Publication details
De Morgan Algebras with Tense Operators
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | De Morgan lattice; De Morgan poset; tense operators; dynamic De Morgan algebra |
| Description | To every propositional logic satisfying double negation law is assigned a De Morgan poset epsilon. Using of axioms for an universal quantifier, we set up axioms for the so-called tense operators G and H on E. The triple D = (epsilon; G, H) is called a (partial) dynamic De Morgan algebra. We solve the following questions: first, if a time frame is given, how to construct tense operators G and H; second, if a (strict) dynamic De Morgan algebra is given, how to find a time frame such that its tense operators G and H can be reached by this construction. In particular, any strict dynamic De Morgan algebra is representable in its Dedekind-MacNeille completion with respect to a suitable countable time frame. |