Coalgebraic coalgebras

Stone coalgebras

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor on the category of sets. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. T...

Topology on Coalgebras

Wellfounded coalgebras

For an endofunctor H an initial algebra I has, by Lambek’s Lemma, invertible structure map, thus, it can be considered as a coalgebra. We call an H-coalgebra wellfounded if it has a coalgebra homomorphism into I. This is equivalent to the wellfoundedness in Taylor’s “Practical Foundations”, defined by means of an induction principle. And it is also equivalent to the recursivity studied by Capre...

Coalgebraic Logic

We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that innnitary modal logic contains characterizing formulas. That is, every model-world pair is characterized up to bisimulation by an innnitary formula. The point of our generalization is to understand this on a deeper level. We do this by studying a frangm...

Coalgebraic Expressions

We show that certain fixpoint expressions used to describe finite Kripke polynomial coalgebras can be seen as coalgebraic modal fixpoint formulae. Both the synthesis of a coalgebra from its expression and the ability to check behavioural equivalence follow from the same tableau construction. There is an associated complete equational logic, analogous to Kleene algebra, which may now be seen as ...