Many-valued modal logics

Abstract
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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Standard Gödel Modal Logics.Xavier Caicedo & Ricardo O. Rodriguez - 2010 - Studia Logica 94 (2):189-214.
How True It is = Who Says It's True.Melvin Fitting - 2009 - Studia Logica 91 (3):335 - 366.
How True It Is = Who Says It’s True.Melvin Fitting - 2009 - Studia Logica 91 (3):335-366.

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