Abstract
In this paper we consider the problem whether for a map φ : A(B) → B there is a relation R on A(B) such that properties of a map φ: B → B are reflected to R. This is a converse problem that J. Järvinen proved in [5]. We give an affirmative answer to the problem. Moreover we give equational bases which characterize properties of the map φ. This means that the classes of some types of algebras form varieties. Hence, there are full correspondence between properties of relations and varieties of modal algebras.