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)