Publication details
On tense MV-algebras
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Fuzzy Sets and Systems |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.fss.2014.06.006 |
| Field | General mathematics |
| Keywords | Tense operators; MV-algebra; Predicate logic |
| Description | 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. |