Quantum B-algebras with involutions
Abstract
The aim of this paper is to define and study the involutive and weakly involutive quantum B-algebras. We prove that any weakly involutive quantum B-algebra is a quantum B-algebra with pseudo-product. As an application, we introduce and investigate the notions of existential and universal quantifiers on involutive quantum B-algebras. It is proved that there is a one-to-one correspondence between the quantifiers on weakly involutive quantum B-algebras. One of the main results consists of proving that any pair of quantifiers is a monadic operator on weakly involutive quantum B-algebras. We investigate the relationship between quantifiers on bounded sup-commutative pseudo BCK-algebras and quantifiers on other related algebraic structures, such as pseudo MV-algebras and bounded Wajsberg hoops.
Cite
@article{arxiv.2002.11316,
title = {Quantum B-algebras with involutions},
author = {Lavinia Corina Ciungu},
journal= {arXiv preprint arXiv:2002.11316},
year = {2020}
}