<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI algebras and many other algebras of logic. In this paper, the notion of deductive system in a pseudo-M algebra is introduced and its elementary properties are investigated. Closed deductive systems are defined and studied. The homomorphic properties of (closed) deductive systems are provided. The concepts of translation deductive systems and R-congruences in pseudo-M algebras are introduced and investigated. It is shown that there is a bijection between closed translation deductive systems and R-congruences. Finally, the construction of quotient algebra 𝒜/<italic>D</italic> of a pseudo-M algebra 𝒜 via a translation deductive system <italic>D</italic> of 𝒜 is given.</p>
</abstract>

The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI algebras and many other algebras of logic. In this paper, the notion of deductive system in a pseudo-M algebra is introduced and its elementary properties are investigated. Closed deductive systems are defined and studied. The homomorphic properties of (closed) deductive systems are provided. The concepts of translation deductive systems and R-congruences in pseudo-M algebras are introduced and investigated. It is shown that there is a bijection between closed translation deductive systems and R-congruences. Finally, the construction of quotient algebra 𝒜/D of a pseudo-M algebra 𝒜 via a translation deductive system D of 𝒜 is given.

Deductive systems of pseudo-M algebras

University of Natural Sciences and Humanities in Siedlce

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Deductive systems of pseudo-M algebras"}

The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI algebras and many other algebras of logic. In this paper, the...

Deductive systems of pseudo-M algebras

Published Online: Jan 30, 2023

Page range: 93 - 116

Received: Jul 30, 2022

Accepted: Nov 06, 2022

DOI: https://doi.org/10.2478/aupcsm-2022-0008

Keywords
pseudo-M, pseudo-CI, pseudo-BCH, pseudo-BCK algebra, (translation) deductive system, congruence, quotient algebra

© 2022 Andrzej Walendziak, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Deductive systems of pseudo-M algebras

Published Online: Jan 30, 2023

Page range: 93 - 116

Received: Jul 30, 2022

Accepted: Nov 06, 2022

DOI: https://doi.org/10.2478/aupcsm-2022-0008

Keywordspseudo-M, pseudo-CI, pseudo-BCH, pseudo-BCK algebra, (translation) deductive system, congruence, quotient algebra

© 2022 Andrzej Walendziak, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
pseudo-M, pseudo-CI, pseudo-BCH, pseudo-BCK algebra, (translation) deductive system, congruence, quotient algebra