Coalgebras and Modal Expansions of Logics.

Abstract: In this paper we construct a setting in which the question of when a logic supports a classical modal expansion can be made precise. Given a fully selfextensional logic , we find sufficient conditions under which the Vietoris endofunctor on -referential algebras can be defined and we propose to define the modal expansions of as the logic that arises from the -coalgebras. As an example, we also show how the Vietoris endofunctor on referential algebras extends the Vietoris endofunctor on Stone spaces. From another point of view, we examine when a category of ''spaces'', ie sets X equipped with an algebra of subsets of X, allows for the definition of powerspaces (and hence transition systems ). [Copyright &y& Elsevier]