Residuation in finite posets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609345" target="_blank" >RIV/61989592:15310/21:73609345 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/pdf/1910.09009.pdf" target="_blank" >https://arxiv.org/pdf/1910.09009.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2021-0021" target="_blank" >10.1515/ms-2021-0021</a>
Alternative languages
Result language
angličtina
Original language name
Residuation in finite posets
Original language description
When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce implication to be everywhere defined and satisfying (left) adjointness with conjunction. We have already studied this problem for the logic of quantum mechanics which is based on an orthomodular poset or the logic of quantum effects based on a so-called effect algebra which is only partial and need not be lattice-ordered. For this, we introduced the so-called operator residuation where the values of implication and conjunction need not be elements of the underlying poset, but only certain subsets of it. However, this approach can be generalized for posets satisfying more general conditions. If these posets are even finite, we can focus on maximal or minimal elements of the corresponding subsets and the formulas for the mentioned operators can be essentially simplified. This is shown in the present paper where all theorems are explained by corresponding examples.
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
4
Country of publishing house
SK - SLOVAKIA
Number of pages
14
Pages from-to
"807 "- 820
UT code for WoS article
000680658600001
EID of the result in the Scopus database
2-s2.0-85107937064