Kripke-style semantics for many-valued logics

Mathematical Logic Quarterly 49 (6):629 (2003)
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Abstract

This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there are important many-valued logics like BL, Ł and Π, which are not even complete with respect to the class of all predicate Kripke frames in which they are valid. Thus although very natural, Kripke semantics seems to be slightly less powerful than algebraic semantics

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Citations of this work

Algebraic Kripke-Style Semantics for Relevance Logics.Eunsuk Yang - 2014 - Journal of Philosophical Logic 43 (4):803-826.
A Note on the First‐Order Logic of Complete BL‐Chains.Petr Hájek & Franco Montagna - 2008 - Mathematical Logic Quarterly 54 (4):435-446.
ŁΠ Logic with Fixed Points.Luca Spada - 2008 - Archive for Mathematical Logic 47 (7-8):741-763.
Arithmetical Complexity of Fuzzy Predicate Logics—a Survey II.Petr Hájek - 2010 - Annals of Pure and Applied Logic 161 (2):212-219.

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