Galois connections and tense operators on q-effect algebras

J 2016

Galois connections and tense operators on q-effect algebras

CHAJDA, Ivan and Jan PASEKA

Basic information

Original name

Galois connections and tense operators on q-effect algebras

Authors

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

Edition

Fuzzy Sets and Systems, AMSTERDAM, ELSEVIER SCIENCE BV, 2016, 0165-0114

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 2.718

RIV identification code

RIV/00216224:14310/16:00088576

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1016/j.fss.2015.05.010

UT WoS

000376779800005

Keywords in English

Effect algebra; q-Effect algebra; Galois q-connection; q-Tense operators; q-Jauch-Piron q-effect algebra; q-Representable q-effect algebra

Abstract

V originále

For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. They presented also a canonical construction of them using the notion of a time frame. Tense operators express the quantifiers "it is always going to be the case that" and "it has always been the case that" and hence enable us to express the dimension of time both in the logic of quantum mechanics and in the many-valued logic. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a time frame such that each of these operators can be obtained by the canonical construction. To approximate physical real systems as best as possible, we introduce the notion of a q-effect algebra and we solve this problem for q-tense operators on q-representable q-Jauch-Piron q-effect algebras. (c) 2015 Elsevier B.V. All rights reserved.

Links

EE2.3.20.0051, research and development project

Name: Algebraické metody v kvantové logice

GA15-15286S, research and development project

Name: Algebraické, vícehodnotové a kvantové struktury pro modelování neurčitosti

Investor: Czech Science Foundation

Files attached

Galois_connections_and_tense_operators_on_q-effect_algebras.pdf

Request the author's version of the file

Citovat

CHAJDA, Ivan and Jan PASEKA. Galois connections and tense operators on q-effect algebras. Fuzzy Sets and Systems. AMSTERDAM: ELSEVIER SCIENCE BV, 2016, vol. 298, September, p. 56-68. ISSN 0165-0114. Available from: https://dx.doi.org/10.1016/j.fss.2015.05.010.

@article{1368608,
   author = {Chajda, Ivan and Paseka, Jan},
   article_location = {AMSTERDAM},
   article_number = {September},
   doi = {http://dx.doi.org/10.1016/j.fss.2015.05.010},
   keywords = {Effect algebra; q-Effect algebra; Galois q-connection; q-Tense operators; q-Jauch-Piron q-effect algebra; q-Representable q-effect algebra},
   language = {eng},
   issn = {0165-0114},
   journal = {Fuzzy Sets and Systems},
   title = {Galois connections and tense operators on q-effect algebras},
   volume = {298},
   year = {2016}
}

TY  - JOUR
ID  - 1368608
AU  - Chajda, Ivan - Paseka, Jan
PY  - 2016
TI  - Galois connections and tense operators on q-effect algebras
JF  - Fuzzy Sets and Systems
VL  - 298
IS  - September
SP  - 56-68
EP  - 56-68
PB  - ELSEVIER SCIENCE BV
SN  - 01650114
KW  - Effect algebra
KW  - q-Effect algebra
KW  - Galois q-connection
KW  - q-Tense operators
KW  - q-Jauch-Piron q-effect algebra
KW  - q-Representable q-effect algebra
N2  - For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. They presented also a canonical construction of them using the notion of a time frame. Tense operators express the quantifiers "it is always going to be the case that" and "it has always been the case that" and hence enable us to express the dimension of time both in the logic of quantum mechanics and in the many-valued logic. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a time frame such that each of these operators can be obtained by the canonical construction. To approximate physical real systems as best as possible, we introduce the notion of a q-effect algebra and we solve this problem for q-tense operators on q-representable q-Jauch-Piron q-effect algebras. (c) 2015 Elsevier B.V. All rights reserved.
ER  -

CHAJDA, Ivan and Jan PASEKA. Galois connections and tense operators on q-effect algebras. \textit{Fuzzy Sets and Systems}. AMSTERDAM: ELSEVIER SCIENCE BV, 2016, vol.~298, September, p.~56-68. ISSN~0165-0114. Available from: https://dx.doi.org/10.1016/j.fss.2015.05.010.

Detailed Information on Publication Record