Some Results in Weak Pseudo-Quasi-Wajsberg Algebras

Abstract

In this paper we continue to investigate weak pseudo-quasi-Wajsberg algebras which are called weak PQW-algebras for short. First, some definitions are recalled and the basic properties of weak PQW-algebras are presented. Next, we define the notions of type-I filters, type-II filters, left weak filters and right weak filters of a weak PQW-algebra and study related properties of them. We also discuss the relation between normal filters and filter congruences on a weak PQW-algebra. Finally, we characterize the relationship between weak PQW-algebras and some bounded residuated quasi-ordered monoids with supplementary conditions.