Publication details

De Morgan Algebras with Tense Operators

Authors

CHAJDA Ivan PASEKA Jan

Type Article in Periodical
Magazine / Source JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING
MU Faculty or unit

Faculty of Science

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.