PASEKA, Jan and Ivan CHAJDA. The Poset-based Logics for the De Morgan Negation and Set Representation of Partial Dynamic De Morgan Algebras. JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING. PHILADELPHIA, PA 19123 USA: OLD CITY PUBLISHING INC, 2018, vol. 31, No 3, p. 213-237. ISSN 1542-3980. |
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@article{1508456, author = {Paseka, Jan and Chajda, Ivan}, article_location = {PHILADELPHIA, PA 19123 USA}, article_number = {3}, keywords = {De Morgan poset; tense operators; (partial) dynamic De Morgan algebra; tense poset-based logic for the De Morgan negation}, language = {eng}, issn = {1542-3980}, journal = {JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING}, title = {The Poset-based Logics for the De Morgan Negation and Set Representation of Partial Dynamic De Morgan Algebras}, url = {https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-31-number-3-2018/mvlsc-31-3-p-213-237/}, volume = {31}, year = {2018} }
TY - JOUR ID - 1508456 AU - Paseka, Jan - Chajda, Ivan PY - 2018 TI - The Poset-based Logics for the De Morgan Negation and Set Representation of Partial Dynamic De Morgan Algebras JF - JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING VL - 31 IS - 3 SP - 213-237 EP - 213-237 PB - OLD CITY PUBLISHING INC SN - 15423980 KW - De Morgan poset KW - tense operators KW - (partial) dynamic De Morgan algebra KW - tense poset-based logic for the De Morgan negation UR - https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-31-number-3-2018/mvlsc-31-3-p-213-237/ L2 - https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-31-number-3-2018/mvlsc-31-3-p-213-237/ N2 - 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. ER -
PASEKA, Jan and Ivan CHAJDA. The Poset-based Logics for the De Morgan Negation and Set Representation of Partial Dynamic De Morgan Algebras. \textit{JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING}. PHILADELPHIA, PA 19123 USA: OLD CITY PUBLISHING INC, 2018, vol.~31, No~3, p.~213-237. ISSN~1542-3980.
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