Pavelka-style completeness in expansions of Łukasiewicz logic

Archive for Mathematical Logic 47 (1):15-23 (2008)
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Abstract

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered

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Algebraic foundations of many-valued reasoning.Roberto Cignoli - 1999 - Boston: Kluwer Academic Publishers. Edited by Itala M. L. D'Ottaviano & Daniele Mundici.
Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.
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An algebraic approach to propositional fuzzy logic.Franco Montagna - 2000 - Journal of Logic, Language and Information 9 (1):91-124.

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