Spreadsheet Order-Logic for Anatomic Pathology.

SPREADSHEET ORDER-LOGIC
FOR ANATOMIC PATHOLOGY.

http://www.netautopsy.org/apep04ss.htm
Long Version: http://www.netautopsy.org/ordrlogc.htm
Short Version: http://www.netautopsy.org/apsp04ss.htm
Perl Script: http://www.netautopsy.org/ordrlogc.txt
Visual Basic Script: http://www.netautopsy.org/ordrlogc.xls
Execution: http://www.netautopsy.org/cgi-bin/ordrlogc.cgi
G. William Moore, MD, PhD [1,3,4].
Lawrence A. Brown, MD [1,3].
Robert H. Burger, MD, MPA [1,2].
Grace F. Kao, MD [1,5].
Grover M. Hutchins, MD [4].
Robert E. Miller, MD [4].

From: Pathology and Laboratory Medicine Service, Baltimore VA Maryland Health Care System, Baltimore, MD [1].
Urology Division, Surgery Service, Baltimore VA Maryland Health Care System, Baltimore, MD [2].
Department of Pathology, University of Maryland School of Medicine, Baltimore, MD [3].
Department of Pathology, The Johns Hopkins Medical Institutions, Baltimore, MD [4].
Department of Dermatology, George Washington University School of Medicine, Washington, DC [5].

U. S. Government Work, uncopyrighted, accepted for publication as an eposter at APIII'2004, at URL:
http://apiii.upmc.edu
Arch Pathol Lab Med. 2005;: in press.

1. PUBLISHED ABSTRACT.

CONTENT. Core doctrines in human pathology, as reflected in consensus conference proceedings, review texts, tumor staging manuals, and pathology reporting protocols, may be organized as hierarchical lists, and transferred to commercial spreadsheet programs, where they are displayed as rectangular tables and analyzed with statistical tests. This report presents a mathematical model and computer script for calculating the logical consistency of such lists.

TECHNOLOGY. Zermelo-Frankel Set Theory and a commercial spreadsheet application with an embedded programming language.

DESIGN. A spreadsheet is a collection of sheets, or folios. Each folio is a rectangular table, with rows, columns, and cells. The present model has a patient-folio and a disease-folio. The patient-folio contains observed and inferred statements for each patient. In the disease-folio, the topmost-leftmost cell contains the origin, and every filled-in cell is either a parent, a child, or both in the disease-hierarchy. Every parent has one-or-more children, placed right and below the parent.

RESULTS. Proofs of consistency, completeness, and computability are given. Classical logic theorems are enriched. Sample spreadsheets are presented in the areas of dermatopathology, genitourinary pathology, and embryology.

CONCLUSIONS. This report proposes a concept-management formalism, in which statements are listed in descending order of importance on spreadsheet software. The formalism retains the syllogistic quality of reasoning in anatomic pathology, but allows some statements to have greater weight than others. The formalism supports previously-developed theories of ethical data collection and contingency table analysis. Mathematical theories can organize medical knowledge and patient data, and enhance clinicopathologic data collection and surveillance.

COMMENT. The commercial spreadsheet used in this investigation is Microsoft® Excel®.

2. EPOSTER OUTLINE.

1. BACKGROUND.

1.1. Core doctrines in human pathology, reflected in:
1.1.1. Consensus conference proceedings (Kao, 2004; Epstein, 1998).
1.1.2. Review texts. (Sinard; Haber, 2000).
1.1.3. Specialty Texts (Bostwick; Miettinnen).
1.1.4. Tumor staging manuals (AJCC).
1.1.5. Tumor classifications (Berman, 2004).
1.1.6. Pathology reporting protocols. (CAP; ADASP).
1.1.7. Continuing Medical Education (Checkpath).
1.2. Organized as hierarchical lists.
1.3. Transferred to commercial spreadsheet programs (Excel VBA).
1.4. Displayed as rectangular tables. Analyzed with statistical tests.
1.5. Mathematical model and computer script (Excel VBA).
1.6. Nandset computing method: finds all solutions (mathematical completeness).
1.7. Determines the logical consistency of lists.
1.8. Computability in polynomial computing resources.
1.9. Modal logic theory of ethical data collection (Moore, 2003).
1.10. Classical logic has no ordering concept: a statement is either true or false or unknown.
1.11. Bayesian logic has too much ordering: exact probability numbers are required, and subject to arithmetic operations.
1.12. Order logic is ordinal only.

2. TECHNOLOGY.

2.1 Zermelo-Frankel Set Theory. (Kleene; Suppes).
C = is a member of.
{} = Ø = empty set.
U = set-union.
/\ =set-intersection.
- = set-subtraction.
c = subset.

2.2 Commercial spreadsheet application. Microsoft® Excel®. (Visual Basic for Applications, Excel 2000).
2.3 Embedded programming language. Microsoft® Visual Basic® for Applications. (Visual Basic for Applications, Excel 2000).
2.4 Perl programming language. (Perl).

3. DESIGN.

3.1. Spreadsheet, Ш: collection of sheets, or folios. Each folio: rectangular table; rows, columns, cells.
3.2. Patient-folio, П: individual patient data.
3.3. Disease-folio, Д: logic of disease.
3.4. Combined-folio, Ш = (П U Д).

4. DEFINITION OF SPREADSHEET.

4.1. Patient-folio, П:
4.1.1. Observed and inferred statements for each patient.
4.1.2. Quantitative, interval, ranked, categorical, and binary data allowed.
4.1.3. All data expressed as true, false, or missing-value statements.

4.1.4. Example:
П İ ♀ ♂

Mary +İ +♀ ~♂

Bill +İ ~♀ +♂

Pat +İ +♀ .

4.1.5. That is: Mary -> İ; Mary -> ♀; Mary -> ~♂; Bill -> İ, etc.
4.2. Disease-folio, Д:
4.2.1. Topmost-leftmost cell: origin, İ^[0], true for all patients.
4.2.2. Every filled-in cell: parent-concept, child-concept, or both.
4.2.3. Every parent-concept has one-or-more children-concepts.
4.2.4. First child-concept, one-step-down-one-step-right from its parent-concept.
4.2.4. Subsequent children of same parent, same column as siblings.
4.2.5. Each parent-cell and its parent-cells implies the inclusive-or of its children-cells.

4.2.6. Example:
Д 0 1 2

1 +İ . .

2 . +♀ .

3 . . ~♂

4 . +♂ .

5 . . ~♀

4.2.7. That is: İ -> (♀ | ♂); İ & ♀ -> ~♂; İ & ♂ -> ~♀.

4.3. Combined-folio, Ш:

4.3.1. Example:
Ш 0 1 2 3

1 Mary . . .

2 . +İ . .

3 . . +♀ .

4 . . . ~♂

5 Bill . . .

6 . +İ . .

7 . . +♂ .

8 . . . ~♀

9 Pat . . .

10 . +İ . .

11 . . +♀ .

12 +İ . . .

13 . +♀ . .

14 . . ~♂ .

15 . +♂ . .

16 . . ~♀ .

П	İ	♀	♂
Mary	+İ	+♀	~♂
Bill	+İ	~♀	+♂
Pat	+İ	+♀	.

Ш	0	1	2	3
1	Mary	.	.	.
2	.	+İ	.	.
3	.	.	+♀	.
4	.	.	.	~♂
5	Bill	.	.	.
6	.	+İ	.	.
7	.	.	+♂	.
8	.	.	.	~♀
9	Pat	.	.	.
10	.	+İ	.	.
11	.	.	+♀	.
12	+İ	.	.	.
13	.	+♀	.	.
14	.	.	~♂	.
15	.	+♂	.	.
16	.	.	~♀	.

5. ISOMORPHIC REPRESENTATIONS OF SPREADSHEET.

5.1. SPREADSHEET-REPRESENTATION. Rectangular tables constructed according to the above rules:

Advantage: Easy-to-read.

Examples:
П İ ♀ ♂

Mary +İ +♀ ~♂

Bill +İ ~♀ +♂

Pat +İ +♀ .

Д 0 1 2

1 +İ . .

2 . +♀ .

3 . . ~♂

4 . +♂ .

5 . . ~♀

5.2. SYMBOLIC-LOGIC-REPRESENTATION. Set of statements of the form: it is true that X; or X implies Y; or X and Y; or X inclusive-or Y; or not-x; where x and y are true-false statements.

Advantage: Traditional logic notation.

Examples:
Mary -> İ.
Mary -> ♀.
Mary -> ~♂.
Bill -> İ.
Bill -> ♂.
Bill -> ~♀.
Pat -> İ.
Pat -> ♀.
İ -> (♀ | ♂).
İ & ♀ -> ~♂.
İ & ♂ -> ~♀.

5.3. NANDSET-REPRESENTATION. Collection of sets of the form: {X, Y, Z,...}, where not all of X, Y, Z,... are true at once.

Advantage: Transparent calculations, i.e., X [+] Y = Z, nandset addition, where X={a, b, ...}, Y={~a, c, ,,,}, and Z={b, c, ...}. Nandset addition, performed exhaustively, completely and consistently defines the system, and may be performed exhaustively after polynomial steps in a suitably constrained system (i.e., not an exponential number of logic expressions). For nandset, X, that belongs to either П or Д and anonymous completely described patient, A, then X is NOT a subset of A.
See: http://www.netautopsy.org/modlthry.htm

Examples:
1. {Mary, ~İ}.
2. {Mary, ~♀}.
3. {Mary, +♂}.
4. {Bill, ~İ}.
5. {Bill, ~♂}.
6. {Bill, +♀}.
7. {Pat, ~İ}.
8. {Pat, ~♀}.
9. {İ, ~♀, ~♂}.
10. {İ, +♀, +♂}.
11. {İ, +♂, +♀}.
Note that nandsets 10 and 11 are redundant (i.e., Zermelo-Frankel sets are order-insensitive).

