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Soft Computing

, Volume 23, Issue 24, pp 12937–12950 | Cite as

Monadic pseudo-equality algebras

  • Shokoofeh GhorbaniEmail author
Foundations
  • 36 Downloads

Abstract

In this paper, we introduce the concept of monadic pseudo-equality algebras and obtain some related properties. We study the relations between monadic pseudo-equality algebras, monadic bounded hoops and monadic pseudo-BCI-algebras. Then, we introduce and study monadic deductive systems and monadic congruences and discuss the relations between them. We use monadic deductive systems to define uniform topology on pseudo-equality algebras and obtain some topological results. Finally, the corresponding logic (monadic invariant pseudo-equality logic) is constructed and the soundness and completeness of this logic are proved based on monadic invariant pseudo-equality algebras.

Keywords

Monadic pseudo-equality algebra Monadic deductive system Uniform structure Monadic invariant pseudo-equality logic 

Notes

Acknowledgements

The author would like to express her thanks to referees for their comments and suggestions which improved the paper.

Compliance with ethical standards

Conflict of interest

The author declares that she has no conflict ofinterest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Pure Mathematics, Faculty of Mathematics and Computer, Mahani Mathematical Research CenterShahid Bahonar University of KermanKermanIran

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