Archive for Mathematical Logic 46 (5-6):347-363 (2007)

Abstract
A method is described for obtaining conjunctive normal forms for logics using Gentzen-style rules possessing a special kind of strong invertibility. This method is then applied to a number of prominent fuzzy logics using hypersequent rules adapted from calculi defined in the literature. In particular, a normal form with simple McNaughton functions as literals is generated for łukasiewicz logic, and normal forms with simple implicational formulas as literals are obtained for Gödel logic, Product logic, and Cancellative hoop logic.
Keywords Fuzzy logic  Normal form  Proof theory  Hypersequents
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DOI 10.1007/s00153-007-0033-7
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References found in this work BETA

A Theorem About Infinite-Valued Sentential Logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.
A Constructive Analysis of RM.Arnon Avron - 1987 - Journal of Symbolic Logic 52 (4):939 - 951.
Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.
Interpolation in Fuzzy Logic.Matthias Baaz & Helmut Veith - 1999 - Archive for Mathematical Logic 38 (7):461-489.

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