2002•Unpublished venueOpen access

Approximating propositional calculi by finite-valued logics

Matthias Baaz, Richard Zach

Abstract

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can be computed from the calculus.>

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Key concepts: T-norm fuzzy logics, Propositional variable, Well-formed formula, Propositional calculus, Monoidal t-norm logic, Intermediate logic, Zeroth-order logic, Kripke semantics