Normal forms for fuzzy logics: a proof-theoretic approach

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Authors:
Petr Cintula
George Metcalfe
Title: Normal forms for fuzzy logics: a proof-theoretic approach
Journal: Archive for Mathematical Logic
Volume 46
Number 5-6
Pages: 347-363
Year: 2007
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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 Lukasiewicz logic, and normal forms with simple implicational formulas as literals are obtained for Godel logic, Product logic, and Cancellative hoop logic.