Sample calculation:
{Pat, ~İ} [+] {İ, +♀, +♂} = {Pat, +♀, +♂}.
{Pat, ~♀} [+] {Pat, +♀, +♂} = {Pat, +♂}

Therefore, one concludes that Pat is not-male.

П	İ	♀	♂
Mary	+İ	+♀	~♂
Bill	+İ	~♀	+♂
Pat	+İ	+♀	.

6. SEMANTIC MODEL: ANONYMOUS COMPLETELY-DESCRIBED PATIENTS.

6.1. ATOMSET of distinct statements (atoms, A), each with definite true-false status.

6.2. Each atom, a C A, is either a unique PATIENT-IDENTIFIER, a DATUM, or a MEDICAL-ENTITY, i.e., A = (P U D U E), (P /\ D) = Ø, (P /\ E) = Ø, (D /\ E) = Ø.

6.3. No self-reference paradoxes, e.g., no patient can be named, "I am not a patient".

6.4. Special medical-entity: İMPORTANCE, İ^[0]. Every patient is important.

6.5. A patient-atom has no negation.

6.6. Each non-patient atom, a C (A-P), has an EXACT NEGATION, ~a C (A-P).

6.7. Set of anonymous completely-described patients, Ю. For every U C Ю:
6.7.1. U c (A-P).

6.7.2. For every U C Ю and u_k C U, ~u_k ~C U.

6.7.3. For every u=(u₁,...,u_Л) C U, there exists a unique INFLECTION POINT, I, at which:
6.7.3.1. For 0< j < I, u^j/u^Л = -1; and

6.7.3.2. For I < k < Л, u^k/u^I = +1.

6.8. Example. Two-level division of female/male, Л = 2, T -> (♂¹ | ♀²).

Ю T⁰ ♀¹ ♀² ♂¹ ♂² Description

1 ~ + + ~ ~ Usual female non-teamster.

2 ~ + ~ ~ + Weak female non-teamster.

3 ~ ~ ~ + + Usual male non-teamster.

4 ~ ~ + + ~ Weak male teamster.

5 + + + ~ ~ Usual female non-teamster.

6 + + ~ ~ + Weak female teamster.

7 + ~ ~ + + Usual male teamster.

8 + ~ + + ~ Weak male teamster.

6.9. Example. Three-level division of female/male, Л = 3, T -> (♂¹ | ♀³).

Ю T⁰ ♀¹ ♀² ♀³ ♂¹ ♂² ♂³ Description

1 ~ + + + ~ ~ ~ Usual female non-teamster.

2 ~ + + ~ ~ ~ + Weaker female non-teamster.

3 ~ + ~ ~ ~ + + Weakest female non-teamster.

4 ~ ~ ~ ~ + + + Usual male non-teamster.

5 ~ ~ ~ + + + ~ Weaker male non-teamster.

6 ~ ~ + + + ~ ~ Weakest male non-teamster.

7 + + + + ~ ~ ~ Usual female teamster.

8 + + + ~ ~ ~ + Weaker female teamster.

9 + + ~ ~ ~ + + Weakest female teamster.

10 + ~ ~ ~ + + + Usual male teamster.

11 + ~ ~ + + + ~ Weaker male teamster.

12 + ~ + + + ~ ~ Weakest male teamster.

6.10. Example. Three-level division of active colitis.

Ю T⁰ ♀¹ ♀² ♀³ ♂¹ ♂² ♂³ Description

1 ~ + + + ~ ~ ~ .

2 ~ + + + ~ ~ ~ .

3 ~ + + + ~ ~ ~ .

Ю T⁰ ♀¹ ♀² ♀³ ♂¹ ♂² ♂³ Description

1 ~ + + + ~ ~ ~ .

2 ~ + + + ~ ~ ~ .

3 ~ + + + ~ ~ ~ .

Ю T⁰ ♀¹ ♀² ♀³ ♂¹ ♂² ♂³ Description

1 ~ + + + ~ ~ ~ .

2 ~ + + + ~ ~ ~ .

3 ~ + + + ~ ~ ~ .

Ю	T⁰	♀¹	♀²	♂¹	♂²	Description
1	~	+	+	~	~	Usual female non-teamster.
2	~	+	~	~	+	Weak female non-teamster.
3	~	~	~	+	+	Usual male non-teamster.
4	~	~	+	+	~	Weak male teamster.
5	+	+	+	~	~	Usual female non-teamster.
6	+	+	~	~	+	Weak female teamster.
7	+	~	~	+	+	Usual male teamster.
8	+	~	+	+	~	Weak male teamster.

Ю	T⁰	♀¹	♀²	♀³	♂¹	♂²	♂³	Description
1	~	+	+	+	~	~	~	Usual female non-teamster.
2	~	+	+	~	~	~	+	Weaker female non-teamster.
3	~	+	~	~	~	+	+	Weakest female non-teamster.
4	~	~	~	~	+	+	+	Usual male non-teamster.
5	~	~	~	+	+	+	~	Weaker male non-teamster.
6	~	~	+	+	+	~	~	Weakest male non-teamster.
7	+	+	+	+	~	~	~	Usual female teamster.
8	+	+	+	~	~	~	+	Weaker female teamster.
9	+	+	~	~	~	+	+	Weakest female teamster.
10	+	~	~	~	+	+	+	Usual male teamster.
11	+	~	~	+	+	+	~	Weaker male teamster.
12	+	~	+	+	+	~	~	Weakest male teamster.

Ю	T⁰	♀¹	♀²	♀³	♂¹	♂²	♂³	Description
1	~	+	+	+	~	~	~	.
2	~	+	+	+	~	~	~	.
3	~	+	+	+	~	~	~	.

Ю	T⁰	♀¹	♀²	♀³	♂¹	♂²	♂³	Description
1	~	+	+	+	~	~	~	.
2	~	+	+	+	~	~	~	.
3	~	+	+	+	~	~	~	.

Ю	T⁰	♀¹	♀²	♀³	♂¹	♂²	♂³	Description
1	~	+	+	+	~	~	~	.
2	~	+	+	+	~	~	~	.
3	~	+	+	+	~	~	~	.

7. EXAMPLE: SEXES.

7.1. NOTATION: {X^[i]} = {xⁱ}. {X^[i} = {xⁱ, xⁱ⁺¹, ..., x^Л}. {X^i]} = {x⁰, x¹, ..., xⁱ}.

7.2. Classical-logic:

Every (important) patient, İ, is either a female, ♀, or a male, ♂. If a patient is female, then the patient is not-male. If a patient is male, then the patient is not-female.
Д 0 1 2

1 +İ^[0] . .

2 . +♀^[0] .

3 . . ~♂^[0]

4 . +♂^[0] .

5 . . ~♀^[0]

7.3. Order-logic:
Every patient, İ, is either a teamster, T or else not-a-teamster, ~T. Among teamsters, males are more frequent than females.
Д 0 1 2

1 +İ^[0] . .

2 . ~T^[0] .

3 . . ♀^[1

4 . . ♂^[2

5 . T^[0] .

6 . . ♂^[1

7 . . ♀^[2

The nandsets are:
{+i⁰, +t⁰, ~t⁰}.
{+i⁰, ~t⁰, ~♀¹, ~♂²}.
{+i⁰, ~t⁰, ~♀², ~♂²} (vacuous).
{+i⁰, +t⁰, ~♂¹, ~♀²}.
{+i⁰, +t⁰, ~♂², ~♀²} (vacuous).

That is, a patient is either a teamster or not; among non-teamsters, females are more frequent than males; and among teamsters, males are more frequent than females.

7.4. Subset table of anonymous completely-described patients, teamsters only, Л=2, T -> (♂¹ | ♀²).

Ю T⁰ ♀¹ ♀² ♂¹ ♂² Description Status

1 + + + ~ ~ Usual female teamster. OK

2 + + ~ ~ + ~~Weak female teamster.~~ Excluded

3 + ~ ~ + + Usual male teamster. OK

4 + ~ + + ~ Weak male teamster. OK

In this table, all males but only usual females take a job as a teamster, i.e., male teamsters (lines 2,3) are more frequent than female teamsters (line 1).

7.5. Subset table of anonymous completely-described patients, teamsters only, Л=3, T -> (♂¹ | ♀³):

Ю T⁰ ♀¹ ♀² ♀³ ♂¹ ♂² ♂³ Description

1 + + + + ~ ~ ~ Usual female teamster.

2 + + + ~ ~ ~ + ~~Weaker female teamster.~~

3 + + ~ ~ ~ + + ~~Weakest female teamster.~~

4 + ~ ~ ~ + + + Usual male teamster.

5 + ~ ~ + + + ~ Weaker male teamster.

6 + ~ + + + ~ ~ Weakest male teamster.

