On residuation in paraorthomodular lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603161" target="_blank" >RIV/61989592:15310/20:73603161 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00500-020-04699-w" target="_blank" >https://link.springer.com/article/10.1007/s00500-020-04699-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-020-04699-w" target="_blank" >10.1007/s00500-020-04699-w</a>

Result language
angličtina
Original language name
On residuation in paraorthomodular lattices
Original language description
Paraorthomodular lattices are quantum structures of prominent importance within the framework of the logico-algebraic approach to (unsharp) quantum theory. However, at the present time it is not clear whether the above algebras may be regarded as the algebraic semantic of a logic in its own right. In this paper, we start the investigation of material implications in paraorthomodular lattices by showing that any bounded modular lattice with antitone involution A can be converted into a left-residuated groupoid if it satisfies a strengthened form of regularity. Moreover, the above condition turns out to be also necessary whenever A is distributive.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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