Send comments and correspondence to: George.Moore4@va.gov
0. ABSTRACT.
Resource Description Framework for Dermatopathology.
G. William Moore, MD, PhD (George.Moore4@va.gov) [1,2,3];
Lawrence A. Brown, MD [1,2]; Grace F. Kao, MD [1,4].
Pathology and Laboratory Medicine Service, Veterans Affairs
Maryland Health Care System, Baltimore, MD [1]; Department of Pathology,
University of Maryland Medical System, Baltimore, MD [2]; Department
of Pathology, The Johns Hopkins Medical Institutions, Baltimore, MD [3];
and Department of Dermatology, George Washington University School
of Medicine, Washington, DC [4].
http://www.netautopsy.org/dermrdfh.htm
Dermatopathology is one of the most complex subspecialties of anatomic
pathology, with a vast number and variety of skin diseases with described
pathologic lesions. An ontology is the core knowledge base and fundamental
assumptions for a field of study. The intellectual content of
dermatopathology may be classified broadly into pattern recognition and
medical reasoning. We propose a medical reasoning ontology for
dermatopathology, consisting of hierarchies of concepts at three levels of
organization: namespace, relationspace, and fuzzyspace (Zadeh's fuzzy logic).
Each concept has exactly one occurrence in the namespace, and exactly one
parent concept. For example, basal vacuolar degeneration, prominent Civatte
bodies, band-like inflammation, and saw-toothing rete pattern, might all have
lichen planus as the parent concept. This namespace specifies a hierarchical
Resource Description Framework, a 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.
In the relationspace, the same name may occur multiply in many contexts,
as for example, anatomic, pathophysiologic, embryologic, environmental
susceptibility, tumor susceptibility, etc. In the fuzzyspace, a single name
may have different levels of certainty in different contexts. For example,
a pigmented skin lesion of long duration would have different fuzzy values,
and therefore a different indication for biopsy, depending upon contextual
factors such as change in size, color, border, bleeding, or ulceration.
The report proposes a mathematical model for this ontology, supported by
mathematical definitions, theorems, and proofs, and examples from
dermatopathology diagnostic principles. The ontology organizes the knowledge
base of dermatopathology in a manner that incorporates both clinical and
pathologic findings, and is available for public scrutiny, copying, and
modification.
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.
Namespace designer must decide: Fundamental organizing principle of the hierarchy: ontologic commitment (Quine).
29. EXAMPLE: LDIP FOR CLASS PATIENT.
Identifier:ldip:Patient
Class Label:Patient
versionInfo (required): 0.1
Registration Authority (required): Association for Pathology Informatics
Language:en
Obligation:optional
Maximum occurrence:Unlimited
Cardinality (required):/[0-9]+/
Datatype: Literal
comment: The patient, unambiguously denoted by the required
ordered quadruple: patient_name (=patient_surname, patient_givenname,
patient_honorific), patient_social_security_number, patient_date_of_birth,
and patient_gender. Includes: patient_insurance.
subClassOf:Person
Contributor:Bill Moore
Date_of_contribution:11-13-2006
30. MONOPARENTALITY ASSUMPTION.
Limited mathematical power.
Limited opportunities for mathematical mischief:
2a. Inconsistency.
2b. Incomputability.
31. BIOMEDICAL SEMANTIC CONTENT (MEANING).
Pair of (metadata, data), bound to unique subject.
Ordered triple: <subject,metadatum,datum>.
Example: <bill_moore,actinic_keratosis,yes>.
Mathematical notation: <argument,function,value>
or <x,f,v>, where:
where □p denotes necessarily p; and
◇p denotes possibly p.
2. Paraphrased: "If you see a dense, superficial dermal band-like
infiltrate with saw-tooth rete ridges, think of lichen planus,
not lichenoid graft-versus-host disease."
Generally: 2n possible patient descriptions for
n propositions.
Set of all possible patient descriptions: truth table.
57. MATHEMATICAL THEOREM.
Mathematically precise statement, provable by deductive,
step-by-step argument.
Similar to arguments in Euclid's (330-275 BC) Elements.
Not all true statements are provable (Gödel, 1931).
All provable statements are true.
58. MATHEMATICAL THEOREMS IN RELATIONSPACE.
Theorem §1. Consistency of Namespace.
Theorem §2. Identity.
Theorem §3. Or-expansion.
Theorem §4. Telescoping.
Theorem §5. Contextualization.
Theorem §6. Intercalation.
Theorem §7. Retirement.
59.
THEOREM §1. CONSISTENCY OF NAMESPACE.
+∀
+p
+q
...
+r
+t
+u
+s
...
is consistent.
60.
THEOREM §2. IDENTITY.
+p
+p
61.
THEOREM §3. OR-EXPANSION.
+p +p
+q ⇒ +q
+q
+q
...
62.
THEOREM §4. TELESCOPING.
+p +p
+q ⇒ +u
+r
+s
+t
+u
63.
