The Logic of Lattice Effect Algebras Based on Induced Groupoids
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597321" target="_blank" >RIV/61989592:15310/19:73597321 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14310/19:00112273
Result on the web
<a href="https://obd.upol.cz/id_publ/333177207" target="_blank" >https://obd.upol.cz/id_publ/333177207</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
The Logic of Lattice Effect Algebras Based on Induced Groupoids
Original language description
Effect algebras were introduced by Foulis and Bennett as the so-called quantum structures which describe quantum effects and are determined by the behaviour of bounded self-adjoint operators on the phase space of the corresponding physical system which is a Hilbert space. From the algebraic point of view, the problem is that effect algebras are only partial ones and hence there can be drawbacks when we apply them for a construction of algebraic semantics of the corresponding logic of quantum mechanics. If the effect algebra in question is lattice-ordered this disadvantage can be overcome by using a representation of an equivalent algebra with everywhere defined operations. In our paper, this algebra is a groupoid equipped with one more unary operation which is an antitone involution. It enables us to introduce suitable axioms and inherence rules for the algebraic semantics of the corresponding logic and to prove that this logic is sound and complete.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING
ISSN
1542-3980
e-ISSN
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Volume of the periodical
33
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
161-175
UT code for WoS article
000486419800002
EID of the result in the Scopus database
2-s2.0-85072623040