Publication details
A Dynamic Effect Algebras with dual operation
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | MATHEMATICS FOR APPLICATIONS |
| MU Faculty or unit | |
| Citation | |
| Web | http://ma.fme.vutbr.cz/archiv/1_1/79_89.pdf |
| Field | General mathematics |
| Keywords | effect algebra; lattice effect algebra; tense operators; dynamic effect algebra |
| Description | Tense operators for MV-algebras were introduced by Diaconescu and Georgescu. Based on their denition Chajda and Kolařík presented the denition 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 denition. We give also a representation theorem for partial S-dynamic effect algebras and its version for strict dynamic effect algebras. |