On n-contractive fuzzy logics

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Authors:
Rostislav Horčík
Carles Noguera
Milan Petrík
Title: On n-contractive fuzzy logics
Journal: Mathematical Logic Quarterly
Volume 53
Number 3
Pages: 268-288
Year: 2007
Preprint




Abstract

It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w.r.t. the class of all finite MTL-chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since every finite MTL-chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced by Ciabattoni, Esteva and Godo, and the axiom of weak cancellation defined by Montagna, Noguera and Horcík. 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, finite model property, decidability and standard completeness.