How to introduce the connective implication in orthomodular posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73603165" target="_blank" >RIV/61989592:15310/21:73603165 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/pdf/1907.10539.pdf" target="_blank" >https://arxiv.org/pdf/1907.10539.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S1793557121500662" target="_blank" >10.1142/S1793557121500662</a>

Result language
angličtina
Original language name
How to introduce the connective implication in orthomodular posets
Original language description
Since orthomodular posets serve as an algebraic axiomatization of the logic of quantum mechanics, it is a natural question how the connective of implication can be defined in this logic. It should be introduced in such a way that it is related with conjunction, i.e. with the partial operation meet, by means of some kind of adjointness. We present here such an implication for which a so-called unsharp residuated poset can be constructed. Then this implication is connected with the operation meet by the so-called unsharp adjointness. We prove that also conversely, under some additional assumptions, such an unsharp residuated poset can be converted into an orthomodular poset and that this assignment is nearly one-to-one.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

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)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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