming, - , Nobel Medicine, 1945. British physician, penicillin and its curative effect in infectious diseases.

Sir Ernst Boris Chain, - , Nobel Medicine, 1945. penicillin and its curative effect in infectious diseases.

Lord Howard Walter Florey, - , Nobel Medicine, 1945. penicillin and its curative effect in infectious diseases.

Joseph Erlanger, - , Nobel Medicine, 1944. differentiated functions of single nerve fibers.

Herbert Spencer Gasser, - , Nobel Medicine, 1944. differentiated functions of single nerve fibers.

Henrik Carl Peter Dam - , Nobel Medicine, 1943. discovery of vitamin k.

Edward Adelbert Doisy - , Nobel Medicine, 1943. chemical nature of vitamin k.

Gerhard Domagk ( - ), Nobel Medicine, 1939. Antibacterial effects of prontosil.

Corneille Jean François Heymans ( - ), Nobel Medicine, 1938. Sinus and aortic mechanisms in regulation of respiration.

Albert Szent-Györgyi von Nagyrapolt, ( - ), Nobel Medicine, 1937. Vitamin C, fumaric acid catalysis.

Sir Henry Hallett Dale ( - ), Nobel Medicine, 1936. chemical transmission of nerve impulses.

Otto Loewi ( - ), Nobel Medicine, 1936. chemical transmission of nerve impulses.

Hans Spemann ( - ), Nobel Medicine, 1935. German biologist, embryologist, organizer effect in embryonic development.

George Hoyt Whipple ( - ), Nobel Medicine, 1934. liver therapy for anemia.

George Richards Minot ( - ), Nobel Medicine, 1934. liver therapy for anemia.

William Parry Murphy ( - ), Nobel Medicine, 1934. liver therapy for anemia.

Thomas Hunt Morgan, - , Nobel Medicine, 1933. role of chromosomes in heredity.

Sir Charles Scott Sherrington ( - ), Nobel Medicine, 1932. functions of neurons.

Lord Edgar Douglas Adrian ( - ), Nobel Medicine, 1932. functions of neurons.

Otto Heinrich Warburg ( - ), Nobel Medicine, 1931. Respiratory enzymes.
Landsteiner Karl Landsteiner ( - ), Nobel Medicine, 1930. Austrian pathologist, human blood groups.
Eijkman Christiaan Eijkman ( - ), Nobel Medicine, 1929. antineuritic vitamin.
Hopkins Sir Frederick Gowland Hopkins, - , Nobel Medicine, 1929. growth-stimulating vitamins.
Nicolle Charles Jules Henri Nicolle, - , Nobel Medicine, 1928. typhus.
Einthoven Willem Einthoven, - , Nobel Medicine, 1924. Electrocardiography.
Einthoven Sir Frederick Grant Banting, - , Nobel Medicine, 1923. Insulin.
Meyerhof Otto Fritz Meyerhof, - , Nobel Medicine, 1922. muscle metabolism.
Richet Charles Robert Richet, - , Nobel Medicine, 1913. Anaphylaxis.
Carrel Alexis Carrel - , Nobel Medicine, 1912. vascular suture, transplantation, blood-vessels, organs.
Gullstrand Allvar Gullstrand, - , Nobel Medicine, 1911. dioptrics of the eye.
Kossel Albrecht Kossel, - , Nobel Medicine, 1910. cell chemistry, proteins, nucleic substances.
Kocher Emil Theodor Kocher, - , Nobel Medicine, 1909. physiology, pathology, surgery of thyroid gland.
Ehrlich Paul Ehrlich - , Nobel Medicine, 1908. immunity.
Laveran Charles Louis Alphonse Laveran, - , Nobel Medicine, 1907. protozoa in causing diseases.
Golgi Camillo Golgi, - , Nobel Medicine, 1906, Italian anatomist, structure of nervous system.
Ramon y Cajal Santiago Ramon y Cajal, - , Nobel Medicine, 1906, Spanish pathologist, structure of nervous system.
Koch Robert Koch, - , Nobel Medicine, 1905, tuberculosis.
Pavlov Ivan Petrovich Pavlov, - , Nobel Medicine, 1904. physiology of digestion.
Ross Sir Ronald Ross, - , Nobel Medicine, 1902. malaria.
Behring Emil Adolf von Behring, - , Nobel Medicine, 1901. Serum therapy for diphtheria.
Krabbe (Knud Krabbe (1885-1961). Danish neurologist.
Krebs (Hans A. Krebs (1900-1981), Nobel Medicine, 1953. British biochemist. Krebs cycle.
Krukenberg (Friedrich Ernst Krukenberg (1871-1946). German pathologist. Krukenberg tumor.
Kuhn (Thomas S. Kuhn (1922-1996), American historian of science.
Kupffer (Karl Wilhelm von Kupffer (1829-1902). German anatomist. Kupffer cells, liver.
Lobachevsky (Nikolai I. Lobachevsky (1792-1856). Russian mathematician. Non-Euclidean geometry.
Markov (Андрей Андреевич Марков = Andreih Andreevich Markov = Andrey Andreevich Markov, (1856-1922). Russian mathematician.
Nikolai Ivanovich Lobachevsky (1792-1856), Russian mathematician.
Rashevsky (Nicholas Rashevsky (1899-1972). American biophysicist, mathematician.

