On n-contractive Fuzzy Logics

0080342 - ÚI 2008 RIV DE eng J - Journal Article
Horčík, Rostislav - Noguera, C. - Petrík, M.
On n-contractive Fuzzy Logics.
[O n-kontraktivních fuzzy logikách.]
Mathematical Logic Quarterly. Roč. 53, č. 3 (2007), s. 268-288. ISSN 0942-5616. E-ISSN 1521-3870
R&D Projects: GA AV ČR 1ET100300517
Institutional research plan: CEZ:AV0Z10300504
Keywords : algebraic logic * fuzzy logics * generalized contraction * generalized excluded middle * left-continuous t-norms * MTL-algebras * non-classical logics * residuated lattices * standard completeness * substructural logics * varieties * weak cancellation
Subject RIV: BA - General Mathematics
Impact factor: 0.317, year: 2007

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.

Článek se zabývá algebraickou sémantikou fuzzy logik splňujících zobecněný axiom kontrakce nebo zobecněný zákon vyloučeného třetího. Pro tyto logiky ukazuje jaké algebraické a logické vlasnosti splňují. Jedná se zejména o lokální konečnost, konečnou vnořitelnost, vlastnost konečných modelů, rozhodnutelnost a standardní úplnost.
Permanent Link: http://hdl.handle.net/11104/0144619