Date: Dec 11, 2012 9:35 PM
Author: fom
Subject: Re: fom  11  CORRECTED  definition of proposition
The ortholattice
TRU
/ \
/ \
/ \
/ \
/ \
/ \
NO ALL
 
 
 
 
 
 
 
 
 
 
 
OTHER SOME
\ /
\ /
\ /
\ /
\ /
\ /
NOT
is a sublattice of the one constructed
from our line names.
Let A be some linguistic expression.
The expressions:
A
NOR(A,A)
NOR(NOR(A,NOR(A,A)),NOR(A,NOR(A,A)))
NOR(NOR(A,A),NOR(NOR(A,A),NOR(A,A)))
label vertices in a lattice corresponding
to the free DeMorgan algebra on one
generator:
TRU



NOR(NOR(A,NOR(A,A)),NOR(A,NOR(A,A)))
/ \
/ \
/ \
A NOR(A,A)
\ /
\ /
\ /
NOR(NOR(A,A),NOR(NOR(A,A),NOR(A,A)))



NTRU.
Then, A is a proposition if and only if all
maps from the free DeMorgan algebra generated
from A into the sublattice from our
20element ortholattice has
TRU > TRU
NOR(NOR(A,NOR(A,A)),NOR(A,NOR(A,A))) > TRU
NTRU > NOT
NOR(NOR(A,A),NOR(NOR(A,A),NOR(A,A))) > NOT
and one of
A > ALL
NOR(A,A) > OTHER
A > SOME
NOR(A,A) > NO
A > OTHER
NOR(A,A) > ALL
A > NO
NOR(A,A) > SOME
Note that the top and bottom correspond to
the ideal points significant to the topology
on the connectivity algebra.