Separability and decidability results for varieties of Jónsson dynamic algebras (Q1866799)

Dynamic algebras were introduced as algebraic counterparts of dynamic logics, i.e. propositional logical systems endowed with a set of modal operators. It is known that there are two approaches to the notion of a dynamic algebra. By \textit{B. Jónsson} [Colloq. Math. Soc. János Bolyai 54, 245-292 (1991; Zbl 0760.03018)], dynamic algebras are Boolean algebras with unary operators with indices in a given Kleene algebra. \textit{V. R. Pratt} [Studia Logica 50, 571-605 (1991; Zbl 0752.03033)] and \textit{D. Kozen} [Inf. Comput. 110, 366-390 (1994; Zbl 0806.68082)] introduced dynamic algebras as two-sorted algebras in the form of Boolean modules. The authors of the paper under review investigate connections between the two approaches. They transfer some results concerning separability and decidability from the two-sorted case to the first one and, moreover, extend them to wide classes of varieties of Jónsson dynamic algebras.