Studia Logica

, Volume 100, Issue 6, pp 1271–1290

Lewis Dichotomies in Many-Valued Logics


DOI: 10.1007/s11225-012-9450-7

Cite this article as:
Bova, S. Stud Logica (2012) 100: 1271. doi:10.1007/s11225-012-9450-7


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.


Parameterized satisfiabilityComplexity dichotomyMany-valued logics

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© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA