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

J 2018

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

PASEKA, Jan and Ivan CHAJDA

Basic information

Original name

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

Authors

PASEKA, Jan (203 Czech Republic, guarantor, belonging to the institution) and Ivan CHAJDA (203 Czech Republic)

Edition

JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING, PHILADELPHIA, PA 19123 USA, OLD CITY PUBLISHING INC, 2018, 1542-3980

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10200 1.2 Computer and information sciences

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.613

RIV identification code

RIV/00216224:14310/18:00101799

Organization unit

Faculty of Science

UT WoS

000455886300002

Keywords in English

De Morgan poset; tense operators; (partial) dynamic De Morgan algebra; tense poset-based logic for the De Morgan negation

Abstract

V originále

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.

Links

GA15-15286S, research and development project

Name: Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti

Investor: Czech Science Foundation

Citovat

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_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}
}

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JF  - JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING
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PB  - OLD CITY PUBLISHING INC
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KW  - (partial) dynamic De Morgan algebra
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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.

Detailed Information on Publication Record