A dynamic Effect Algebras with Dual Operation
Jan Paseka, Jiří Janda · Mathematics for Applications · 2012
Tense operators for MV-algebras were introduced by Diaconescu and Georgescu.Based on their definition Chajda and Kolařík presented the definition of tense operators for lattice effect algebras.Chajda and Paseka tackled the problem of axiomatizing tense operators on an effect algebra by introducing the notion of a partial dynamic effect algebra.They also gave representation theorems for dynamic effect algebras.We continue to extend their work for partial S-dynamic effect algebras i.e. in the case when tense operators satisfy required conditions also for the dual effect algebraic operation •.We show that whenever tense operators are total our stronger notion coincides with their definition.We give also a representation theorem for partial S-dynamic effect algebras and its version for strict dynamic effect algebras.