Dynamic Order Algebras as an Axiomatization of Modal and Tense
Logics

J 2015

Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics

CHAJDA, Ivan and Jan PASEKA

Basic information

Original name

Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics

Authors

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

Edition

International Journal of Theoretical Physics, NEW YORK, Springer, 2015, 0020-7748

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 1.041

RIV identification code

RIV/00216224:14310/15:00085221

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s10773-015-2510-9

UT WoS

000364224200014

Keywords in English

Propositional logic; Modal logic; Bounded poset; Tense logic; Tense operators; Dynamic order algebra

Abstract

V originále

The aim of the paper is to introduce and describe tense operators in every propositional logic which is axiomatized by means of an algebra whose underlying structure is a bounded poset or even a lattice. We introduce the operators G, H, P and F without regard what propositional connectives the logic includes. For this we use the axiomatization of universal quantifiers as a starting point and we modify these axioms for our reasons. At first, we show that the operators can be recognized as modal operators and we study the pairs (P, G) as the so-called dynamic order pairs. Further, we get constructions of these operators in the corresponding algebra provided a time frame is given. Moreover, we solve the problem of finding a time frame in the case when the tense operators are given. In particular, any tense algebra is representable in its Dedekind-MacNeille completion. Our approach is fully general, we do not relay on the logic under consideration and hence it is applicable in all the up to now known cases.

Links

EE2.3.20.0051, research and development project

Name: Algebraické metody v kvantové logice

Citovat

CHAJDA, Ivan and Jan PASEKA. Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics. International Journal of Theoretical Physics. NEW YORK: Springer, 2015, vol. 54, No 12, p. 4327-4340. ISSN 0020-7748. Available from: https://dx.doi.org/10.1007/s10773-015-2510-9.

@article{1320843,
   author = {Chajda, Ivan and Paseka, Jan},
   article_location = {NEW YORK},
   article_number = {12},
   doi = {http://dx.doi.org/10.1007/s10773-015-2510-9},
   keywords = {Propositional logic; Modal logic; Bounded poset; Tense logic; Tense operators; Dynamic order algebra},
   language = {eng},
   issn = {0020-7748},
   journal = {International Journal of Theoretical Physics},
   title = {Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics},
   volume = {54},
   year = {2015}
}

TY  - JOUR
ID  - 1320843
AU  - Chajda, Ivan - Paseka, Jan
PY  - 2015
TI  - Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics
JF  - International Journal of Theoretical Physics
VL  - 54
IS  - 12
SP  - 4327-4340
EP  - 4327-4340
PB  - Springer
SN  - 00207748
KW  - Propositional logic
KW  - Modal logic
KW  - Bounded poset
KW  - Tense logic
KW  - Tense operators
KW  - Dynamic order algebra
N2  - The aim of the paper is to introduce and describe tense operators in every propositional logic which is axiomatized by means of an algebra whose underlying structure is a bounded poset or even a lattice. We introduce the operators G, H, P and F without regard what propositional connectives the logic includes. For this we use the axiomatization of universal quantifiers as a starting point and we modify these axioms for our reasons. At first, we show that the operators can be recognized as modal operators and we study the pairs (P, G) as the so-called dynamic order pairs. Further, we get constructions of these operators in the corresponding algebra provided a time frame is given. Moreover, we solve the problem of finding a time frame in the case when the tense operators are given. In particular, any tense algebra is representable in its Dedekind-MacNeille completion. Our approach is fully general, we do not relay on the logic under consideration and hence it is applicable in all the up to now known cases.
ER  -

CHAJDA, Ivan and Jan PASEKA. Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics. \textit{International Journal of Theoretical Physics}. NEW YORK: Springer, 2015, vol.~54, No~12, p.~4327-4340. ISSN~0020-7748. Available from: https://dx.doi.org/10.1007/s10773-015-2510-9.

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