How to introduce the connective implication in orthomodular posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73603165" target="_blank" >RIV/61989592:15310/21:73603165 - isvavai.cz</a>

Výsledek na webu

<a href="https://arxiv.org/pdf/1907.10539.pdf" target="_blank" >https://arxiv.org/pdf/1907.10539.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S1793557121500662" target="_blank" >10.1142/S1793557121500662</a>

Jazyk výsledku

angličtina

Název v původním jazyce

How to introduce the connective implication in orthomodular posets

Popis výsledku v původním jazyce

Since orthomodular posets serve as an algebraic axiomatization of the logic of quantum mechanics, it is a natural question how the connective of implication can be defined in this logic. It should be introduced in such a way that it is related with conjunction, i.e. with the partial operation meet, by means of some kind of adjointness. We present here such an implication for which a so-called unsharp residuated poset can be constructed. Then this implication is connected with the operation meet by the so-called unsharp adjointness. We prove that also conversely, under some additional assumptions, such an unsharp residuated poset can be converted into an orthomodular poset and that this assignment is nearly one-to-one.

Název v anglickém jazyce

How to introduce the connective implication in orthomodular posets

Popis výsledku anglicky

Since orthomodular posets serve as an algebraic axiomatization of the logic of quantum mechanics, it is a natural question how the connective of implication can be defined in this logic. It should be introduced in such a way that it is related with conjunction, i.e. with the partial operation meet, by means of some kind of adjointness. We present here such an implication for which a so-called unsharp residuated poset can be constructed. Then this implication is connected with the operation meet by the so-called unsharp adjointness. We prove that also conversely, under some additional assumptions, such an unsharp residuated poset can be converted into an orthomodular poset and that this assignment is nearly one-to-one.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

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

2021

Kód důvěrnosti údajů

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

Název periodika

Asian-European Journal of Mathematics

ISSN

1793-5571

e-ISSN

—

Svazek periodika

14

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

8

Strana od-do

"2150066-1"-"2150066-8"

Kód UT WoS článku

000626401600019

EID výsledku v databázi Scopus

2-s2.0-85086005826