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A proof of standard completeness for Esteva and Godo's logic MTL
Studia Logica 70 (2):183-192 (2002)
Abstract
In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0, 1]. We use this result to show that Esteva and Godo''s logic MTL is complete with respect to interpretations into commutative residuated lattices on [0, 1]. This solves an open problem raised in.My notes
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Citations of this work
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.
On the standard and rational completeness of some axiomatic extensions of the monoidal t-Norm logic.Francesc Esteva, Joan Gispert, Lluís Godo & Franco Montagna - 2002 - Studia Logica 71 (2):199 - 226.
An Algebraic Proof of Completeness for Monadic Fuzzy Predicate Logic.Jun Tao Wang & Hongwei Wu - forthcoming - Review of Symbolic Logic:1-27.
Free Algebras in Varieties of Glivenko MTL-algebras Satisfying the Equation 2(x2) = (2x)2.Roberto Cignoli & Antoni Torrens Torrell - 2006 - Studia Logica 83 (1-3):157-181.
Nonassociative substructural logics and their semilinear extensions: Axiomatization and completeness properties: Nonassociative substructural logics.Petr Cintula, Rostislav Horčík & Carles Noguera - 2013 - Review of Symbolic Logic 6 (3):394-423.
References found in this work
Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.
Triangular Norms.Erich Peter Klement, Radko Mesiar & Endre Pap - 2000 - Dordrecht, Netherland: Springer.
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