On n-contractive fuzzy logics: first results

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Carles Noguera
Francesc Esteva
Joan Gispert
Title of the chapter: On n-contractive fuzzy logics: first results
Title of the book: Uncertainty and Intelligent Information Systems
Bernadette Bouchon-Meunier
Ronald R. Yager
Christophe Marsala
Maria Rifqi
Publisher: World Scientific
Year: 2008


In order to reach a deeper understanding of the structure of fuzzy logics, some very general new logics are defined. Namely, we consider the extensions of MTL by adding the generalized contraction and excluded middle laws and we enrich this family by means of the axiom of weak cancellation and the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Omega} operator. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embeddability property, decidability and standard completeness.