The Logic of Lattice Effect Algebras Based on Induced Groupoids

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216224:14310/19:00112273

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

The Logic of Lattice Effect Algebras Based on Induced Groupoids

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The Logic of Lattice Effect Algebras Based on Induced Groupoids

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING

ISSN

1542-3980

e-ISSN

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Svazek periodika

33

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

161-175

Kód UT WoS článku

000486419800002

EID výsledku v databázi Scopus

2-s2.0-85072623040