[Inquiry] Peirce's Rules Of Inference

[Jon Awbrey]

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PROI.  Note 3

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Responding to messages by John Sowa and Frithjof Dau on the CG List:

It ''has'' been a while since I was read up on P=?=NP, but I think
it's still important to emphasize that the model-theoretic question
of propositional satisfiability (PSAT), whether a proposition has any
satisfying interpretation (truth-value assignment that makes it true)
is not the same as the proof-theoretic question of proof complexity.
Of course, there's an obvious logical relation, but the translation
of that relation into the corresponding computational complexities
always seemed a bit tricky just as I remember it.

In my own work on Alpha Graphs I found myself forced, all against my
initial inclinations, to move from the proof-theoreric vein to more
model-theoretic modes of approach.  For the sake of propositional
calculus, I am using "model-theoretic" in the rather weak sense
of truth tables and boolean expansions.

If one is interested in using Alpha Graphs as a practical data-modeling
language, then one is forced to work with contingent propositions and
equational (reversible) rules of inference, in effect, to ask for
succinct normal forms that preserve ''all'' of the models
(satisfying interpretations) of given propositions.

It turns out that Peirce's system of alpha graphs, and even more so
its extension to cactus graphs, is especially good at supplying
succinct normal forms for propositional calculus formulas.

Jon Awbrey

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