Date: Dec 11, 2012 9:36 PM
Author: fom
Subject: Re: fom - 12 - CORRECTED - lexical blocking


Let A and B be propositions.

Let A be asserted as true.

Then B is in relation to
A according to whether or
not there exists a deduction
of

IMP(A,NOR(B,B))


If such a deduction exists,
then the subsequent assertion
of B is lexically blocked.

The corresponding relation
in orthocomplemented lattices
is called orthogonality.

Lattice polynomials are built
from meets and joins. The
expression above is equivalent
to

NOR(NOR(NOR(A,A),B),NOR(A,A),B))

that corresponds with

-A \/ B


To establish correspondence
between the lattice polynomials
and the transformation rules
of the deductive system, one must
have that every mapping F from
the non-atomic propositions into
the lattice




TRU

/ \
/ \
/ \
/ \
/ \
/ \

NO ALL

| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |

OTHER SOME

\ /
\ /
\ /
\ /
\ /
\ /

NOT





be such that

F(NOR(x,x)) = -F(x)

and

F(NOR(NOR(x,y),NOR(x,y))) = F(x) \/ F(y)