silver_1 at mindspring.com
Thu Sep 7 14:06:32 EDT 2006
Dear Bill and FOM-ers,
> ->a sentence in propositional logic that's either an atomic
> sentence or
> ->the negation of one? ... I think it's an unfortunate name for
> this kind
> ->of sentence and would welcome a better one,
> Given "atomic", above, I was going to suggest "molecular",
> but that would better apply to any compound proposition.
> So how about "ionic"?
TERRIFIC idea!!! I'd love to use it in some stuff I've been
writing, attempting to connect elementary discrete math with
sentential and first-order logic. Unfortunately, "literal" has
taken hold in the "Quine-McCluskey Algorithm", thanks to Quine's
introduction of the term (By the way, has anyone heard *anything*
of McCluskey independently? Other than his name in the title of the
algorithm, he doesn't seem to exist.)
I've looked up the early Kleene in "Intro to Meta.", Church's book,
and Tarski's big book. Nothing.
I'm almost tempted to use "ionic" anyway and just say that terms
aren't standardized and often differ from book to book. There are
even many different definitions of a sentence in "disjunctive normal
I'd still love to know if someone arrived at a different term for
"literal" prior to Quine's articles on Prime Implicants and that sort
of thing. (It seems like something Church would have dealt with,
but as I say I haven't found anything.)
Thomas Forster suggested I ask Dana Scott.. Another excellent
source would be Martin Davis. Are you out there, Martin? William
Tait would be another excellent source. Also, I wouldn't be
surprised if Allen Hazen knew something about this....
This also sounds like something Smullyan might have contributed to
at some point--sort of seems like his cup of tea, doesn't it?
(Wouldn't be at all surprised to see a tree depiction reducing dnf
expressions step-by-step to minimal ones.)
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