Archive for Mathematical Logic

, Volume 46, Issue 5–6, pp 347–363

# Normal forms for fuzzy logics: a proof-theoretic approach

• Petr Cintula
• George Metcalfe
Article

## 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

## Mathematics Subject Classification (2000)

03B22 03B47 03B52 03B50 06F35 03G99

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