Lewis Dichotomies in Many-Valued Logics

Studia Logica 100 (6):1271-1290 (2012)
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
Keywords Parameterized satisfiability  Complexity dichotomy  Many-valued logics
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DOI 10.1007/s11225-012-9450-7
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Alfred Horn (1969). Free L-Algebras. Journal of Symbolic Logic 34 (3):475-480.

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