Д	0	1	2
1	+İ^[0]	.	.
2	.	+♀^[0]	.
3	.	.	~♂^[0]
4	.	+♂^[0]	.
5	.	.	~♀^[0]

Д	0	1	2
1	+İ^[0]	.	.
2	.	~T^[0]	.
3	.	.	♀^[1
4	.	.	♂^[2
5	.	T^[0]	.
6	.	.	♂^[1
7	.	.	♀^[2

Ю	T⁰	♀¹	♀²	♂¹	♂²	Description	Status
1	+	+	+	~	~	Usual female teamster.	OK
2	+	+	~	~	+	~~Weak female teamster.~~	Excluded
3	+	~	~	+	+	Usual male teamster.	OK
4	+	~	+	+	~	Weak male teamster.	OK

Ю	T⁰	♀¹	♀²	♀³	♂¹	♂²	♂³	Description
1	+	+	+	+	~	~	~	Usual female teamster.
2	+	+	+	~	~	~	+	~~Weaker female teamster.~~
3	+	+	~	~	~	+	+	~~Weakest female teamster.~~
4	+	~	~	~	+	+	+	Usual male teamster.
5	+	~	~	+	+	+	~	Weaker male teamster.
6	+	~	+	+	+	~	~	Weakest male teamster.

In this table, all males but only usual females take a job as a teamster, i.e., male teamsters (lines 4,5,6) are much more frequent than female teamsters (line 1).

8. THEOREMS.

8.1. THEOREM 1. Classical-logic inclusive-or.
The spreadsheet:
Д 0 1

1 +İ^[0] .

2 . +A^[0]

3 . ~A^[0]

is vacuous.
Proof. The only nandset is: {i⁰, ~a⁰, +a⁰}, which is vacuous, since it excludes no anonymous completely-decribed patient.

8.2. THEOREM 2. Classical-logic and.
The spreadsheet:

Д 0 1 2

1 +İ^[0] . .

2 . +A^[0] .

3 . . ~A^[0]

is contradictory.
Proof. The nandsets are: {i⁰, ~a⁰} [+] {i⁰, +a⁰, +a⁰} = Ø, which is contradictory, since it excludes all anonymous completely-decribed patients.

8.3. THEOREM 3. Order-logic inclusive-or.
The spreadsheet:

Д 0 1

1 +İ^[0] .

2 . +A^[1

3 . ~A^[2

is NOT vacuous.
Proof. The nandsets are: {+i⁰, ~a¹, +a²} and {+i⁰, ~a², +a²}. The first nandset is not vacuous, since it excludes the anonymous completely-decribed patient, {+i⁰, ~a⁰, ~a¹, +a²}

8.4. THEOREM 4. Order-logic and.
The spreadsheet:
Д 0 1 2

1 +İ^[0] . .

2 . +A^[1 .

3 . . ~A^[2

is contradictory.
Proof. The nandsets are: {+i⁰, ~a¹}; {+i⁰, ~a²}; {+i⁰, +a¹, +a²}; and {+i⁰, +a², +a²} = {+i⁰, +a²}. Then {+i⁰, ~a²} [+] {+i⁰, +a²} = Ø, which is contradictory.

Д	0	1
1	+İ^[0]	.
2	.	+A^[0]
3	.	~A^[0]

Д	0	1	2
1	+İ^[0]	.	.
2	.	+A^[0]	.
3	.	.	~A^[0]

Д	0	1
1	+İ^[0]	.
2	.	+A^[1
3	.	~A^[2

Д	0	1	2
1	+İ^[0]	.	.
2	.	+A^[1	.
3	.	.	~A^[2

9. PROSTATE CARCINOMA.

Simple model for prostate cancer diagnosis.

Legend:
PBX=prostate-biopsy.
PSA=serum-prostate-specific-antigen.
PRC=prostate-carcinoma.
USX=urinary-symptoms.
PFX=pathologic-fracture.
□=necessarily.
□²=necessarily necessarily.
□^k=necessarily^k.
#=it is requested that.

Д 0 1 2 3 4

0 +İ⁰ . . . .

1 . +İ⁰ . . .

2 . . ♂ . .

3 . . . ~♀ .

4 . . ♀ . .

5 . . . ~♂ .

6 . . . . □⁴~PRC

7 . +İ⁰ . . .

8 . . ~□^kX . .

9 . . □^kX . .

10 . . . □^k-1X .

11 . +İ⁰ . . .

12 . . ~♂ . .

13 . . ♂ . .

14 . . . ~>60Y .

15 . . . >60Y .

16 . . . . □²+PRC

17 . . ♂ . .

18 . . . ~USX .

19 . . . +USX .

20 . . . . □²+PRC

21 . . ♂ . .

22 . . . ~PFX .

23 . . . +PFX .

24 . . . . □⁴+PRC

25 . . ♂ . .

26 . . . ~□²+PRC .

27 . . . □²+PRC .

28 . . . . #PSA.

29 . . . □³+PRC .

30 . . . . #PBX.

Д	0	1	2	3	4
0	+İ⁰	.	.	.	.
1	.	+İ⁰	.	.	.
2	.	.	♂	.	.
3	.	.	.	~♀	.
4	.	.	♀	.	.
5	.	.	.	~♂	.
6	.	.	.	.	□⁴~PRC
7	.	+İ⁰	.	.	.
8	.	.	~□^kX	.	.
9	.	.	□^kX	.	.
10	.	.	.	□^k-1X	.
11	.	+İ⁰	.	.	.
12	.	.	~♂	.	.
13	.	.	♂	.	.
14	.	.	.	~>60Y	.
15	.	.	.	>60Y	.
16	.	.	.	.	□²+PRC
17	.	.	♂	.	.
18	.	.	.	~USX	.
19	.	.	.	+USX	.
20	.	.	.	.	□²+PRC
21	.	.	♂	.	.
22	.	.	.	~PFX	.
23	.	.	.	+PFX	.
24	.	.	.	.	□⁴+PRC
25	.	.	♂	.	.
26	.	.	.	~□²+PRC	.
27	.	.	.	□²+PRC	.
28	.	.	.	.	#PSA.
29	.	.	.	□³+PRC	.
30	.	.	.	.	#PBX.

10. ACTIVE COLITIS.

Simple model for active colitis.

Д 0 1 2

0 +İ . .

1 . ~colitis .

2 . +colitis .

3 . . +infectious colitis.

4 . . +pseudomembranous colitis.

5 . . +radiation colitis.

6 . . +ischemic colitis.

7 . . +microscopic colitis.

8 . . +diversion colitis.

9 . . +self-limited colitis.

10 . . +focal active colitis.

11 . . +inflammatory bowel disease.

11. DERMATOPATHOLOGY.

Simple model for skin biopsy diagnosis.

Д 0 1 2 3 4

0 +İ . . . .

1 . ~skin. . . .

2 . +skin. . . .

3 . . non-neoplastic dermatoses. . .

4 . . . inflammatory dermatoses. .

5 . . . . acute inflammatory dermatoses.

6 . . . . chronic inflammatory dermatoses.

7 . . . . granulomatous inflammatory dermatoses.

8 . . . . infectious dermatoses.

9 . . . vesiculobullous dermatoses. .

10 . . . follicular dermatoses. .

11 . . . atrophic dermatoses. .

12 . . . connective-tissue dermatoses. .

13 . . . reactive dermatoses. .

14 . . neoplastic dermatoses. . .

15 . . . keratinocytic neoplastic dermatoses. .

16 . . . appendageal neoplastic dermatoses. .

17 . . . fibroblastic neoplastic dermatoses. .

18 . . . melanocytic neoplastic dermatoses. .

12. EMBRYOLOGY.

Simple model for embryonic microanatomy, third week.

Д 0 1 2 3 4

0 +İ . . . .

1 . <Three weeks. . . .

2 . +Three weeks. . . .

3 . . +Amnionic cavity. . .

4 . . +Ectoderm. . .

5 . . . +Lateral ectoderm. .

6 . . . +Neuro-ectoderm. .

7 . . +Mesoderm. . .

7 . . . +Paraxial mesoderm. .

8 . . . +Somite. .

9 . . . +Intermediate mesoderm. .

10 . . . +Lateral plate mesoderm. .

11 . . . . +Somatic mesoderm.

12 . . . . +Splanchnic mesoderm.

13 . . +Entoderm. . .

14 . . +Intra-embryonic Coelom. . .

1 . >Three weeks. . . .

From Dr. Berman's Cancer Classification, based upon the embryologic origin of tumor stem cells.
embryonic
    primitive
        primitive_differentiating
           totipotent_or_multipotent_differentiating
           limited_differentiating
        germ cell
        primitive_non_differentiating
    non_primitive
        endoderm_or_ectoderm
            endoderm_or_ectoderm_surface
            endoderm_or_ectoderm_endocrine
            endoderm_or_ectoderm_parenchymal
            odontogenic_epithelium
        mesoderm
            mesenchyme
                connective_tissue
                    muscle
                    fibrous_tissue
                    vascular
                    adipose_tissue
                    bone_cartilage
                heme_lymphoid
            non_mesenchymal_mesoderm
                coelomic
                    coelomic_ductal
                    coelomic_cavities
                    coelomic_gonadal
                sub_coelomic
                    sub_coelomic_gonadal
                    sub_coelomic_endocrine
                    sub_coelomic_nephric
        neuroectoderm_neural_plate
            neural_tube
               neural_tube_parenchyma
               neural_tube_lining
            neural_crest
               peripheral_nervous_system
               neural_crest_endocrine
               neural_crest_melanocytic
Ю 0 1 2 3 4 5 6

0 +İ . . . . . .

1 . +Embryonic. . . . . .

