fom
Posts:
1,027
Registered:
12/4/12
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Re: fom - 11 - CORRECTED - definition of proposition
Posted:
Dec 11, 2012 9:35 PM
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The ortholattice
TRU
/ \
/ \
/ \
/ \
/ \
/ \
NO ALL
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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
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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)))
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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
20-element 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.
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