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On tense MV-algebras

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BOTUR Michal PASEKA Jan

Rok publikování 2015
Druh Článek v odborném periodiku
Časopis / Zdroj Fuzzy Sets and Systems
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
Doi http://dx.doi.org/10.1016/j.fss.2014.06.006
Obor Obecná matematika
Klíčová slova Tense operators; MV-algebra; Predicate logic
Popis The main aim of this article is to study tense MV-algebras which are just MV-algebras with new unary operations G and H which express a universal time quantifiers. Tense MV-algebras were introduced by D. Diaconescu and G. Georgescu. Using a new notion of an fm-function between MV-algebras we settle a half of their Open problem about representation for some classes of tense MV-algebras, i.e., we show that any tense semisimple MV-algebra is induced by a time frame analogously to classical works in this field of logic. As a by-product we obtain a new characterization of extremal states on MV-algebras. Our method gives a general framework for representing functions with the so-called Jauch-Piron property (including MV-morphisms) between MV-algebras. (C) 2014 Elsevier B.V. All rights reserved.

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