Approximating propositional calculi by finite-valued logics

Baaz, Matthias, and Richard Zach. 1994. “Approximating Propositional Calculi by Finite-Valued Logics.” In 24th International Symposium on Multiple-Valued Logic, 1994. Proceedings, 257–263. Los Alamitos: IEEE Press. https://doi.org/10.1109/ISMVL.1994.302193.

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.

Note: An extended version is available on arXiv:math/0203204

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