Normal forms for fuzzy logics: a proof-theoretic approach |
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Authors: | Petr Cintula George Metcalfe |
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Institution: | (1) Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic;(2) Department ofMathematics, Vanderbilt University, Nashville, TN 37212, USA |
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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 ?ukasiewicz logic, and normal forms with simple implicational formulas as literals are obtained for Gödel logic, Product logic, and Cancellative hoop logic. |
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Keywords: | Fuzzy logic Normal form Proof theory Hypersequents |
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