The Poset-based Logics for the De Morgan Negation and Set Representation of Partial Dynamic De Morgan Algebras
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-31-number-3-2018/mvlsc-31-3-p-213-237/ |
| Keywords | De Morgan poset; tense operators; (partial) dynamic De Morgan algebra; tense poset-based logic for the De Morgan negation |
| Description | By a De Morgan algebra is meant a bounded poset equipped with an antitone 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. |
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