Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics
The result's identifiers
Result code in 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>
Alternative codes found
RIV/00216224:14310/15:00085221
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraic methods in Quantum Logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Theoretical Physics
ISSN
0020-7748
e-ISSN
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Volume of the periodical
54
Issue of the periodical within the volume
12
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
4327-4340
UT code for WoS article
000364224200014
EID of the result in the Scopus database
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