Algebraic structures formalizing the logic of effect algebras incorporating time dimension

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Algebraic structures formalizing the logic of effect algebras incorporating time dimension

Original language description

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..

Czech name

—

Czech description

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Type

J_imp - 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

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2024

Confidentiality

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

Name of the periodical

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

1337-2211

Volume of the periodical

74

Issue of the periodical within the volume

6

Country of publishing house

SK - SLOVAKIA

Number of pages

16

Pages from-to

"1353 "- 1368

UT code for WoS article

001371821400015

EID of the result in the Scopus database

2-s2.0-85217066091