Kalmbach implication in orthomodular posets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00133648" target="_blank" >RIV/00216224:14310/23:00133648 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1109/ismvl57333.2023.00015" target="_blank" >http://dx.doi.org/10.1109/ismvl57333.2023.00015</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/ISMVL57333.2023.00015" target="_blank" >10.1109/ISMVL57333.2023.00015</a>
Alternative languages
Result language
angličtina
Original language name
Kalmbach implication in orthomodular posets
Original language description
We show that for every orthogonal lub-complete poset P = (P,≤,′, 0, 1), we can introduce multiple-valued implications sharing properties with quantum implications presented for orthomodular lattices by Kalmbach. We call them classical implication, Kalmbach implication, and non-tolens implication.If the classical implication satisfies the order property, then the corresponding orthologic becomes classical and vice versa. If the Kalmbach or non-tolens implication meets the order property, then the corresponding orthologic becomes quantum and vice versa. A related result for the modus ponens rule is obtained.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
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)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
53rd International Symposium on Multiple-Valued Logic (ISMVL 2023)
ISBN
9781665464161
ISSN
0195-623X
e-ISSN
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Number of pages
6
Pages from-to
18-23
Publisher name
IEEE
Place of publication
New Jersey, USA
Event location
Matsue, Shimane
Event date
May 22, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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