2 . . +Primitive
embryonic. . . . .

3 . . . +Primitive
differentiating
embryonic. . . .

4 . . . . +Totipotent
or_multipotent
primitive
differentiating
embryonic. . .

5 . . . . +Limited
primitive
differentiating
embryonic. . .

6 . . . +Germ_cell
embryonic. . . .

7 . . . +Primitive
non_differentiating
embryonic. . . .

8 . . +Non-primitive
embryonic. . . . .

9 . . . +Endoderm
or_ectoderm. . . .

10 . . . . +Endoderm
or_ectoderm
surface. . .

11 . . . . +Endoderm
or_ectoderm
endocrine. . .

12 . . . . +Endoderm
or_ectoderm
parenchymal. . .

13 . . . . +Odontogenic
epithelium. . .

14 . . . +Mesoderm. . . .

15 . . . . +Mesenchyme. . .

16 . . . . . +Connective
tissue. .

17 . . . . . . +Muscle.

18 . . . . . . +Fibrous_tissue.

19 . . . . . . +Vascular.

20 . . . . . . +Adipose_tissue.

21 . . . . . . +Bone_cartilage.

22 . . . . +Non-mesenchymal
mesoderm. . .

23 . . . . . +Coelomic
mesoderm. .

24 . . . . . . +Coelomic
ductal
mesoderm.

25 . . . . . . +Coelomic
cavity
mesoderm.

26 . . . . . . +Coelomic
gonadal
mesoderm.

27 . . . . . +Subcoelomic
mesoderm. .

28 . . . . . . +Subcoelomic
gonadal
mesoderm.

29 . . . . . . +Subcoelomic
endocrine
mesoderm.

30 . . . . . . +Subcoelomic
nephric
mesoderm.

Ю	0	1	2	3	4	5	6
0	+İ	.	.	.	.	.	.
1	.	+Embryonic.	.	.	.	.	.
2	.	.	+Primitive embryonic.	.	.	.	.
3	.	.	.	+Primitive differentiating embryonic.	.	.	.
4	.	.	.	.	+Totipotent or_multipotent primitive differentiating embryonic.	.	.
5	.	.	.	.	+Limited primitive differentiating embryonic.	.	.
6	.	.	.	+Germ_cell embryonic.	.	.	.
7	.	.	.	+Primitive non_differentiating embryonic.	.	.	.
8	.	.	+Non-primitive embryonic.	.	.	.	.
9	.	.	.	+Endoderm or_ectoderm.	.	.	.
10	.	.	.	.	+Endoderm or_ectoderm surface.	.	.
11	.	.	.	.	+Endoderm or_ectoderm endocrine.	.	.
12	.	.	.	.	+Endoderm or_ectoderm parenchymal.	.	.
13	.	.	.	.	+Odontogenic epithelium.	.	.
14	.	.	.	+Mesoderm.	.	.	.
15	.	.	.	.	+Mesenchyme.	.	.
16	.	.	.	.	.	+Connective tissue.	.
17	.	.	.	.	.	.	+Muscle.
18	.	.	.	.	.	.	+Fibrous_tissue.
19	.	.	.	.	.	.	+Vascular.
20	.	.	.	.	.	.	+Adipose_tissue.
21	.	.	.	.	.	.	+Bone_cartilage.
22	.	.	.	.	+Non-mesenchymal mesoderm.	.	.
23	.	.	.	.	.	+Coelomic mesoderm.	.
24	.	.	.	.	.	.	+Coelomic ductal mesoderm.
25	.	.	.	.	.	.	+Coelomic cavity mesoderm.
26	.	.	.	.	.	.	+Coelomic gonadal mesoderm.
27	.	.	.	.	.	+Subcoelomic mesoderm.	.
28	.	.	.	.	.	.	+Subcoelomic gonadal mesoderm.
29	.	.	.	.	.	.	+Subcoelomic endocrine mesoderm.
30	.	.	.	.	.	.	+Subcoelomic nephric mesoderm.

Berman JJ.
http://www.biomedcentral.com/1471-2407/4/10

Willis RA.
The borderland of embryology and pathology.

13. LINKAGE TO MODAL LOGIC THEORY:
ETHICAL DATA COLLECTION.

13.0. M = highest level of certainty. H = last interval in time.
ÇШ = all true logical consequences of spreadsheet Ш.
çШ = all computed consequences of spreadsheet Ш.
Theorem: çШ = ÇШ.

13.1. Double-negative rule. The double-negative of each atomic-statement equals the positive of that atomic-statement.
13.1.1. For every +a C A, -a C A, -a ~= a, ++a = +a, and --a = +a.
13.1.2. For every +a C A, $^ka = $^ka; #a=#-a; !a=!-a..
13.2. Progressive certainty rule. A more-certain atomic-statement implies a less-certain atomic-statement.
13.2.1. ($^ka->$^k-1a)@Д₀.
13.2.2. Nandset definition: {+$^ka,-$^k-1a} C Д₀ for every k, 1 < k < M-1 and a C A.
13.3. Data-absolute rule. An observed-datum is equally true or false or missing-value at all levels of certainty.
13.3.1. ($d->$^Md)@Д₀.
13.3.2. Nandset definition: {$d,-$^Md} C Д₀, for every d C D.
13.4. Hippocratic rule. Data should be not collected unless needed (Hippocratic).
13.4.1. (-#d->-!d)@Д₀.
13.4.2. Nandset definition: {-#d,+!d} C Д₀, for d C D.
13.5. Conative rule. Necessary data should be collected if the patient consents (conative).
13.5.1. ((-$d&#d)->!d)@Д₀.
13.5.2. Nandset definition: {-$d,+#d,-!d} C Д₀, for d C D.
13.6. Vexative rule. Data or demanded in order of medical need.
13.6.1. keð..d-vexative: (□^ke&□^kð, ...,&-$d)->(#d| □^k+1-e) @ Д₀.
13.6.2. Nandset definition: {+$^ke,e,+$^kð,ð,..,-$d,-#d, -$^k+1e} C Д₀, for 1 < k < M-2, ðC D, and e C E.
13.7. Ontology rule. Necessary data increase one's certainty of medical entities.
13.7.1. (□^kð..)-> (□^ke|□^k+1-e) @ Д₀, 1<k<M-2.
What is □^M-e?
Or, more interestingly, what is □^∞-e?
13.7.2. Nandset definition: {+$^kð,ð,..,-e,-$^k+1e} C Д₀, for 1 < k < M-2, d C D, ð c (D - {+d,-d}).
13.8. Ethical data collection rule. All ethical data are either positive, negative, failed-attempt, or not-attempted.
13.8.0. If d is d-Hippocratic, then there exists at most one I, 1 < I < H, such that:
13.8.1. (POS-DATA): +$d, +d, +!d true for Д_I, xor
13.8.2. (NEG-DATA): +$d, -d, +!d true for Д_I, xor
13.8.3. (FAIL-DATA): -$d, +!d true for Д_I, xor
13.8.4. (NOTRY-DATA): -$d, +$d, -#d, +#d, -!d, +!d not true for Д_I.
13.9. Cover Rule. Entities are re-calculated at each moment in time, based upon available evidence at the time; Data, once collected, are never changed or forgotten.
13.9.1. It is true that -$^ka @ C_I if and only if it is not true that $^ka @ ÇД_I
13.9.2. Nandset definition: {$^ka} C C_I if and only if {-$^ka} ~ C ÇД_I, for 1 < I < H, 1 < k < M, and a C A.

14. CONTINGENCY TABLE ANALYSIS.

Evidence-based statistical measures for order-logic.

14.1. A 2×2 CONTINGENCY TABLE is a rectangular table in which one binary factor (example: sex, ♀ vs. ♂) is compared to a second binary factor (example: teamster, ~T vs. T):
Д ♀ ♂ .

~T a b v

+T c d w

. x y z

14.2. Now suppose that 250 female employees and 250 male employees from a particular shipping company are surveyed, and the OBSERVED VALUES for totals, are as follows:
Д ♀ ♂ .

~T 245 205 450

+T 5 45 50

. 250 250 500
Is the result statistically significant? That is, are there disproportionately more male-teamsters than female-teamsters?

14.3. The raw-data values, 245=a, 205=b, 5=c, 45=d, are the cell-totals. The row-sum values, 245+205=450=v and 5+45=50=w are the row-totals. The column-sum values, 245+5=250=x and 205+45=250=y are the column-totals. The sum of all cell-totals, which equals the the sum of the row-totals, as well as the sum of the column-totals, is the grand-total, a+b+c+d=v+w=x+y=z.

14.4. The usual statistical analysis procedures are: the X² test and the Fisher exact test. In these tests, we obtain EXPECTED VALUES for totals, as follows:
Д ♀ ♂ .

~T A B V

+T C D W

. X Y Z

where V=v; W=w; X=x; Y=y; and Z=z (i.e., marginal and grand totals are equal to observed); and A=(V×X)/Z; B=(V×Y)/Z; C=(W×X)/Z; and D=(W×Y)/Z. For the example: A=225, B=225, C=25, D=25, V=450, U=50, W=50, Z=500.

14.5. In the TOKEN SWAP TEST, one starts with the expected value of, say, the upper left cell, A, and adds (or subtracts) tokens from A, one by one, until A -> A=1 -> A+2 -> -> a, in a manner that the marginal totals remain constant. That is, if A -> A+1, then B -> B-1, C -> C-1, D -> D+1, so that V = (A+1)+(B-1) = v, W = (C-1)+(D+1) = w, X = (A+1)+(C-1) = x, and Y = (B-1)+(D+1) = y, Thus, in general, if A -> -> A+q, then B -> B-q, C -> C-q, and D -> D+q.