Lobachevsky (Cyrillic: Николай Иванович Лобачевский = Nikolaih Ivanovich Lobachevskiih = Nicolai Ivanovich Lobachevsky (1792-1856) Russian mathematician.

Mendeleyev (Cyrillic: Дмитрй Иванович Менделеев = Dmitrih Ivanovich Mendeleev = Dmitri Ivanovich Mendeleyev (1834-1907). Russian chemist.

Lobachevsky (Николай Иванович Лобачевский = Nikolaih Ivanovich Lobachevskiih = Nicolai Ivanovich Lobachevsky (1792-1856) Russian mathematician.

Mendeleyev (Дмитрй Иванович Менделеев = Dmitrih Ivanovich Mendeleev = Dmitri Ivanovich Mendeleyev (1834-1907). Russian chemist.

Kernig (Владимир Михайлович Керниг = Vladimir Mikhaihlovich Kernig = Vladimir Mikhailovich Kernig (1840-1917). Russian-German internist.

Markov ( Андрей Андреевич Марков = Andreih Andreevich Markov = Andrey Andreevich Markov

Metchnikoff ( Илья Ильич Мечников = Ilohah Ilohich Mechnikov = Ilya Ilych Mechnikov

Kolmogorov ( Андрей Николаевич Колмогоров = Andreih Nikolaevich Kolmogorov = Andrey Nikolaevich Kolmogorov

Chebyshev ( Пафнътий Львович Чебышев = Pafnytiih Lohvovich Chebyhshev = Pafnuty Lvovich Chebyhshév

Rashevsky (Николай Рашевский = Nikolaih Rashevskiih = Nicholas Rashevsky, Russian-American biomathematician.

Tschaikowsky (Петр Ильич Чайковский = Petr Ilohich Chaihkovskiih = Pëtr Ilych Tschaikowsky (1840-1893), Russian composer.

Moussorgsky (Модест Петрович Мусоргский = Modest Petrovich Musorgskiih = Modest Petrovich Moussorgsky (1839-1881), Russian composer.

Ippolitov-Ivanov (Иполйтев Иванев = Ipolihtev Ivanev = Ippolitov-Ivanov, Russian composer

Horowitz (Владимир хоровиц = Vladimir Horovith = Vladimir Horowitz, Russian-American pianist.

Kazarinoff (Николай Донатович Казаринев = Nikolaih Donatovich Kazarinev = Nicolas Donatovich Kazarinoff, American mathematician.

Kazarinoff (Донат Казаринев = Donat Kazarinev = Donat K. Kazarinoff, American mathematician.

Gorbachev (Cyrillic: Михайл Горбачев = Mikhaihl Gorbachev = Mikhail Gorbachev, Russian prime minister.

Khrushchev (Cyrillic: Никита Хрущев = Nikita Khruxhev = Nikita Khrushchev, Russian prime minister.

Brezhnev (Cyrillic: Леонйд Брежнев = Leonihd Brezhnev = Leonid Brezhnev, Russian prime minister.

Khachaturian (Cyrillic: Арам Хачатурян = Aram Khachaturahn = Aram Khachaturian, Russian-Armenian composer.

Bunyakovsky (Cyrillic: Буняковский = Bunahkovskiih = Bunyakovsky, Russian mathematician, Cauchy-Bunyakovsky- Schwartz inequality.

Scriabin (Cyrillic: Скриябин = Skriahbin = Scriabin, Russian composer.

Prokofieff (Cyrillic: Прокофиев = Prokofiev = Prokofieff, Russian composer

Glazunov (Александр Глазунев = Aleksandr Glazunev = Alexander Glazunov, Russian composer.

