The logic induced by effect algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603607" target="_blank" >RIV/61989592:15310/20:73603607 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs00500-020-05188-w" target="_blank" >https://link.springer.com/article/10.1007%2Fs00500-020-05188-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-020-05188-w" target="_blank" >10.1007/s00500-020-05188-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The logic induced by effect algebras

Popis výsledku v původním jazyce

Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E, we investigate a natural implication and prove that the implication reduct of E is term equivalent to E. Then, we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras. For effect algebras which need not be lattice-ordered, we introduce a certain kind of implication which is everywhere defined but whose result need not be a single element. Then, we study effect implication algebras and prove the correspondence between these algebras and effect algebras satisfying the ascending chain condition. We present an axiom system in Gentzen style also for not necessarily lattice-ordered effect algebras and prove that it is an algebraic semantics for the logic induced by finite effect algebras.

Název v anglickém jazyce

The logic induced by effect algebras

Popis výsledku anglicky

Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras E, we investigate a natural implication and prove that the implication reduct of E is term equivalent to E. Then, we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras. For effect algebras which need not be lattice-ordered, we introduce a certain kind of implication which is everywhere defined but whose result need not be a single element. Then, we study effect implication algebras and prove the correspondence between these algebras and effect algebras satisfying the ascending chain condition. We present an axiom system in Gentzen style also for not necessarily lattice-ordered effect algebras and prove that it is an algebraic semantics for the logic induced by finite effect algebras.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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

2020

Kód důvěrnosti údajů

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

Název periodika

SOFT COMPUTING

ISSN

1432-7643

e-ISSN

—

Svazek periodika

24

Číslo periodika v rámci svazku

19

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

14275-14286

Kód UT WoS článku

000552594700001

EID výsledku v databázi Scopus

2-s2.0-85088651175