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 a Ivan CHAJDA

Základní údaje

Originální název

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

Autoři

PASEKA, Jan a Ivan CHAJDA

Vydání

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

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10200 1.2 Computer and information sciences

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.613

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/18:00101799

Organizační jednotka

Přírodovědecká fakulta

UT WoS

000455886300002

EID Scopus

2-s2.0-85055649891

Klíčová slova anglicky

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

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 25. 4. 2019 16:31, Mgr. Tereza Miškechová

Anotace

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.

Návaznosti

GA15-15286S, projekt VaV

Název: Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti

Investor: Grantová agentura ČR, Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti

Citovat

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.

@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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