THEOREM §5. CONTEXTUALIZATION.
+p +p
+p ⇒ +q
+q +r
+p +s
+r
+s
64. THEOREM §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
65. THEOREM §7. RETIREMENT.
Procedure for removing a subhierarchy (obsolete concept), without
disturbing the remainder of the hierarchy.
+p +p
+p ⇒ +q
+q
+r
+p
-r
66. MATHEMATICAL THEOREMS: PROOF STRATEGIES.
Translate the statement into nandsets.
Verify that all nandsets are negative.
Example: +p ⇒ (+q ⇒ +p).
Whitehead/Russell Transformation: -p|-q|+p.
Nandset: {+p,+q,-p}.
Since ±p∈{+p,+q,-p},
the nandset is vacuous, and the theorem is proved.
67. THEOREMS OF CLASSICAL/MODAL LOGIC.
1.1. CCpCqrCCpqCpr.
Restated: (+p ⇒ (+q ⇒ +r)) ⇒
((+p ⇒ +q) ⇒ (+p ⇒ +r)). Proof: Nandsets {-p,-p,+p,-r}, {-p,+q,+p,-r}, {-q,-p,+p,-r},
{-q,+q,+p,-r}, {+r,-p,+p,-r}, and {+r,+q,+p,-r} are vacuous.
Live Proof:
1.1.1. Nandset {-p,-p,+p,-r}:
1.1.2. Nandset {-p,+q,+p,-r}:
1.1.3. Nandset {-q,-p,+p,-r}:
1.1.4. Nandset {-q,+q,+p,-r}:
1.1.5. Nandset {+r,-p,+p,-r}:
1.1.6. Nandset {+r,+q,+p,-r}:
1.2. CpCqp. Restated: +p ⇒ (+q ⇒ +p). Proof:
Nandset: {-p,+q,-p} is vacuous.
Live Proof:
1.3. CCpqCpp. Restated: (+p ⇒ +q) ⇒
(+p ⇒ +p). Proof:
Nandsets {-p,+p,-p} and {+q,+p,-p}.
are vacuous.
Live Proof:
1.4. Cpp. Restated: (+p ⇒ +p). Proof:
Nandset {+p,-p} is vacuous.
Live Proof:
1.5. CCpqCCqrCpr.
Restated: (+p ⇒ +q) ⇒ ((+q ⇒ +r) ⇒
(+p ⇒ +r)).
Proof: Nandsets {-p,-p,+p,-r}, {-p,+r,+p,-r}, {+q,-p,+p,-r},
and {+q,+r,+p,-r} are vacuous.
Live Proof:
1.5.1. Nandset {-p,-p,+p,-r}:
1.5.2. Nandset {-p,+r,+p,-r}:
1.5.3. Nandset {+q,-p,+p,-r}:
1.5.4. Nandset {+q,+r,+p,-r}:
68. SUMMARY OF RESULTS.
Mathematical consistency.
200 theorems of classical and modal logic.
Intercalation Theorem (inserting new concepts).
Retirement Theorem (removing obsolete concepts).
69. CONCLUSIONS.
Organize knowledge of dermatopathology.
Format of the semantic worldwide web.
Incorporates clinical and pathologic findings.
4. APPENDIX A. PROOFS.
THEOREM §1. CONSISTENCY OF NAMESPACE.
+∀
+p +q
...
+r
+t
+u
+s
...
is consistent.
Proof: It suffices construct a set for which no nandset in the
namespace
hierarchy is a subset. Construct the set {+∀,+p,+q,+r,+s,+t,+u}.
The nandsets of the
namespace
hierarchy are: {+∀,-p},
{+∀,+p,-q}, {+∀,+p,+q,...,-r,-s},
{+∀,+p,+q,...,+s,...}, and
{+∀,+p,+q,...,+r,-t,-u},....
The constructed set is not a superset of any of the
namespace
hierarchy nandsets.
THEOREM §2. IDENTITY.
+p
+p
Proof: Restated: (+p ⇒ +p). Nandset: {+p,-p}
is vacuous.
Live Proof:
THEOREM §3. OR-EXPANSION.
+p +p
+q ⇒ +q
+q
+q
...
Proof:
Restated: ((+p ⇒ +q) ⇒ (+p ⇒ (+q |+q |+q |...)).
Nandsets {-p,+p,-q,-q,-q,...} and {+q,+p,-q,-q,-q, ...}
are vacuous.
Live Proof:
Proof: Restated: (+p ⇒ (+r|+s)) ⇒ ((+p & +q)
⇒ (+r|+s)). Nandsets {-p,+p,+q,-r,-s}, {+r,+p,+q,-r,-s},
and {+s,+p,+q,-r,-s} are vacuous.
Live Proof:
THEOREM §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
Proof:
Restated:
((+p ⇒ (+q|+r))
& (+p ⇒ (+s|+t))
⇒
(+p ⇒ (+q|+r)).
