A dynamic Effect Algebras with Dual Operation

Abstract

Tense operators for MV-algebras were introduced by Diaconescu and Georgescu. Based on their de nition Chajda and Kola r k presented the de nition of tense operators for lattice e ect algebras. Chajda and Paseka tackled the problem of axiomatizing tense operators on an e ect algebra by introducing the notion of a partial dynamic e ect algebra. They also gave representation theorems for dynamic e ect algebras. We continue to extend their work for partial S-dynamic e ect algebras i.e. in the case when tense operators satisfy required conditions also for the dual e ect algebraic operation . We show that whenever tense operators are total our stronger notion coincides with their de nition. We give also a representation theorem for partial S-dynamic e ect algebras and its version for strict dynamic e ect algebras.