Coalgebraic Modal Logic

Coalgebra provides a general mathematical framework for various kinds of state-based transition systems. Examples include data streams, (infinite) labelled trees, Kripke structures, and weighted/probabilistic transition systems. For the specification of properties of these systems various tailor-made modal logics have been developed. Examples are basic modal logic, graded modal logic and probabilistic modal logic. Coalgebraic modal logic places all these logics under one umbrella such that their properties can be studied on the level of coalgebras rather than for each system type separately.  

In this talk I will give a brief introduction to coalgebra and coalgebraic modal logics and I am going to survey some of the results that have been obtained concerning soundness, completeness, expressivity and decidability of these logics. In particular, I want to focus on a completeness result for Moss' coalgebraic logic that shows that there are coalgebraic logics for the above mentioned examples of systems that can be axiomatised in a uniform way.