Inexact residuation in effect algebras

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Inexact residuation in effect algebras

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Inexact residuation in effect algebras

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-09869L" target="_blank" >GF20-09869L: Ortomodularita z různých pohledů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING

ISSN

1542-3980

e-ISSN

1542-3999

Svazek periodika

38

Číslo periodika v rámci svazku

1-2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

57- 79

Kód UT WoS článku

000733593800004

EID výsledku v databázi Scopus

2-s2.0-85128927314