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.
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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
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
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
Tags AKR, rivok
Tags International impact, Reviewed
Changed by Changed by: prof. RNDr. Jan Paseka, CSc., učo 1197. Changed: 13/12/2015 08:54.
Abstract
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 projectName: Algebraické metody v kvantové logice
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