Algebraic structures formalizing the logic of effect algebras incorporating time dimension

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73626982" target="_blank" >RIV/61989592:15310/24:73626982 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.degruyter.com/journal/key/ms/74/6/html" target="_blank" >https://www.degruyter.com/journal/key/ms/74/6/html</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/ms-2024-0098" target="_blank" >10.1515/ms-2024-0098</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Algebraic structures formalizing the logic of effect algebras incorporating time dimension

Popis výsledku v původním jazyce

Effect algebras were introduced in order to describe the structure of effects, i.e. events in quantum mechanics. They are partial algebras describing the logic behind the corresponding events. It is natural to ask how to introduce the logical connective implication in this logic. For lattice ordered effect algebras this task was already solved. We concentrate on effect algebras which need not be lattice ordered since they better describe the events occuring in quantum physical systems. Although an effect algebra is only partial, we find a logical connective implication which is everywhere defined. However, such implication is &quot;unsharp&quot; because its ouputs for given pairs of entries need not be elements of the underlying effect algebra but may be subsets of mutually incomparable elemets. We introduce such an implication together with its adjoint functor representing conjunction. Then we consider the so-called tense operators on effect algebras for a given time frame with a given time preference relation. Finally, for a given tense operators and given time set we describe two methods how to construct a time preference relation such that the given tense operators are either comparable with or equaivalent to those induced by this time frame..

Název v anglickém jazyce

Algebraic structures formalizing the logic of effect algebras incorporating time dimension

Popis výsledku anglicky

Effect algebras were introduced in order to describe the structure of effects, i.e. events in quantum mechanics. They are partial algebras describing the logic behind the corresponding events. It is natural to ask how to introduce the logical connective implication in this logic. For lattice ordered effect algebras this task was already solved. We concentrate on effect algebras which need not be lattice ordered since they better describe the events occuring in quantum physical systems. Although an effect algebra is only partial, we find a logical connective implication which is everywhere defined. However, such implication is &quot;unsharp&quot; because its ouputs for given pairs of entries need not be elements of the underlying effect algebra but may be subsets of mutually incomparable elemets. We introduce such an implication together with its adjoint functor representing conjunction. Then we consider the so-called tense operators on effect algebras for a given time frame with a given time preference relation. Finally, for a given tense operators and given time set we describe two methods how to construct a time preference relation such that the given tense operators are either comparable with or equaivalent to those induced by this time frame..

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

1337-2211

Svazek periodika

74

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

16

Strana od-do

"1353 "- 1368

Kód UT WoS článku

001371821400015

EID výsledku v databázi Scopus

2-s2.0-85217066091