14.6. When A+q -> A+q+1, then there are B-q tokens that may be drawn from the upper right cell and D-q tokens that may be drawn from the lower left cell. But when A+q -> A+q-1, B-q+1 tokens that may be drawn from the upper right cell and D-q+1 tokens that may be drawn from the lower left cell. Thus there are ... swaps that increase A+q to A+q+1, and ... swaps that decrease A+q to A+q-1. This generates a token swap distribution.....

14.7. The superiority of the token swap test over traditional contingency table analysis is that one can initialized the expected values at A+Q, ... , based upon your medical experience, where max(-A,-D) < Q < min(B,C). For example, if one expects that male teamsters would be twice as numerous as female teamsters, then one could force 2×C = D, and solve for Q. In traditional analyses, Q is required to be zero.

14.8. In this report, we suggest that the token swap test is a more appropriate analysis, since the expected values of the cell-totals are not preset by statistical theory, but can be manipulated according to medical experience.

Д	♀	♂	.
~T	a	b	v
+T	c	d	w
.	x	y	z

Д	♀	♂	.
~T	245	205	450
+T	5	45	50
.	250	250	500

Д	♀	♂	.
~T	A	B	V
+T	C	D	W
.	X	Y	Z

15. DISCUSSION.

15.1. Two intellectual pillars of anatomic pathology informatics: image-recognition; concept-management.
15.2. Concepts in in descending order of importance on spreadsheet.
15.3. Syllogistic quality of reasoning in anatomic pathology.
15.4. Some statements with greater weight than others.
15.5. Formalism is ordinal, not cardinal,
15.6. Stepwise character of medical intentions and therapies.
15.7. Reduces to classical symbolic logic if all superscripts are zero.
15.8. Supports theories of ethical data collection and contingency table analysis.
15.9. Mathematical theories can organize medical knowledge and patient data.
15.10. Can enhance clinicopathologic data collection and surveillance.

П	.	.
.	Bill	♂

in spreadsheet notation; as Bill -> ♂ in symbolic logic notation; and as {Bill, ~♂} in nandset notation, i.e., Bill and ~♂ are not all true at once.

9B. In the PATIENT-FOLIO, П, rows in the patient-folio correspond to individual patients, and columns correspond to observations/data and medical-entities. The zeroth column in the patient-folio is the list of unique identifiers for each patient. Column 1 in the patient-folio is a hypothetical entity, denoted İ, called İMPORTANCE. By fiat, every patient is important, so that the value of each cell in column 1 is TRUE. All other patient-folio-cells may assume the values TRUE(+), FALSE (~), or MISSING-VALUE (=empty-cell). These patient-folio-columns contain the true/false/missing-value status of DATA (complaints, medical history, physical findings, laboratory values, statements of consent, etc.); or MEDICAL-ENTITIES (body-site, cancer, inflammation, necrosis, etc.), as applied to that patient. Quantitative, interval, ranked, and categorical data are reformulated as true-false statements. Initially, only data-cells (but not necessarily ALL the data-cells) are FILLED-IN as true or false for a particular patient. Each initial element of the patient-folio assumes ORDER ZERO. For example:

П	0	1	2	3
1	Mary	+İ	+♀	~♂
2	Bill	+İ	~♀	+♂
3	Pat	+İ	+♀	~♂
4	Leslie	+İ	~♀	+♂

In this patient-folio, Mary and Pat are female-not-male; and Bill and Leslie are male-not-female. Note that Pat and Leslie are ambiguous given-names.

9C. In the disease-folio, the topmost-leftmost cell contains the İMPORTANCE-ORIGIN, İ⁰. The topmost row and leftmost column are otherwise empty. Every filled-in cell is either a parent or a child or both. Every parent has one-or-more children. The first child is placed one-step-down-one-step-right from its parent. Subsequent children of the same parent are placed in the same column as their siblings, in consecutive rows, unless they have their own children. Each row has one-and-only-one filled-in cell, up through the final row. Each column has at least one filled-in cell, up through the final column. Every child has exactly one parent. For the first child in a sibship, the parent appears one-step-up-one-step-left from that child. For subsequent children in the sibship, their parent appears one-step-left and the first filled-in-cell-up. There are nrow rows, and each row contains exactly one filled-in cell. At each parent in the disease-folio, the classical symbolic logic expression for this parent-cell is: (İ & ... great-grandparent & grandparent & parent) implies (child₁ or child₂ or child₃ or ...). For example, the following disease-folio asserts that female implies not-male and male implies not-female:

Д	0	1	2
1	+İ	.	.
2	.	+♀	.
3	.	.	~♂
4	.	+♂	.
5	.	.	~♀

In this disease-folio, there are three parents: the filled-in-cells in rows 1, 2, and 4. There are four children: the filled-in-cells in rows 2, 3, 4, and 5. There are three firstborns: the filled-in-cells in rows 2, 3, and 5. The parent of row-2 is row-1; the parent of row-3 is row-2; and the parent of row-5 is row-2. There are three implications in classical symbolic logic asserted by this disease-folio, as follows:

İ implies +♀ or +♂.
İ and +♀ implies ~♂.
İ and +♂ implies ~♀.

The three firstborns in this disease-folio, correspond to rows 2, 3, and 5. Each of the implications in the disease-folio corresponds to a unique firstborn:

Row 2: İ implies +♀ or +♂.
Row 3: İ and +♀ implies ~♂.
Row 5: İ and +♂ implies ~♀.

10. SEMANTIC MODEL: ANONYMOUS COMPLETELY DESCRIBED PATIENTS.

10A. The SEMANTIC MODEL for this spreadsheet is the universe, Ю, of ANONYMOUS, COMPLETELY-DESCRIBED PATIENTS (ACDPs), where each row is an ACDP, and each column is a datum/entity. In classical symbolic logic, Ю is the TRUTH TABLE. Each row may have an ORDER-NUMBER for that datum/entity, where order ranges from 1 to Л. If all order-numbers are zero, then the semantic model satisfies the axioms of classical symbolic logic.

Ю	1	2	3
1	+İ	+♀	+♂
2	+İ	+♀	~♂
3	+İ	~♀	+♂
4	+İ	~♀	~♂
5	~İ	+♀	+♂
6	~İ	+♀	~♂
7	~İ	~♀	+♂
8	~İ	~♀	~♂

10B. The set theory model employs an ATOMSET of distinct, statements (atoms, A), each of which has a definite true-false status (no self-reference paradoxes). Each atom is either a unique PATIENT-IDENTIFIER, a DATUM, or a MEDICAL-ENTITY, with a special medical-entity, called İMPORTANCE-ORIGIN, İ⁰. A patient-atom has no negation. Each non-patient atom, a C (A-P), has an EXACT NEGATION, ~a C (A-P), that is also an atom. There is a ORDERATOMSET, Q, where for each a C (A-P), there exists an aⁱ C Q, 0 < i < Л. Each member of an ACDP, ю C Ю, has the property that: if aⁱ C ю, then ~aⁱ ~C ю; Furthermore, this ю C Ю has an ultimate element, a^Л C ю c Q, and an INFLECTION POINT, I, 0 < I < Л, such that ~a^j C ю, where 0 < j < I, and +a^k C ю, where I < k < Л. That is, a^j/a^Л = -1 for 0 < j < I, and a^k/a^Л = +1 for I < k < Л.

10C. To each classical symbolic logic expression, there corresponds exactly one NANDSET, i.e., a set of conditions that cannot all be true at once. It is demonstrated in this report that if X is a nandset for the spreadsheet, and X c Y, then Y is a nandset for the spreadsheet. The universal operation for nandsets is: NANDSET ADDITION, [+]. It is demonstrated that if X, Y are nandsets for the spreadsheet, then X [+] Y is a nandset for the spreadsheet. Furthermore, an exhaustive operation of nandset-additions is possible in polynomial time, and suffices to find all logical consequences of the initial spreadsheet.

11. EXAMPLE: SEXES.

11A. For the sake of discussion, let us assert that there are exactly two sexes, male and female, and that every patient has at least one sex.

7. EXAMPLE: SEXES.

Classical-logic:

Every (important) patient, İ, is either a female, ♀, or a male, ♂. If a patient is female, then the patient is not-male. If a patient is male, then the patient is not-female.
Д 0 1 2

1 +İ^[0] . .

2 . +♀^[0] .

3 . . ~♂^[0]

4 . +♂^[0] .

5 . . ~♀^[0]

Order-logic:
Every patient, İ, is either a teamster, T or else not-a-teamster, ~T. Among teamsters, males are more frequent than females.
Д 0 1 2

1 +İ^[0] . .

2 . ~T^[0] .

3 . . ♀^[1

4 . . ♂^[2

5 . T^[0] .

6 . . ♂^[1

7 . . ♀^[2

The nandsets are:
{+i⁰, +t⁰, ~t⁰}.
{+i⁰, ~t⁰, ~♀¹, ~♂²}.
{+i⁰, ~t⁰, ~♀², ~♂²} (vacuous).
{+i⁰, +t⁰, ~♂¹, ~♀²}.
{+i⁰, +t⁰, ~♂², ~♀²} (vacuous).

