Inexact residuation in effect algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73609351" target="_blank" >RIV/61989592:15310/22:73609351 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Inexact residuation in effect algebras
Original language description
We study the connections of effect and pseudoeffect algebras to sub-structural logics which are defined by means of residuated lattices and posets. Avoiding conditionally residuated structures where adjointness holds only for those elements for which the operations appearing in the adjointness condition are defined, we choose to globally define an implication, thereby however relaxing the requirement of its value being unique. We call such an implication inexact. In this approach, conjunction in effect algebras is naturally defined as a partial operation derived from the partial addition operation, and implication is given via the lower cone of two elements instead of their infimum. It turns out that the obtained structure satisfies some kind of adjointness. We also extend our methods to cover pseudoeffect algebras introduced by Dvurecenskij and Vetterlein.
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
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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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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