The Poset-based Logics for the De Morgan Negation and Set Representation of Partial Dynamic De Morgan Algebras

摘要

By a De Morgan algebra is meant a bounded poset equipped with an anlitone involution considered as negation. Such an algebra can be considered as an algebraic axiomatization of a propositional logic satisfying the double negation law. Our aim is to introduce the so-called tense operators in every De Morgan algebra for to get an algebraic counterpart of a tense logic with negation satisfying the double negation law which need not be Boolean.Following the standard construction of tense operators G and H by a frame we solve the following question: if a dynamic De Morgan algebra is given, how to find a frame such that its tense operators G and H can be reached by this construction.Finally, using the apparatus obtained during the solution of the above question, we prove the finite model property and decidability of the tense poset-based logic for the De Morgan negation.