That is, a patient is either a teamster or not; among non-teamsters, females are more frequent than males; and among teamsters, males are more frequent than females.

Subset table of anonymous completely-described patients, teamsters only:
Ю T⁰ ♀¹ ♀² ♂¹ ♂² Description Status

1 + + + ~ ~ Usual female. OK

2 + + ~ ~ + ~~Weak female.~~ Excluded

3 + ~ ~ + + Usual male. OK

4 + ~ + + ~ Weak male. OK

In this table, all males but only usual females take a job as a teamster.

Д	0	1	2
1	+İ^[0]	.	.
2	.	+♀^[0]	.
3	.	.	~♂^[0]
4	.	+♂^[0]	.
5	.	.	~♀^[0]

Д	0	1	2
1	+İ^[0]	.	.
2	.	~T^[0]	.
3	.	.	♀^[1
4	.	.	♂^[2
5	.	T^[0]	.
6	.	.	♂^[1
7	.	.	♀^[2

Ю	T⁰	♀¹	♀²	♂¹	♂²	Description	Status
1	+	+	+	~	~	Usual female.	OK
2	+	+	~	~	+	~~Weak female.~~	Excluded
3	+	~	~	+	+	Usual male.	OK
4	+	~	+	+	~	Weak male.	OK

11B. In the DISEASE-FOLIO, Д c Ш, of the spreadsheet-representation, Ш, rows are listed in order of the İMPORTANCE, İ, of a particular datum/entity. Each filled-in cell in Д is either a DATUM, D, or an ENTITY, E. Every filled-in cell is either a PARENT or a CHILD, or both. The upper-left-cell, or ultimate parent, or İMPORTANCE-ORIGIN, contains İ⁰, and the topmost row and leftmost column are otherwise empty. Every occurrence of İ in a disease-folio (or in a patient-folio) is İ⁰. Every parent has one-or-more children. The first child is placed one-step-down-one-step-right from its parent. Subsequent children of the same parent are placed in the same column as their siblings, in consecutive rows, unless they have their own children. Each row has one-and-only-one filled-in cell, up through the final row, denoted row Д_R. Each column has at least one filled-in cell, up through the final column, denoted column Д_C. Every child has exactly one parent. For the first child in a sibship, the parent appears one-step-up-one-step-left from that child. For subsequent children in the sibship, their parent appears one-step-left and the first filled-in-cell-up.

In a simple spreadsheet example, Д, we assert that every patient is either male or female, with no other possibilities:

Д	0	1
0	+İ	.
1	.	+♀
2	.	+♂

It is convenient to label the medical-descriptors by the row in which they occur, namely:

Д	0	1
0	+İ⁰	.
1	.	+♀¹
2	.	+♂²

11C. Now let us consider the row-numbers as negative powers-of-two, in a PROBABILISTIC/BAYES INTERPRETATION. Worldwide, females are slightly more numerous than males. We may consider two minor occupational groups: teamsters and nurses. (I am guessing:) Teamsters are more numerous than nurses. Among teamsters, males are considerably more numerous than females. Among nurses, females are considerably more numerous than males. Therefore, if Bill's sex were unknown, but one knows that (i.e., has data that) Bill is a teamster, then it is reasonable (but not absolute) to conclude that Bill is a male. Likewise, if Mary's sex were unknown, but one knows that Mary is a nurse, then it is reasonable (but not absolute) to conclude that Mary is a female. This vignette is summarized as:

Д	0	1	2
0	+İ^[0]	.	.
1	.	~teamster, ~nurse^[0]	.
2	.	.	+♀^[1
3	.	.	+♂^[2
4	.	+teamster^[0]	.
5	.	.	+♂^[1
6	.	.	+♀^[2
7	.	+nurse.⁷	.
8	.	.	+♀^[1
9	.	.	+♂^[2

The default-order for each element is the row-number. However, we hold in reserve the right to change any of the orders of any of the elements in the disease-folio, except for İ⁰. By fiat, every occurrence of İ in a disease-folio is İ⁰; and every occurrence of ~İ in a disease-folio is ~İ⁰;

11D. Finally, we might wish to include the information that every male is not a female, and every female is not a male, as follows:

Д	0	1	2	3
0	+İ⁰	.	.	.
1	.	+İ⁰	.	.
2	.	.	non-teamster non-nurse².	.
3	.	.	.	+♀³
4	.	.	.	+♂⁴
5	.	.	teamster⁵.	.
6	.	.	.	+♂⁶
7	.	.	.	+♀⁷
8	.	.	nurse.⁸	.
9	.	.	.	+♀⁹
10	.	.	.	+♂¹⁰
11	.	+İ⁰	.	.
12	.	.	+♀¹	.
13	.	.	.	~♂¹
14	.	.	+♂¹	.
15	.	.	.	~♀¹

In this example, Д, but not Д, may be used to fill in the missing data in П₁, so that П₁ becomes П₀.

12. DESCRIPTION OF ORDER SYMBOLIC LOGIC FOR DISEASE-FOLIO.

12A. The hierarchical architecture of the disease-folio can be expressed in the notation of classical symbolic logic. Every parent, P, in the disease-folio, Д, has one-or-more children, C₁, C₂, C₃, C₄, .... The first child C₁, is placed one-step-down-one-step-right from its parent, P. Subsequent children of the same parent C₂, C₃, C₄,..., are placed in the same column as their siblings. In classical symbolic logic, we say: P -> (C₁ | C₂ | C₃ | C₄ | ...), where | denotes inclusive-or. The NANDSET for this expression is: {+P, ~C₁, ~C₂, ~C₃, ~C₄, ...}, where ~ denotes NOT, i.e., not all of +P, ~C₁, ~C₂, ~C₃, ~C₄, ..., can be true at once. Furthermore, if C₁ has one-or-more children, i.e., grandchildren of P, namely, G₁, G₂, G₃, G₄, ..., then in classical symbolic logic, we say: (P & C₁) -> (G₁ | G₂ | G₃ | G₄ | ...), where & denotes logical-and. The nandset for this classical logic expression is: {+P, +C₁, ~G₁, ~G₂, ~G₃, ~G₄, ...}.

Д	0	1	2	3
0	+İ	.	.	.
1	.	+P	.	.
2	.	.	+C₁	.
3	.	.	.	+G₁
4	.	.	.	+G₂
5	.	.	.	+G₃
6	.	.	.	+G₄
7	.	.	+C₂	.
8	.	.	+C₃	.
9	.	.	+C₄	.

12B. The ZERMELO-FRANKEL SET THEORY REPRESENTATION FOR SPREADSHEET ORDER-LOGIC consists of the ATOMSET, A, that is comprised of atoms, a, ~a, b, ~b, c, ~c, ....., i.e., A = {+a, ~a, +b, ~b, +c, ~c, .....}, Each atom, a, has one-and-only-one negation, denoted ~a, i.e, for every {a} c A, there exists a unique {~a} c A, where a ~= ~a. Each atom has Л DIMENSIONS, where {..., a,...} = {..., a¹,...} = {..., ₁a,...}, {..., ₂a,...}, {..., ₃a,...}, ..., {..., _Лa,...}; {..., a²,...} = {..., ₂a,...}, {..., ₃a,...}, ..., {..., _Лa,...}; and {..., a^Л,...} = {..., _Лa,...}. Counter Л corresponds to the number of lines/rows in the disease-folio, R_Д. The zeroth and negative rows are undefined, i.e., aⁱ is undefined for non-positive rows.

12C. For both the PATIENT-FOLIO, П, and the DISEASE-FOLIO, Д, it is convenient to perform calculations on NANDSETS. A NANDSET, X = {a, b, c, ...}, is a set of conditions that cannot all be true at once. Advantage of the nandset: order-neutral, unlike ->. By definition, there exists no nandset, X, and no {aⁱ}, {~a^j} c A, such that {aⁱ, ~a^j} c X. Such a nandset is called VACUOUS. Also, by definition of dimension, if i < j and {aⁱ} c X, then {a^j} c X, but not necessarily vice-versa. Finally, if nandsets {aⁱ}, {~a^j} c X, then set X is INCONSISTENT.

15. RESULTS: ACTIVE COLITIS.

15A. In a simple example, let us assert that active colitis, AC², can only have three causes: ulcerative colitis, UC³; Crohn's disease, CD⁴; and infectious colitis, IC⁵, in that order. Then the corresponding nandset is: {AC², ~UC³, ~CD⁴, ~IC⁵}. We say that: {AC², ~UC³, ~CD⁴, ~IC⁵} C Д. That is, if the patient has AC², then the patient cannot also lack UC³, CD⁴, and IC⁵. In the COMMENT SECTION of the surgical pathology report, the pathologist might write: the differential diagnosis includes: UC³, CD⁴, or IC⁵. Furthermore, the pathologist's report may RANK the differential diagnosis frequency, diagnostic certainty, therapeutic susceptibility, etc.

15B. For the patient, Smith, with AC², the patient-folio-nandset is: {Smith, ~AC²} C П. We may COMBINE two nandsets, with NANDSET ADDITION, ⊕, as described below. In this example, {Smith, ~AC²} ⊕ {AC², ~UC³, ~CD⁴, ~IC⁵} -> {Smith, ~UC³, ~CD⁴, ~IC⁵}; read: Smith has either UC³, CD⁴, or IC⁵, in that order.

