Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established.
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Fuzzy Topology and Łukasiewicz Logics From the Viewpoint of Duality Theory.Yoshihiro Maruyama - 2010 - Studia Logica 94 (2):245-269.
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A Duality for the Algebras of a Łukasiewicz N + 1-Valued Modal System.Bruno Teheux - 2007 - Studia Logica 87 (1):13-36.
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