Krassimir T. Atanassov (1995)
Mathware and Soft Computing
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It is shown that the axioms of the intuitionistic logic can be proved as theorems in the frames of the intuitionistic fuzzy logic.
Dov Gabbay, George Metcalfe, Nicola Olivetti (2004)
RACSAM
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Fuzzy logics based on t-norms and their residua have been investigated extensively from a semantic perspective but a unifying proof theory for these logics has, until recently, been lacking. In this paper we survey results of the authors and others which show that a suitable proof-theoretic framework for fuzzy logics is provided by hypersequents, a natural generalization of Gentzen-style sequents. In particular we present hypersequent calculi for the logic of left-continuous t-norms...
Newton C. A. da Costa, Diego Marconi (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In questa nota gli Autori descrivono nuovi sistemi di logica (detta «paracompleta») connessi con la logica della vaghezza («fuzzy logic») e con le logiche paraconsistenti.
Newton C. A. da Costa, Diego Marconi (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In questa nota gli Autori descrivono nuovi sistemi di logica (detta «paracompleta») connessi con la logica della vaghezza («fuzzy logic») e con le logiche paraconsistenti.
Rostislav Horčík, Mirko Navara (2002)
Kybernetika
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The validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve. We summarize characterizations of validation sets of -fuzzy logics and extend them to the case of -fuzzy logics.
Peter Vojtáš (2000)
Kybernetika
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In this paper we argue that for fuzzy unification we need a procedural and declarative semantics (as opposed to the two valued case, where declarative semantics is hidden in the requirement that unified terms are syntactically – letter by letter – identical). We present an extension of the syntactic model of unification to allow near matches, defined using a similarity relation. We work in Hájek’s fuzzy logic in narrow sense. We base our semantics on a formal model of fuzzy logic programming...
Francesc Esteva, Pere García, Lluis. Godo, Ricardo O. Rodríguez (1998)
Mathware and Soft Computing
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The paper introduces a general axiomatic notion of approximation mapping, a mapping that associates to each crisp proposition p a fuzzy set representing approximately p. It is shown how it can be obtained through fuzzy relations, which are at least reflexive. We study the corresponding multi-modal systems depending on the properties satisfied by the approximate relation. Finally, we show some equivalences between possibilistic logical consequences and global/local logical consequences...
Alejandro Sobrino (1999)
Mathware and Soft Computing
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The notion of degree of truth used in fuzzy logic can be interpreted in terms of partial truth or in terms of utility. By investigating how these interpretations fit in with Tarski's definition of truth, this paper explores some of their implications and their consequences for the foundations and credibility of fuzzy logic.