Institutionalising Many-Sorted Coalgebraic Modal Logic

Abstract

[4] describes a modal logic for coalgebras of certain polynomial endofunctors on Set. This logic is here generalised to endofunctors on categories of sorted sets. The structure of the endofunctors considered is then exploited in order to define ways of moving from (coalgebras of) one endofunctor to (coalgebras of) another, and to equip them with translations between the associated modal languages. Furthermore, the resulting translations are shown to preserve and reflect the satisfaction of modal formulae by coalgebras.