De Morgan Algebras with Tense Operators
Ivan Chajda and Jan Paseka
To every propositional logic satisfying double negation law is assigned a De Morgan poset ε. Using of axioms for an universal quantifier, we set up axioms for the so-called tense operators G and H on ε. The triple D = (ε; 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.
Keywords: De Morgan lattice, De Morgan poset, tense operators, dynamic De Morgan algebra.