[FOM] Re: Truth value algorithm for tokens

[Sandy Hodges]

> Is this not the satisfiability (SAT) problem?

>  If gap is allowed as a value, then we have the multivalued
satisfiablility problem.
> let Boolean variables a1, a2 and a3 represent Token a being true,
false and gap, respectively

> Charlie Volkstorf

You have coded the fact that token a is
~ Fa(d) & (0=0 <=> Fa(c))
as:

> a1 <=> (~d2^c2)

However it could be the case that token d is not false, and token c is
false, without token a being true.   This could happen if token a is
gap.   Furthermore, if you modify your proposal to read

[ a1 => (~d2 ^ c2) ] ^ [ (~d2 ^ c2) => (a1 or a3) ]

which is the correct condition, then the model which calls all tokens
gap, would satisfy the conditions, but that woudn't make it right.   The
additional condition which I am proposing, which can be roughly stated
as not calling more things gap than we need to (while at the same time
being able to justify which are gap) cannot, I think, be stated in such
a way as to make the problem a simple one of satisfiability.

If the definition which I am proposing of what it means for a token to
be gap were to be generally accepted, or even regarded as an interesting
candidate, then the question might arise of how we could more
efficiently assign values to large sets of tokens, consistent with my
proposal.   At that point, ideas from satisfiability research would be
worth considering, even if there is no way to turn the problem into an
ordinary satisfiability problem.

------- -- ---- - --- -- --------- -----
Sandy Hodges / Alameda,  California,   USA
mail to SandyHodges at attbi.com will reach me.