Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F15%3A33155730" target="_blank" >RIV/61989592:15310/15:33155730 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14310/15:00085221

Výsledek na webu

<a href="http://link.springer.com/article/10.1007%2Fs10773-015-2510-9" target="_blank" >http://link.springer.com/article/10.1007%2Fs10773-015-2510-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10773-015-2510-9" target="_blank" >10.1007/s10773-015-2510-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics

Popis výsledku v původním jazyce

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 operatorsand 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 thetense 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 t

Název v anglickém jazyce

Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics

Popis výsledku anglicky

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 operatorsand 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 thetense 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 t

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraické metody v kvantové logice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

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Svazek periodika

54

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

4327-4340

Kód UT WoS článku

000364224200014

EID výsledku v databázi Scopus

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