Many-valued modal logics


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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Melvin Fitting
CUNY Graduate Center

Citations of this work

Modal logics with Belnapian truth values.Serge P. Odintsov & Heinrich Wansing - 2010 - Journal of Applied Non-Classical Logics 20 (3):279-304.
On Ignorance and Contradiction Considered as Truth-Values.Didier Dubois - 2008 - Logic Journal of the IGPL 16 (2):195-216.
Pavelka-style fuzzy justification logics.Meghdad Ghari - 2016 - Logic Journal of the IGPL 24 (5):743-773.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Many-Valued Logics.J. B. Rosser & A. R. Turquette - 1954 - British Journal for the Philosophy of Science 5 (17):80-83.
Possible worlds and many truth values.S. K. Thomason - 1978 - Studia Logica 37 (2):195 - 204.
Many-Valued Modal Propositional Calculi.Pascal Ostermann - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (4):343-354.

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