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},
are vacuous.
Live Proof:
THEOREM §7. RETIREMENT. Procedure for removing a subhierarchy (obsolete concept), without
disturbing the remainder of the hierarchy.
+p +p
+p ⇒ +q
+q
+r
+p
-r
Proof:
Restated:
((+p ⇒ (+q|+r))
&
(+p ⇒ -r))
⇒
(+p ⇒ +q)
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},
are vacuous.
Live Proof:
5. APPENDIX B. RDF RESOURCES.
Resource Description Framework (RDF) is a family of World Wide Web Consortium
(W3C) specifications originally designed as a metadata model but which has
come to be used as a general method of modeling information, through
a variety of syntax formats.
The RDF metadata model is based upon the idea of making statements about
resources in the form of subject-predicate-object expressions, called triples
in RDF terminology. The subject denotes the resource, and the predicate
denotes traits or aspects of the resource and expresses a relationship
between the subject and the object. For example, one way to represent
the notion "The sky has the color blue" in RDF is as a triple of specially
formatted strings: a subject denoting "the sky", a predicate denoting "has
the color", and an object denoting "blue".
This mechanism for describing resources is a major component in what
is proposed by the W3C's Semantic Web activity: an evolutionary stage of the
World Wide Web in which automated software can store, exchange, and use
machine-readable information distributed throughout the web, in turn enabling
users to deal with the information with greater efficiency and certainty.
RDF's simple data model and ability to model disparate, abstract concepts has
also led to its increasing use in knowledge management applications unrelated
to Semantic Web activity.
1. The purpose of RDF is to promulgate a standard for
data representation that can be read automatically by web-crawlers throughout
the internet, such as google.com and yahoo.com.
2. An abstracted RDF file is a hierarchical list, easily
read by human readers.
3. An ONTOLOGY is a Platonic description of essential reality.
4. Contrast: what one can see (observation, accident);
what one can know (epistemology); what one can believe (doxology);
other aspects of perceiving reality.
5. Metaphysical commitments or presuppositions embodied
in natural sciences.
6. Example: belief that a cancer can metastasize.
7. In medical informatics, ontology is a structured list
of concepts and relations among concepts.
8. 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.
9. There are currently no PUBLIC RDF ontologies
focused upon skin diseases.
TRANSFER DAUGHTER FILE, dermdhtr.txt,
INTO .xml-FORMATTED MODULE, $dermxmlm.txt
10. Each line in the input daughter-file, dermdhtr.txt,
generates one template in the .xml-formatted output module,
$dermxmlm.txt.
11. Each daughter has exactly one mother.
12. The zeroth (implicit) daughter is Class.
13. The first daughter is Anypatient.
14. Each daughter line is split by a plus-sign, +.
15. Blanks before + represent INDENTATION.
16. The first daughter, Anypatient,
is indented with a SINGLE BLANK SPACE.
17. Each subsequent line in the daughter-file, dermdhtr.txt,
is indented EXACTLY THREE SPACES RIGHT of its mother.
18. All sisters are at the same level of indentation.
19. Each daughter generates exactly one RDF module
in the .xml-formatted output module, $dermxmlm.txt.
Variables:
INPTPATH: Internal name for input daughter file, dermdhtr.txt.
OUTPPATH: Internal name for output .xml-module, $dermxmlm.txt
$tmplt[]: Boilerplate variable for .xml-module, $dermxmlm.txt
$daughter[]: Daughter-array, corresponding to lines in file dermdhtr.txt.
$mother[]: Mother-array, corresponding to lines in file dermdhtr.txt.
$iline: line number for lines in input file, dermdhtr.txt.
$inline: current input line text in input file, dermdhtr.txt.
$nrlines: number of input text lines in input file, dermdhtr.txt.
$splft: current input line text in input file, dermdhtr.txt, left of +.
$sprgt: current input line text in input file, dermdhtr.txt, right of +.
$lensplft: length of $splft.
$lensprgt: length of $sprgt.
$depth[]: depth of indentation for the line.
1. Weedon D.
Skin Pathology. Second Edition.
New York: Churchill Livingstone. 2002;:.
ISBN: 0443070695, 1100 pages.
2. Barnhill R.
Textbook of Dermatopathology. Second Edition.
New York: McGraw-Hill Professional. 2004;:.
ISBN: 0071396608, 912 pages.
3. Macdonald D, Ben-Gashir M, Robson A.
Dermatopathology.
New York: Blackwell Publishing, Inc. 2007;:.
ISBN: 1405107790, 528 pages.
4. Brehmer-Andersson E.
Dermatopathology. First Edition.
New York: Springer. 2006;:.
ISBN: 354030245X, 254 pages.
5. McKee PH, Calonje JE, Granter SR.
Pathology of the Skin. With CD-ROMs and with Clinical Correlations.
Third Edition.
New York: Mosby. 2005;:.
ISBN: 0323036724, 2112 pages.