Properties of implication in effect algebras
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609277" target="_blank" >RIV/61989592:15310/21:73609277 - isvavai.cz</a>
Výsledek na webu
<a href="https://www.degruyter.com/document/doi/10.1515/ms-2021-0001/html" target="_blank" >https://www.degruyter.com/document/doi/10.1515/ms-2021-0001/html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2021-0001" target="_blank" >10.1515/ms-2021-0001</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Properties of implication in effect algebras
Popis výsledku v původním jazyce
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serve as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of quantum mechanics, more precisely as an algebraic semantics of these logics. Because every productive logic is equipped with implication, we introduce here such a concept and demonstrate its properties. In particular, we show that this implication is connected with conjunction via a certain "unsharp" residuation which is formulated on the basis of a strict unsharp residuated poset. Though this structure is rather complicated, it can be converted back into an effect algebra and hence it is sound. Further, we study the Modus Ponens rule for this implication by means of so-called deductive systems and finally we study the contraposition law.
Název v anglickém jazyce
Properties of implication in effect algebras
Popis výsledku anglicky
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serve as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of quantum mechanics, more precisely as an algebraic semantics of these logics. Because every productive logic is equipped with implication, we introduce here such a concept and demonstrate its properties. In particular, we show that this implication is connected with conjunction via a certain "unsharp" residuation which is formulated on the basis of a strict unsharp residuated poset. Though this structure is rather complicated, it can be converted back into an effect algebra and hence it is sound. Further, we study the Modus Ponens rule for this implication by means of so-called deductive systems and finally we study the contraposition law.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
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)
Ostatní
Rok uplatnění
2021
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Mathematica Slovaca
ISSN
0139-9918
e-ISSN
—
Svazek periodika
71
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
SK - Slovenská republika
Počet stran výsledku
12
Strana od-do
"523 "- 534
Kód UT WoS článku
000663038900001
EID výsledku v databázi Scopus
2-s2.0-85108514812