Normal forms for fuzzy logics: a proof-theoretic approach
|Title:||Normal forms for fuzzy logics: a proof-theoretic approach|
|Journal:||Archive for Mathematical Logic|
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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.