Studia Logica 71 (2):227-245 (2002)
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Abstract |
The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono''s Kripke semantics for the predicate version of FLew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order.
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Keywords | Philosophy Logic Mathematical Logic and Foundations Computational Linguistics |
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Reprint years | 2004 |
DOI | 10.1023/A:1016500922708 |
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Citations of this work BETA
Distinguished Algebraic Semantics for T -Norm Based Fuzzy Logics: Methods and Algebraic Equivalencies.Petr Cintula, Francesc Esteva, Joan Gispert, Lluís Godo, Franco Montagna & Carles Noguera - 2009 - Annals of Pure and Applied Logic 160 (1):53-81.
Algebraic Kripke-Style Semantics for Relevance Logics.Eunsuk Yang - 2014 - Journal of Philosophical Logic 43 (4):803-826.
Supersound Many-Valued Logics and Dedekind-MacNeille Completions.Matteo Bianchi & Franco Montagna - 2009 - Archive for Mathematical Logic 48 (8):719-736.
Crawley Completions of Residuated Lattices and Algebraic Completeness of Substructural Predicate Logics.Hiroakira Ono - 2012 - Studia Logica 100 (1-2):339-359.
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