fom
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Registered:
12/4/12


Re: fom  11  CORRECTED  definition of proposition
Posted:
Dec 11, 2012 9:35 PM


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.

