The logic induced by effect algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603607" target="_blank" >RIV/61989592:15310/20:73603607 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs00500-020-05188-w" target="_blank" >https://link.springer.com/article/10.1007%2Fs00500-020-05188-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-020-05188-w" target="_blank" >10.1007/s00500-020-05188-w</a>
Alternative languages
Result language
angličtina
Original language name
The logic induced by effect algebras
Original language description
Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E, we investigate a natural implication and prove that the implication reduct of E is term equivalent to E. Then, we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras. For effect algebras which need not be lattice-ordered, we introduce a certain kind of implication which is everywhere defined but whose result need not be a single element. Then, we study effect implication algebras and prove the correspondence between these algebras and effect algebras satisfying the ascending chain condition. We present an axiom system in Gentzen style also for not necessarily lattice-ordered effect algebras and prove that it is an algebraic semantics for the logic induced by finite effect algebras.
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
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SOFT COMPUTING
ISSN
1432-7643
e-ISSN
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Volume of the periodical
24
Issue of the periodical within the volume
19
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
14275-14286
UT code for WoS article
000552594700001
EID of the result in the Scopus database
2-s2.0-85088651175