Dostoyevsky (Фиодор Достоевский = Fiodor Dostoevskiih = Fyodor Dostoevsky, Russian writer.

Gogol (Николай Гогол = Nikolaih Gogol = Nikolai Gogol, Russian writer.

Shostakovich (Дмитрй Шостакович = Dmitrih Shostakovich = Dmitri Shostakovich, Russian composer.

Stravinsky (Игор Стравинский = Igor Stravinskiih = Igor Stravinsky, Russian-American composer.

Pavlov (Павлев = Pavlev = Pavlov, Russian physician. Ivan Petrovich Pavlov, - , Nobel Medicine, 1904. physiology of digestion.

Romanowsky (Романовский = Romanovskiih = Romanovsky. Biological stain.

Rachmaninoff (Рахманинев = Rakhmaninev = Rachmaninoff, Russian composer.

Rimsky-Korsakoff (Римский Корсакев = Rimskiih Korsakev = Rimsky Korsakoff, Russian composer.

Rostropovich (Мтитислав Ростропович = Mtitislav Rostropovich = Mtitislav Rostropovich, Russian cellist.

Tolstoy (Лео Толстой = Leo Tolstoih = Leo Tolstoy, Russian writer.

Last updated: 3/16/2009, by G. William Moore, MD, PhD.

MODAL LOGIC THEORY FOR PATHOLOGY INFERENCE. DRAFT COPY ONLY. 3/16/2009. G. William Moore, MD, PhD. Lawrence A. Brown, MD. Robert H. Burger, MD, MPA. Grover M. Hutchins, MD. Robert E. Miller, MD. http://www.netautopsy.org/modlthry.htm

SCREEN 1. DISCLAIMER.

SCREEN 2. ABSTRACT.

RATIONALE.

MODAL LOGIC: PROSTATE CANCER EXAMPLE.

FREQUENTLY ASKED QUESTIONS.

SCREEN 3. TABLE OF CONTENTS.

SCREEN 4. SKETCH OF MATHEMATICAL MODEL.

SCREEN 5. WORD MODEL: OUTLINE.

SCREEN 6. INTRODUCTION.

SCREEN 7. HYPOTHETICAL AUTOPSY REPORT.

SCREEN 8. UMLS-ENCODED HYPOTHETICAL AUTOPSY REPORT

SCREEN 9. HIPAA: HEALTH INSURANCE PORTABILITY AND ACCOUNTABILITY ACT.

SCREEN 10. PRIVACY AND CLINICOPATHOLOGIC RESEARCH. (Moore et al, 2001)

SCREEN 11. AUTOPSY EXAMPLE: SICKLE CELL CRISIS.

SCREEN 12. CONTINGENCY TABLE ANALYSIS: BASIC DEFINITION.

SCREEN 13. CONTINGENCY TABLE ANALYSIS: HYPOTHETICAL EXAMPLE.

SCREEN 14. CONTINGENCY TABLE ANALYSIS: THREE-DIMENSIONAL TABLE (CONTINGENCY CUBE).

TOKEN SWAP CUBE : PLANAR PROJECTIONS.

SCREEN 15. CONTINGENCY TABLE ANALYSIS: PROBLEMS WITH CLASSICAL TESTS.

SCREEN 16. CONTINGENCY TABLE ANALYSIS: BALANCED TABLE.

SCREEN 17. CONTINGENCY TABLE ANALYSIS: UNBALANCED TABLE.

SCREEN 18. TOKEN SWAP TEST: MISCLASSIFICATION PARADIGM.

SCREEN 19. CONTINGENCY TABLE ANALYSIS. NEYMAN-PEARSON CONDITION.

SCREEN 20. CONFIDENCE REGIONS: NEYMAN-PEARSON CONDITION.

SCREEN 20A. CONFIDENCE REGIONS: NEYMAN-PEARSON CONDITION.

SCREEN 21. CONTINGENCY TABLE ANALYSIS: PROOF OF THE NEYMAN-PEARSON CONDITION.

SCREEN 22. THE ARGUMENT.

SCREEN 23. SCHRÖDINGER'S CAT.

SCREEN 24. SUMMARY OF RULES: SET THEORY FORMULATION.

SCREEN 25. METHOD OF PROOF: ILLUSTRATED TABLES.

