Dynamic effect algebras and their representations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00062906" target="_blank" >RIV/00216224:14310/12:00062906 - isvavai.cz</a>

Alternative codes found

RIV/61989592:15310/12:33145905

Result on the web

<a href="http://dx.doi.org/10.1007/s00500-012-0857-x" target="_blank" >http://dx.doi.org/10.1007/s00500-012-0857-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-012-0857-x" target="_blank" >10.1007/s00500-012-0857-x</a>

Result language

angličtina

Original language name

Dynamic effect algebras and their representations

Original language description

For lattice effect algebras, the so-called tense operators were already introduced by Chajda and KolaA (TM) ik. 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 toexpress the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be onlypartial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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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)

Publication year

2012

Confidentiality

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

Name of the periodical

Soft computing

ISSN

1432-7643

e-ISSN

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Volume of the periodical

16

Issue of the periodical within the volume

10

Country of publishing house

US - UNITED STATES

Number of pages

9

Pages from-to

1733-1741

UT code for WoS article

000308532700009

EID of the result in the Scopus database

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