| PASEKA, Jan a 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, roč. 31, č. 3, s. 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 a 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, roč.~31, č.~3, s.~213-237. ISSN~1542-3980.
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