Sub-implicative filters in quasi-ordered relational systems [Articol]

Abstract

The concept of sub-implicability of BCI-algebras was introduced in 2000. Then that concept was applied to the algebraic structures of residuated lattices (2011), KU-algebras (2017), BH-algebras (2018) and BCK-algebras (2021). In this paper, the idea of sub-implicability is applied to quasi-ordered residuated systems. A criterion for recognizing this type of filter in a quasi-ordered residuated system has been found and, in addition, some important features of this concept have been established.