```Date: Dec 11, 2012 9:35 PM
Author: fom
Subject: Re: fom - 11 - CORRECTED - definition of proposition

The ortholattice                TRU               /   \             /       \           /           \         /               \       /                   \     /                       \   NO                         ALL    |                         |    |                         |    |                         |    |                         |    |                         |    |                         |    |                         |    |                         |    |                         |    |                         |    |                         |  OTHER                      SOME     \                       /       \                   /         \               /           \           /             \       /               \   /                NOTis a sublattice of the one constructedfrom our line names.Let A be some linguistic expression.The expressions:ANOR(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 correspondingto the free DeMorgan algebra on onegenerator:                   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 allmaps from the free DeMorgan algebra generatedfrom A into the sublattice from our20-element ortholattice hasTRU --> TRUNOR(NOR(A,NOR(A,A)),NOR(A,NOR(A,A))) --> TRUNTRU --> NOTNOR(NOR(A,A),NOR(NOR(A,A),NOR(A,A))) --> NOTand one ofA --> ALLNOR(A,A) --> OTHERA --> SOMENOR(A,A) --> NOA --> OTHERNOR(A,A) --> ALLA --> NONOR(A,A) --> SOMENote that the top and bottom correspond tothe ideal points significant to the topologyon the connectivity algebra.
```