✦ LIBER ✦

On n -contractive fuzzy logics

✍ Scribed by Rostislav Horčík; Carles Noguera; Milan Petrík

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 285 KB
Volume: 53
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200610044

No coin nor oath required. For personal study only.

✦ Synopsis

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 each finite MTL‐chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced in [9] and the axiom of weak cancellation defined in [31]. 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. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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