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 a Jan PASEKA

Základní údaje

Originální název

Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics

Autoři

CHAJDA, Ivan (203 Česká republika) a Jan PASEKA (203 Česká republika, garant, domácí)

Vydání

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

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 1.041

Kód RIV

RIV/00216224:14310/15:00085221

Organizační jednotka

Přírodovědecká fakulta

DOI

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

UT WoS

000364224200014

Klíčová slova anglicky

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

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 13. 12. 2015 08:54, prof. RNDr. Jan Paseka, CSc.

Anotace

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.

Návaznosti

EE2.3.20.0051, projekt VaV

Název: Algebraické metody v kvantové logice

Citovat

CHAJDA, Ivan a Jan PASEKA. Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics. International Journal of Theoretical Physics. NEW YORK: Springer, 2015, roč. 54, č. 12, s. 4327-4340. ISSN 0020-7748. Dostupné z: 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 a Jan PASEKA. Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics. \textit{International Journal of Theoretical Physics}. NEW YORK: Springer, 2015, roč.~54, č.~12, s.~4327-4340. ISSN~0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-015-2510-9.

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