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Lewis Dichotomies in Many-Valued Logics

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Abstract

In 1979, H. Lewis shows that the computational complexity of the Boolean satisfiability problem dichotomizes, depending on the Boolean operations available to formulate instances: intractable (NP-complete) if negation of implication is definable, and tractable (in P) otherwise [21]. Recently, an investigation in the same spirit has been extended to nonclassical propositional logics, modal logics in particular [2, 3]. In this note, we pursue this line in the realm of many-valued propositional logics, and obtain complexity classifications for the parameterized satisfiability problem of two pertinent samples, Kleene and Gödel logics.

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  1. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Simone Bova

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  1. Simone Bova
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Bova, S. Lewis Dichotomies in Many-Valued Logics. Stud Logica 100, 1271–1290 (2012). https://doi.org/10.1007/s11225-012-9450-7

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