Data Empty (Fig. 3403):

Data Positive (Fig. 3404):

Data Negative (Fig. 3405):

Data Failure (Fig. 3406):

SCREEN 26. METHOD OF PROOF: AUTOMATED THEOREM PROVER. SIMPLE PROSTATE MODEL: STEP 1. 60 YEAR OLD MALE.

SCREEN 27. METHOD OF PROOF: AUTOMATED THEOREM PROVER. SIMPLE PROSTATE MODEL: STEP 2. 60 YEAR OLD MALE, ELEVATED PSA.

SCREEN 28. METHOD OF PROOF: AUTOMATED THEOREM PROVER. SIMPLE PROSTATE MODEL: STEP 2a. 60 YEAR OLD MALE, ELEVATED PSA.

SCREEN 29. METHOD OF PROOF: AUTOMATED THEOREM PROVER. SIMPLE PROSTATE MODEL: STEP 2b. 60 YEAR OLD MALE, ELEVATED PSA.

SCREEN 30. METHOD OF PROOF: AUTOMATED THEOREM PROVER. SIMPLE PROSTATE MODEL: STEP 3. 60 YEAR OLD MALE, ELEVATED PSA, POSITIVE PROSTATE BIOPSY.

SCREEN 31. METHOD OF PROOF: AUTOMATED THEOREM PROVER.

SCREEN 32. METHOD OF PROOF: AUTOMATED THEOREM PROVER.

SCREEN 33. METHOD OF PROOF: AUTOMATED THEOREM PROVER.

SCREEN 34. METHOD OF PROOF: AUTOMATED THEOREM PROVER.

SCREEN 35. METHOD OF PROOF: AUTOMATED THEOREM PROVER.

SCREEN 36. METHOD OF PROOF: AUTOMATED THEOREM PROVER.

SCREEN 37. METHOD OF PROOF: LIVE PROOF OF COROLLARY 1.

SCREEN 38. METHOD OF PROOF: TWO CLASSES OF PROPOSITIONS: DATA AND MEDICAL ENTITIES.

SCREEN 39. METHOD OF PROOF: NINE RULES OF RELATIONSHIP.

SCREEN 40. METHOD OF PROOF: NAND, NANDSETS.

SCREEN 41. METHOD OF PROOF: GREEN, YELLOW, RED NANDSETS.

SCREEN 42. METHOD OF PROOF: NON-VIOLATION OF QUARANTINE.

SCREEN 43. METHOD OF PROOF: EMPTY DATASET IS CONSISTENT.

SCREEN 44. METHOD OF PROOF: EMPTY DATASET SATISFIES OCCAM'S RAZOR.

SCREEN 45. ZERMELO-FRANKEL SET THEORY (ZFST).

SCREEN 46. ZERMELO-FRANKEL SET THEORY.

SCREEN 47. NO PARADOX OF SELF REFERENCE.

SCREEN 48. BASIC CONCEPTS OF THE THEORY.

THEOREM §6.1. CONSISTENCY OF RDF CLASSES.

THEOREM §6.2. IDENTITY.

THEOREM §6.3. OR-EXPANSION.

THEOREM §6.4. TELESCOPING.

THEOREM §6.5. CONTEXTUALIZATION.

THEOREM §6.6. INTERCALATION.

THEOREM §6.7. RETIREMENT.

SCREEN 49. COMPLEMENTIZERS: DICITUR HOMERUM CAECUM ESSE.

SCREEN 50. MODAL/FUZZY LOGIC AND COMPLEMENTIZERS.

SCREEN 51: MODAL/FUZZY LOGIC: ST PETER'S RULE.

SCREEN 52: SUTTON'S LAW.

SCREEN 53. BASIC DEFINITIONS.

SCREEN 54. RULE 1. DOUBLE-NEGATIVE=POSITIVE. COMPLEMENTIZERS ABSORB NEGATIVES.

SCREEN 55. RULE 2. KNOWLEDGE-LADDER.

SCREEN 56. RULE 3. DATA-ABSOLUTE.

SCREEN 57. RULE 4. d-HIPPOCRATIC.

SCREEN 58. RULE 5. d-CONATIVE.

SCREEN 59. RULE 6. keδ..d-VEXATIVE.

SCREEN 60. RULE 7. kδ...e-ONTOLOGIC.

SCREEN 61. RULE 8. ETHICAL-DATIVE.

SCREEN 62. RULE 9. COVER.

