An institution of modal logics for coalgebras

This paper presents a modular framework for the specification of certain inductivelydefined coalgebraic types. Modal logics for coalgebras of polynomial endofunctors on the category of sets have been studied in [16,8]. These logics are here generalised to endofunctors on categories of sorted sets, in order to allow collections of interrelated types to be specified simultaneously. The inductive nature of the coalgebraic types considered is then used to formalise semantic relationships between different types, and to define translations between the associated logics. The resulting logical framework is shown to be an institution, whose specifications and specification morphisms admit final and respectively cofree models.