The Logic of Lattice Effect Algebras Based on Induced Groupoids

J 2019

The Logic of Lattice Effect Algebras Based on Induced Groupoids

CHAJDA, Ivan; Helmut LAENGER a Jan PASEKA

Základní údaje

Originální název

The Logic of Lattice Effect Algebras Based on Induced Groupoids

Autoři

CHAJDA, Ivan; Helmut LAENGER a Jan PASEKA

Vydání

JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING, PHILADELPHIA, OLD CITY PUBLISHING INC, 2019, 1542-3980

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.703

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/19:00112273

Organizační jednotka

Přírodovědecká fakulta

UT WoS

000486419800002

EID Scopus

2-s2.0-85072623040

Klíčová slova anglicky

D-poset; effect algebra; lattice effect algebra; antitone involution; effect groupoid; groupoid-based logic

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 28. 3. 2020 15:56, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

MUNI/G/1211/2017, interní kód MU

Název: Grupové techniky a kvantová informace (Akronym: GRUPIK)

Investor: Masarykova univerzita, Grupové techniky a kvantová informace, INTERDISCIPLINARY - Mezioborové výzkumné projekty

Citovat

CHAJDA, Ivan; Helmut LAENGER a Jan PASEKA. The Logic of Lattice Effect Algebras Based on Induced Groupoids. JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING. PHILADELPHIA: OLD CITY PUBLISHING INC, 2019, roč. 33, č. 3, s. 161-175. ISSN 1542-3980.

@article{1601838,
   author = {Chajda, Ivan and Laenger, Helmut and Paseka, Jan},
   article_location = {PHILADELPHIA},
   article_number = {3},
   keywords = {D-poset; effect algebra; lattice effect algebra; antitone involution; effect groupoid; groupoid-based logic},
   language = {eng},
   issn = {1542-3980},
   journal = {JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING},
   title = {The Logic of Lattice Effect Algebras Based on Induced Groupoids},
   url = {https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-33-number-3-2019/mvlsc-33-3-p-161-175/},
   volume = {33},
   year = {2019}
}

TY  - JOUR
ID  - 1601838
AU  - Chajda, Ivan - Laenger, Helmut - Paseka, Jan
PY  - 2019
TI  - The Logic of Lattice Effect Algebras Based on Induced Groupoids
JF  - JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING
VL  - 33
IS  - 3
SP  - 161-175
EP  - 161-175
PB  - OLD CITY PUBLISHING INC
SN  - 15423980
KW  - D-poset
KW  - effect algebra
KW  - lattice effect algebra
KW  - antitone involution
KW  - effect groupoid
KW  - groupoid-based logic
UR  - https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-33-number-3-2019/mvlsc-33-3-p-161-175/
L2  - https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-33-number-3-2019/mvlsc-33-3-p-161-175/
N2  - 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.
ER  -

CHAJDA, Ivan; Helmut LAENGER a Jan PASEKA. The Logic of Lattice Effect Algebras Based on Induced Groupoids. \textit{JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING}. PHILADELPHIA: OLD CITY PUBLISHING INC, 2019, roč.~33, č.~3, s.~161-175. ISSN~1542-3980.

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