Join-semilattices whose principal filters are pseudocomplemented

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73614847" target="_blank" >RIV/61989592:15310/22:73614847 - isvavai.cz</a>

Výsledek na webu

<a href="http://mat76.mat.uni-miskolc.hu/mnotes/download_article/3854.pdf" target="_blank" >http://mat76.mat.uni-miskolc.hu/mnotes/download_article/3854.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.18514/MMN.2022.3854" target="_blank" >10.18514/MMN.2022.3854</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Join-semilattices whose principal filters are pseudocomplemented

Popis výsledku v původním jazyce

This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudo -complemented lattices. The pseudocomplement of a V b in the section [b, 1] is denoted by a -b and can be considered as the connective implication in a certain kind of intuitionistic logic. Contrary to the case of Brouwerian semilattices, sections need not be distributive lattices. This essentially allows possible applications in non-classical logics. We present a connection of the semilattices mentioned in the beginning with the so-called non-classical implication semilattices which can be converted into I-algebras having everywhere defined operations. Moreover, we relate our structures to sectionally and relatively residuated semilattices which means that our logical structures are closely connected with substructural logics. We show that I-algebras form a congruence distributive, 3-permutable and weakly regular variety.

Název v anglickém jazyce

Join-semilattices whose principal filters are pseudocomplemented

Popis výsledku anglicky

This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudo -complemented lattices. The pseudocomplement of a V b in the section [b, 1] is denoted by a -b and can be considered as the connective implication in a certain kind of intuitionistic logic. Contrary to the case of Brouwerian semilattices, sections need not be distributive lattices. This essentially allows possible applications in non-classical logics. We present a connection of the semilattices mentioned in the beginning with the so-called non-classical implication semilattices which can be converted into I-algebras having everywhere defined operations. Moreover, we relate our structures to sectionally and relatively residuated semilattices which means that our logical structures are closely connected with substructural logics. We show that I-algebras form a congruence distributive, 3-permutable and weakly regular variety.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

2022

Kód důvěrnosti údajů

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

Název periodika

Miskolc Mathematical Notes

ISSN

1787-2405

e-ISSN

1787-2413

Svazek periodika

23

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

19

Strana od-do

"559 "- 577

Kód UT WoS článku

000885368300003

EID výsledku v databázi Scopus

2-s2.0-85143813639