Date: Dec 7, 2012 2:08 AM
Author: fom
Subject: fom - 02 - logical constants

What follows it the presentation of

logical constants in the form of a

projective geometry on 21-names.

The namespace conforms with a typical

presentation of finite projective

geometries using difference sets.

There are three collineations which

shall be named:

Negation:

axis-

THIS

line elements-

THIS SOME OTHERS NO ALL

Contraposition:

axis-

THIS

line elements-

THIS LEQ XOR NTRU TRU

Conjugation:

axis-

THIS

line elements-

THIS FLIP LET DENY FIX

All admissible projectivities for the dual plane

shall fix these lines.

The list that follows takes the form:

Line Name: {list of line elements}

A 21-point projective plane has 21 lines:

NTRU: {THIS, SOME, OTHER, NO, ALL}

THIS: {THIS, NTRU, LEQ, XOR, TRU}

LEQ: {THIS, IF, NIMP, IMP, NIF}

XOR: {THIS, OR, NAND, AND, NOR}

TRU: {THIS, FLIP, LET, DENY, FIX}

SOME: {SOME, NTRU, IMP, NAND, FIX}

IMP: {SOME, LEQ, NIF, OR, DENY}

NAND: {SOME, XOR, IF, NOR, LET}

FIX: {SOME, TRU, NIMP, AND, FLIP}

OTHER: {OTHER, NTRU, IF, OR, FLIP}

IF: {OTHER, LEQ, NIMP, NAND, LET}

OR: {OTHER, XOR, IMP, AND, DENY}

FLIP: {OTHER, TRU, NIF, NOR, FIX}

NO: {NO, NTRU, NIF, AND, LET}

NIF: {NO, LEQ, IMP, NOR, FLIP}

AND: {NO, XOR, NIMP, OR, FIX}

LET: {NO, TRU, IF, NAND, DENY}

ALL: {ALL, NTRU, NIMP, NOR, DENY}

NIMP: {ALL, LEQ, IF, AND, FIX}

NOR: {ALL, XOR, NIF, NAND, FLIP}

DENY: {ALL, TRU, IMP, OR, LET}

===========================================

A difference set presentation is given by:

18: {0, 9, 11, 4, 3}

0: {0, 18, 8, 6, 1}

8: {0, 10, 19, 13, 14}

6: {0, 16, 12, 2, 15}

1: {0, 7, 17, 5, 20}

9: {9, 18, 13, 12, 20}

13: {9, 8, 14, 16, 5}

12: {9, 6, 10, 15, 17}

20: {9, 1, 19, 2, 7}

11: {11, 18, 10, 16, 7}

10: {11, 8, 19, 12, 17}

16: {11, 6, 13, 2, 5}

7: {11, 1, 14, 15, 20}

4: {4, 18, 14, 2, 17}

14: {4, 8, 13, 15, 7}

2: {4, 6, 19, 16, 20}

17: {4, 1, 10, 12, 5}

3: {3, 18, 19, 15, 5}

19: {3, 8, 10, 2, 20}

15: {3, 6, 14, 12, 7}

5: {3, 1, 13, 16, 17}