SCREEN 63. THEOREM 1a. THEOREM 1. CONSISTENCY OF B0

MODAL LOGIC THEORY
FOR PATHOLOGY INFERENCE.
DRAFT COPY ONLY.
3/16/2009.
G. William Moore, MD, PhD.
Lawrence A. Brown, MD.
Robert H. Burger, MD, MPA.
Grover M. Hutchins, MD.
Robert E. Miller, MD.
http://www.netautopsy.org/modlthry.htm

MODAL LOGIC:
PROSTATE CANCER EXAMPLE.

SCREEN 8. UMLS-ENCODED
HYPOTHETICAL AUTOPSY REPORT

SCREEN 9. HIPAA:
HEALTH INSURANCE
PORTABILITY AND ACCOUNTABILITY ACT.

SCREEN 10. PRIVACY AND
CLINICOPATHOLOGIC RESEARCH. (Moore et al, 2001)

SCREEN 11. AUTOPSY EXAMPLE:
SICKLE CELL CRISIS.

SCREEN 12. CONTINGENCY TABLE ANALYSIS:
BASIC DEFINITION.

SCREEN 13. CONTINGENCY TABLE ANALYSIS:
HYPOTHETICAL EXAMPLE.

SCREEN 14. CONTINGENCY TABLE ANALYSIS:
THREE-DIMENSIONAL TABLE (CONTINGENCY CUBE).

SCREEN 15. CONTINGENCY TABLE ANALYSIS:
PROBLEMS WITH CLASSICAL TESTS.

SCREEN 16. CONTINGENCY TABLE ANALYSIS:
BALANCED TABLE.

SCREEN 17. CONTINGENCY TABLE ANALYSIS:
UNBALANCED TABLE.

SCREEN 19. CONTINGENCY TABLE ANALYSIS.
NEYMAN-PEARSON CONDITION.

SCREEN 20. CONFIDENCE REGIONS:
NEYMAN-PEARSON CONDITION.

SCREEN 20A. CONFIDENCE REGIONS:
NEYMAN-PEARSON CONDITION.

SCREEN 21. CONTINGENCY TABLE ANALYSIS:
PROOF OF THE NEYMAN-PEARSON CONDITION.

SCREEN 24. SUMMARY OF RULES:
SET THEORY FORMULATION.

SCREEN 25. METHOD OF PROOF:
ILLUSTRATED TABLES.

SCREEN 26. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 1.
60 YEAR OLD MALE.

SCREEN 27. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 2.
60 YEAR OLD MALE, ELEVATED PSA.

SCREEN 28. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 2a.
60 YEAR OLD MALE, ELEVATED PSA.

SCREEN 29. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 2b.
60 YEAR OLD MALE, ELEVATED PSA.

SCREEN 30. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.
SIMPLE PROSTATE MODEL: STEP 3.
60 YEAR OLD MALE, ELEVATED PSA, POSITIVE PROSTATE BIOPSY.

SCREEN 31. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

SCREEN 32. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

SCREEN 33. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

SCREEN 34. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

SCREEN 35. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

SCREEN 36. METHOD OF PROOF:
AUTOMATED THEOREM PROVER.

SCREEN 37. METHOD OF PROOF:
LIVE PROOF OF COROLLARY 1.

SCREEN 38. METHOD OF PROOF:
TWO CLASSES OF PROPOSITIONS:
DATA AND MEDICAL ENTITIES.

SCREEN 39. METHOD OF PROOF:
NINE RULES OF RELATIONSHIP.

SCREEN 40. METHOD OF PROOF:
NAND, NANDSETS.

SCREEN 41. METHOD OF PROOF:
GREEN, YELLOW, RED NANDSETS.

SCREEN 42. METHOD OF PROOF:
NON-VIOLATION OF QUARANTINE.

SCREEN 43. METHOD OF PROOF:
EMPTY DATASET IS CONSISTENT.

SCREEN 44. METHOD OF PROOF:
EMPTY DATASET SATISFIES OCCAM'S RAZOR.

SCREEN 49. COMPLEMENTIZERS:
DICITUR HOMERUM CAECUM ESSE.

SCREEN 51: MODAL/FUZZY LOGIC:
ST PETER'S RULE.

SCREEN 54. RULE 1. DOUBLE-NEGATIVE=POSITIVE.
COMPLEMENTIZERS ABSORB NEGATIVES.

SCREEN 63. THEOREM 1a. THEOREM 1. CONSISTENCY OF B₀

SCREEN 72. THEOREMS.₀

SCREEN 71. THEOREMS.₀

SCREEN 73. THEOREM 1. CONSISTENCY OF B₀