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)