Quasi-Algebras versus Regular Algebras - Part I

Starting from quasi-Wajsberg algebras (which are generalizations of Wajsberg algebras), whose regular sets are Wajsberg algebras, we introduce a theory of quasi-algebras versus, in parallel, a theory of regular algebras. We introduce the quasi-RM, quasi-RML, quasi-BCI, (commutative, positive implica...

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Main Author: A. Iorgulescu
Format: Article
Language:English
Published: Alexandru Ioan Cuza University of Iasi 2015-06-01
Series:Scientific Annals of Computer Science
Online Access:http://www.info.uaic.ro/bin/download/Annals/XXV1/XXV1_4.pdf
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spelling doaj-a8944c7e6b76485e93886055f3b144d62020-11-25T01:22:59ZengAlexandru Ioan Cuza University of IasiScientific Annals of Computer Science1843-81212248-26952015-06-01XXV18913110.7561/SACS.2015.1.89Quasi-Algebras versus Regular Algebras - Part IA. IorgulescuStarting from quasi-Wajsberg algebras (which are generalizations of Wajsberg algebras), whose regular sets are Wajsberg algebras, we introduce a theory of quasi-algebras versus, in parallel, a theory of regular algebras. We introduce the quasi-RM, quasi-RML, quasi-BCI, (commutative, positive implicative, quasi-implicative, with product) quasi-BCK, quasi-Hilbert and quasi-Boolean algebras as generalizations of RM, RML, BCI, (commutative, positive implicative, implicative, with product) BCK, Hilbert and Boolean algebras respectively. In Part I, the first part of the theory of quasi-algebras - versus the first part of a theory of regular algebras - is presented. We introduce the quasi-RM and the quasi-RML algebras and we present two equivalent definitions of quasi-BCI and of quasi-BCK algebras.http://www.info.uaic.ro/bin/download/Annals/XXV1/XXV1_4.pdf
collection DOAJ
language English
format Article
sources DOAJ
author A. Iorgulescu
spellingShingle A. Iorgulescu
Quasi-Algebras versus Regular Algebras - Part I
Scientific Annals of Computer Science
author_facet A. Iorgulescu
author_sort A. Iorgulescu
title Quasi-Algebras versus Regular Algebras - Part I
title_short Quasi-Algebras versus Regular Algebras - Part I
title_full Quasi-Algebras versus Regular Algebras - Part I
title_fullStr Quasi-Algebras versus Regular Algebras - Part I
title_full_unstemmed Quasi-Algebras versus Regular Algebras - Part I
title_sort quasi-algebras versus regular algebras - part i
publisher Alexandru Ioan Cuza University of Iasi
series Scientific Annals of Computer Science
issn 1843-8121
2248-2695
publishDate 2015-06-01
description Starting from quasi-Wajsberg algebras (which are generalizations of Wajsberg algebras), whose regular sets are Wajsberg algebras, we introduce a theory of quasi-algebras versus, in parallel, a theory of regular algebras. We introduce the quasi-RM, quasi-RML, quasi-BCI, (commutative, positive implicative, quasi-implicative, with product) quasi-BCK, quasi-Hilbert and quasi-Boolean algebras as generalizations of RM, RML, BCI, (commutative, positive implicative, implicative, with product) BCK, Hilbert and Boolean algebras respectively. In Part I, the first part of the theory of quasi-algebras - versus the first part of a theory of regular algebras - is presented. We introduce the quasi-RM and the quasi-RML algebras and we present two equivalent definitions of quasi-BCI and of quasi-BCK algebras.
url http://www.info.uaic.ro/bin/download/Annals/XXV1/XXV1_4.pdf
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