Normal forms for fuzzy logics: a proof-theoretic approach

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 G¨odel logic, Product logic, and Cancellative hoop logic. Keywords fuzzy logic · normal form · proof theory · hypersequents Mathematics Subject Classification (2000) 03B22 · 03B47 · 03B52 · 03B50 · 06F35 · 03G99

• Type: Journal
• Year: 2007
• Where: AML
• Authors: Petr Cintula, George Metcalfe
• Keywords: AML 2007, Conjunctive Normal Forms, Logic, Normal Form