Д	0	1	2
0	+İ	.	.
1	.	~AC	.
2	.	+AC	.
3	.	.	+UC
4	.	.	+CD
5	.	.	+IC

19. In a SPREADSHEET example:

Д	0	1	2	3
0	+İ	.	.	.
1	.	~colitis	.	.
2	.	+colitis	.	.
3	.	.	+infectious colitis.	.
4	.	.	+pseudomembranous colitis.	.
5	.	.	+radiation colitis.	.
6	.	.	+ischemic colitis.	.
7	.	.	+microscopic colitis.	.
8	.	.	.	+lymphocytic colitis.
9	.	.	.	+collagenous colitis.
10	.	.	+diversion colitis.	.
11	.	.	+self-limited colitis.	.
12	.	.	+focal active colitis.	.
13	.	.	+inflammatory bowel disease.	.
14	.	.	.	+ulcerative colitis.
15	.	.	.	+Crohn's disease.

...............

20. In a still more complete example:


 İ
     ~colitis
     +colitis.
        +infectious colitis.
        +pseudomembranous colitis.
        +radiation colitis.
        +ischemic colitis.
        +microscopic colitis.
           +lymphocytic colitis.
           +collagenous colitis.
        +diversion colitis.
        +self-limited colitis.
        +focal active colitis.
        +inflammatory bowel disease.
           +ulcerative colitis.
           +Crohn's colitis.
     +colitis.
        infectious colitis.
           acute onset.
           short duration.
           fever.
           diarrhea.
           crypt abscesses.
           goblet cell depletion.
           amebic colitis.
              amebic colitis.
                 trophozooites.
                 Entamoeba histolytica.
                 typical organisms: 40µm, abundant pink cytoplasm.
                    ingested erythrocytes.
              amebic colitis.
                 focal ulceration.
                 patchy ulcers.
                    cecum.
                    appendix.
                    rectosigmoid.
        pseudomembranous colitis.
           recent antibiotic administration.
           diarrhea.
           abdominal pain.
           pseudomembranes on endoscopy.
        radiation colitis.
           > 45,000 rads to colon.
           acute or chronic inflammation.
           diarrhea.
           abdominal pain.
           dusky mucosa endoscopically.
           edema endoscopically.
           loss of superficial vascularity endoscopically.
           acute phase radiation colitis.
              edema.
              vascular dilatation.
              acute cryptitis.
              superficial ulceration.
           chronic phase radiation colitis.
              stromal fibrosis.
              atypical fibroblasts.
              thickened subepithelial collagen.
              glandular atrophy.
              glandular distortion.
              vascular fibrosis.
              vascular intimal thickening.
              enlarged endothelial cells.
        ischemic colitis.
           elderly patient.
           acute onset.
           diarrhea.
           abdominal pain.
           nausea.
           vomiting.
           hematochezia.
           mild ischemic colitis.
              superficial hemorrhage.
              patchy mucosal necrosis.
              dilated vasculature.
              regenerating crypts.
           severe ischemic colitis.
              crypt dropout.
              acute inflammation.
              acute cryptitis.
              coagulative necrosis.
           late ischemic colitis.
              granulation tissue.
              scarring.
        microscopic colitis.
           microscopic colitis.
              watery diarrhea.
                 normal colonoscopy.
              usually ♀.
           microscopic colitis.
              lymphocytic colitis.
                 increased chronic inflammation in lamina propria.
                    >20 intraepithelial lymphocytes per 100 enterocytes.
              collagenous colitis.
                 thickened subepithelial collagen.
                 feathery strands of collogen between glands.
                 Paneth cell metaplasia.
                 mixed inflammation, lamina propria.
                 patchy denuded epithelium.
                 naked lamina propria.
        diversion colitis.
           colon excluded from fecal stream.
           prominent lymphoid aggregates.
           neutrophils, rare crypt abscess.
           normal crypt architecture.
        self-limited colitis.
           self-limited colitis.
              self-limited, short-lived clinical course.
              sudden onset, diarrhea, abdominal pain.
           self-limited colitis.
              acute phase self-limited colitis.
                 lamina propria hemorrhage, congestion.
                 detached, necrotic surface epithelium.
                 prominent acute inflammation, > chronic inflammation.
                 no crypt distortion.
              chronic phase self-limited colitis.
                 lamina propria fibrosis.
                 crypt distortion.
        focal active colitis.
           patchy neutrophilic infiltrates.
           without glandular distortion.
           without crypt abscesses.
        inflammatory bowel disease.
           inflammatory bowel disease.
              mixed inflammation of lamina propria.
              plasma cells reaching to muscularis mucosae.
              glandular mucus depletion.
              occasional Paneth cell metaplasia.
           inflammatory bowel disease.
              ulcerative colitis.
                 dense lymphoplasmacytic and neutrophilic infiltrate.
                 typically infiltrate limited to mucosa.
                 typically involves rectum, without skip lesions.
                 may involve entire colon = pancolitis.
                 may spill into ileum = backwash ileitis.
                 irregular areas of ulceration.
                 surrounding islands of preserved mucosa = pseudopolyps.
                 normal serosa.
              Crohn's colitis.
                 fissuring.
                    penetrate muscularis propria.
                    serosal involvement.
                 acute inflammation.
                 granulomas.
                 patchy transmural chronic inflammation.
                 intervening normal areas = skip lesions.

14. RESULTS: PROSTATE CARCINOMA.

14A. Another example: PROSTATE CANCER, where the variables are:

♂ = male.
♀ = female.
prc = prostate-cancer.
psa = prostate-specific-antigen.
pfx = pathologic-fracture positive for prostate-cancer.
pbx = prostate-biopsy.
>30 = >30 years old.
>60 = >60 years old.
usx = urinary tract symptoms.
□ = necessarily; □² = necessarily-necessarily,....
# = intentionally.

Note that if a statement about a patient is necessarily² true, then the statement is necessarily true; if a statement about a patient is necessarily³ true, then the statement is necessarily² true; ....

14B. NARRATIVE: Every patient is important. Every important patient is either: male (♂) or female (♀), not both and not neither. For every condition X, necessarilyⁱ⁺¹X implies necessarilyⁱX.
Every (important) male necessarily¹ has prostate cancer, at the lowest level (□+prc). Every female necessarily⁴ does not have prostate cancer. If a male is >60 years old, or has urinary tract symptoms, then he necessarily² has prostate cancer. If a male has a pathologic fracture positive for prostate cancer, then he necessarily⁴ has prostate cancer.
If a male necessarily² has prostate cancer, then his physician intends to obtain a prostatic-specific-antigen test. If the male has a positive a prostatic-specific-antigen test, then he necessarily³ has prostate cancer. If a male necessarily³ has prostate cancer, then his physician intends to perform a prostate biopsy.
If a male either presents with a pathologic-fracture containing prostate cancer, or has a positive prostate-biopsy, then he necessarily⁴ has prostate cancer, and should receive therapy.

14C. Prostate cancer. SPREADSHEET.

Д	0	1	2	3	4	5
0	+İ⁰	.	.	.	.	.
1	.	+İ⁰	.	.	.	.
2	.	.	♂	.	.	.
3	.	.	.	~♀	.	.
4	.	.	♀	.	.	.
5	.	.	.	~♂	.	.
6	.	.	.	.	□⁴~prostate-cancer	.
7	.	+İ⁰	.	.	.	.
8	.	.	~□^kX	.	.	.
9	.	.	□^kX	.	.	.
10	.	.	.	□^k-1X	.	.
11	.	+İ⁰	.	.	.	.
12	.	.	~♂	.	.	.
13	.	.	♂	.	.	.
14	.	.	.	~>60	.	.
15	.	.	.	>60	.	.
16	.	.	.	.	□²+prostate-cancer	.
17	.	.	♂	.	.	.
18	.	.	.	~urinary symptoms	.	.
19	.	.	.	urinary symptoms	.	.
20	.	.	.	.	□²+prostate-cancer	.
21	.	.	♂	.	.	.
22	.	.	.	~pathologic fracture.	.	.
23	.	.	.	pathologic fracture.	.	.
24	.	.	.	.	□⁴+prostate-cancer	.
25	.	.	♂	.	.	.
26	.	.	.	~□²+prostate-cancer	.	.
27	.	.	.	□²+prostate-cancer.	.	.
28	.	.	.	.	request serum PSA.	.
29	.	.	.	□³+prostate-cancer.	.	.
30	.	.	.	.	request prostate biopsy.	.

18. RESULTS: EMBRYOLOGY.

23. Another example: Approach to the Embryo. NARRATIVE.

23a. Approach to the Embryo. SPREADSHEET.



 +Carnegie Embryologic Developmental Horizons/Staging
      +Stage 1.
          +Zygote.
      +Stage 2.
      +Stage 3.
      +Stage 4.
      +Stage 5.
      +Stage 6.
      +Stage 7.
      +Stage 8.
      +Stage 9.
      +Stage 10.
      +Stage 11.
      +Stage 12.
      +Stage 13.
      +Stage 14.
      +Stage 15.
      +Stage 16.
      +Stage 17.
      +Stage 18.
      +Stage 19.
      +Stage 20.
      +Stage 21.
      +Stage 22.
      +Stage 23.

23b. Approach to the Embryo. SPREADSHEET.


