Modal operators on BCK-algebras

Abstract

In this paper, modal operators on BCK-algebras, especially BCK-algebras with condition (S) are introduced and several properties and characterizations of them are investigated. Also, it is investigated under what conditions these modal operators form a lattice. Furthermore, some special modal operators are introduced and their properties and characterizations of them are obtained, especially in some classes of BCK-algebras such as positive implicative BCK- algebras.