Properties of implication in effect algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609277" target="_blank" >RIV/61989592:15310/21:73609277 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyter.com/document/doi/10.1515/ms-2021-0001/html" target="_blank" >https://www.degruyter.com/document/doi/10.1515/ms-2021-0001/html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2021-0001" target="_blank" >10.1515/ms-2021-0001</a>
Alternative languages
Result language
angličtina
Original language name
Properties of implication in effect algebras
Original language description
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serve as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of quantum mechanics, more precisely as an algebraic semantics of these logics. Because every productive logic is equipped with implication, we introduce here such a concept and demonstrate its properties. In particular, we show that this implication is connected with conjunction via a certain "unsharp" residuation which is formulated on the basis of a strict unsharp residuated poset. Though this structure is rather complicated, it can be converted back into an effect algebra and hence it is sound. Further, we study the Modus Ponens rule for this implication by means of so-called deductive systems and finally we study the contraposition law.
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
10101 - Pure mathematics
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematica Slovaca
ISSN
0139-9918
e-ISSN
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Volume of the periodical
71
Issue of the periodical within the volume
3
Country of publishing house
SK - SLOVAKIA
Number of pages
12
Pages from-to
"523 "- 534
UT code for WoS article
000663038900001
EID of the result in the Scopus database
2-s2.0-85108514812