 ~Three weeks.
 +Three weeks.
     +Amnionic cavity.
     +Ectoderm.
         +Lateral ectoderm.
         +neuro-ectoderm.
     +Mesoderm: dorsal-to-ventral.
         +Paraxial mesoderm.
         +somite.
         +Intermediate mesoderm.
              +cervical intermediate mesoderm.
              +thoracic-lumbar intermediate mesoderm.
                   +nephrogenic cord.
                        +excretory urinary system.
                             +nephrotomes.
                                  +nephric tubular epithelium.
                                  +nephric tubular lumen.
                                  +opening into intra-embryonic coelom.
         +lateral plate mesoderm.
              +somatic mesoderm.
              +Splanchnic mesoderm.
     +Entoderm.
     +Intra-embryonic coelom.

16. RESULTS: DERMATOPATHOLOGY.

24. Another example: Approach to the Skin. NARRATIVE.

24a. Approach to the Skin. SPREADSHEET.

Д	0	1	2	3	4
0	+İ	.	.	.	.
1	.	~skin.	.	.	.
2	.	+skin.	.	.	.
3	.	.	non-neoplastic dermatoses.	.	.
4	.	.	.	inflammatory dermatoses.	.
5	.	.	.	.	acute inflammatory dermatoses.
6	.	.	.	.	chronic inflammatory dermatoses.
7	.	.	.	.	granulomatous inflammatory dermatoses.
8	.	.	.	.	infectious dermatoses.
9	.	.	.	vesiculobullous dermatoses.	.
10	.	.	.	follicular dermatoses.	.
11	.	.	.	atrophic dermatoses.	.
12	.	.	.	connective-tissue dermatoses.	.
13	.	.	.	reactive dermatoses.	.
14	.	.	neoplastic dermatoses.	.	.
15	.	.	.	keratinocytic neoplastic dermatoses.	.
16	.	.	.	appendageal neoplastic dermatoses.	.
17	.	.	.	fibroblastic neoplastic dermatoses.	.
18	.	.	.	melanocytic neoplastic dermatoses.	.

25. Another example: PSORIASIFORM DERMATITIS. NARRATIVE.

26. PSORIASIFORM DERMATITIS. SPREADSHEET.

Д	0	1	2	3	4
0	+İ	.	.	.	.
1	.	~skin.	.	.	.
2	.	+skin.	.	.	.
3	.	.	~PSORIASIFORM DERMATITIS.	.	.
4	.	.	+PSORIASIFORM DERMATITIS.	.	.
5	.	.	.	Psoriasis	.
6	.	.	.	.	Munro microabscess.
7	.	.	.	Healed psoriasis.	.
8	.	.	.	Prurigo nodularis.	.

27. Another example: LICHENOID INTERFACE DERMATITIS. NARRATIVE.

28. LICHENOID INTERFACE DERMATITIS. SPREADSHEET.

Д	0	1	2	3	4
0	+İ	.	.	.	.
1	.	~skin.	.	.	.
2	.	+skin.	.	.	.
3	.	.	~LICHENOID INTERFACE DERMATITIS.	.	.
4	.	.	+Lichenoid interface dermatitis.	.	.
5	.	.	.	Connective Tissue Disease, e.g., Lupus erythematosus.	.
6	.	.	.	Lichen planus.	.
7	.	.	.	Photodermatitis.	.
8	.	.	.	Drug reaction.	.
9	.	.	.	Lichen sclerosus et atrophicus.	.
10	.	.	.	Poikiloderma atrophicans vasculare.	.
11	.	.	.	Graft-vs-host disease.	.
12	.	.	.	Lichen nitidus.	.
13	.	.	.	Lichenoid actinic keratosis.	.
14	.	.	.	Secondary syphilis.	.
15	.	.	.	.	superficial dermal plasma cell proliferation.
16	.	.	.	Arthropod bite reaction.	.
17	.	.	.	Lichenoid benign keratosis.	.
18	.	.	.	Parapsoriasis.	.
19	.	.	.	Chronic progressive pigmented purpura.	.
20	.	.	.	Mycosis fungoides, patch stage.	.
21	.	.	.	.	Pautrier microabscess.
22	.	.	.	.	Spongiform pustule of Kogoj.

29. Another example: ERYTHRODERMA. NARRATIVE.

30. ERYTHRODERMA. SPREADSHEET.

Д	0	1	2	3	4
0	+İ	.	.	.	.
1	.	~skin.	.	.	.
2	.	+skin.	.	.	.
3	.	.	~ERYTHRODERMA.	.	.
4	.	.	+ERYTHRODERMA.	.	.
5	.	.	.	Sezary syndrome.	.
6	.	.	.	Seborrheic dermatitis.	.
7	.	.	.	Psoriasis.	.
8	.	.	.	Drug reaction.	.
9	.	.	.	Toxic epidermal necrolysis.	.
10	.	.	.	Sunburn. Radiation burn. First degree burn.	.
11	.	.	.	Visceral malignancies with erythema.	.
12	.	.	.	Pityriasis rubra pilaris.	.

31. Another example: Vesicular dermatitis. NARRATIVE.

32. Vesicular dermatitis. SPREADSHEET.

Д	0	1	2	3	4
0	+İ	.	.	.	.
1	.	~dermatitis.	.	.	.
2	.	+dermatitis.	.	.	.
3	.	.	~vesicular dermatitis.	.	.
4	.	.	+vesicular dermatitis.	.	.
5	.	.	.	+subcorneal pustule.	.
6	.	.	.	.	+subcorneal pustular dermatosis.
7	.	.	.	.	dermatophytosis.
8	.	.	.	.	bullous impetigo.
9	.	.	.	+intraepidermal acantholytic vesicular dermatitis.	.
10	.	.	.	.	pemphigus vulgaris.
11	.	.	.	.	Darier's disease.
12	.	.	.	.	Hailey-Hailey disease.
13	.	.	.	.	Grover's disease.
14	.	.	.	.	Herpesvirus infection.
15	.	.	.	.	Staphylococcal scalded skin syndrome.
16	.	.	.	+subepidermal vesicular dermatitis.	.
17	.	.	.	.	epidermolysis bullosa acquisita.
18	.	.	.	.	porphyria cutanea tarda.
19	.	.	.	.	bullous pemphigoid.
20	.	.	.	.	herpes gestationis.
21	.	.	.	.	dermatitis herpetiformis.
22	.	.	.	.	linear IgA dermatosis.
23	.	.	.	.	subacute cutaneous lupus erythematosus.

33. Vesicular dermatitis. FLOW CHART.


 İ
     ~dermatitis.
     +dermatitis.
        ~vesicular dermatitis.
        +vesicular dermatitis.
           subcorneal pustule.
           intraepidermal acantholytic vesicular dermatitis.
           subepidermal vesicular dermatitis.
        +vesicular dermatitis.
           +subcorneal pustule.
              subcorneal pustular dermatosis.
                 subcorneal pustular dermatosis.
                    Sneddon-Wilkinson disease.
                 subcorneal pustular dermatosis.
                    subcorneal neutrophils, rare eosinophils.
                    mild epidermal spongiosis.
                    superficial perivascular neutrophilic infiltrate.
              dermatophytosis.
                 positive PAS/GMS stain for dermatophytosis.
              bullous impetigo.
                 subcorneal neutrophils, rare eosinophils.
                 mild epidermal spongiosis.
                 superficial perivascular neutrophilic infiltrate.
           +intraepidermal acantholytic vesicular dermatitis.
              pemphigus vulgaris.
                 widespread acantholysis.
                 middle-aged or older.
                 fragile, flaccid bullae.
                 intra-epidermal acantholytic vesicular dermatosis.
                 suprabasal clefts and blisters
                 acantholysis extends to follicles.
                 epidermal spongiosis and eosinophils.
                 ~corps ronds and grains.
              Darier's disease.
                 Darier's disease.
                    keratosis follicularis.
                 Darier's disease.
                    autosomal dominant.
                    slowly progressive, hyperkeratotic papules.
                       follicular distribution.
                    suprabasal acantholysis.
                    clefts or lacunae.
                    corps ronds and grains.
              Hailey-Hailey disease.
                  Hailey-Hailey disease.
                     benign familial pemphigus.
                  Hailey-Hailey disease.
                     autosomal dominant.
                     acantholysis, epidermal hyperplasia.
                     full-thickness acantholysis.
                     no hair-follicle involvement.
              Grover's disease.
                  Grover's disease.
                     transient acantholytic dermatosis.
                  Grover's disease.
                     spongiosis.
                     small, focal acantholysis.
              Herpesvirus infection.
                  acantholysis.
                  multinucleated cells.
                  typical Herpes cytopathic changes.
              Staphylococcal scalded skin syndrome.
                  focal acantholysis.
                  cleavage plane in granular layer.
            +subepidermal

Д	0	1	2	3	4
0	+İ	.	.	.	.
1	.	<Three weeks.	.	.	.
2	.	+Three weeks.	.	.	.
3	.	.	+Amnionic cavity.	.	.
4	.	.	+Ectoderm.	.	.
5	.	.	.	+Lateral ectoderm.	.
6	.	.	.	+Neuro-ectoderm.	.
7	.	.	+Mesoderm.	.	.
7	.	.	.	+Paraxial mesoderm.	.
8	.	.	.	+Somite.	.
9	.	.	.	+Intermediate mesoderm.	.
10	.	.	.	+Lateral plate mesoderm.	.
11	.	.	.	.	+Somatic mesoderm.
12	.	.	.	.	+Splanchnic mesoderm.
13	.	.	+Entoderm.	.	.
14	.	.	+Intra-embryonic Coelom.	.	.
1	.	>Three weeks.	.	.	.