On Tense MV-algebras

TL;DR

This paper studies tense MV-algebras, introducing new representation results for certain classes and providing a novel characterization of extremal states, advancing the understanding of their algebraic and logical structure.

Contribution

It proves that tense semisimple MV-algebras can be represented by time frames, addressing an open problem and introducing a new notion of fm-functions between MV-algebras.

Findings

Tense semisimple MV-algebras are induced by time frames.

A new characterization of extremal states on MV-algebras.

Resolution of half of the open problem on representation of tense MV-algebras.

Abstract

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. Diagonescu and G. Georgescu. Using a new notion of an fm-function between MV-algebras we \zruseno{will prove} \zmena{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.