# Coalgebraic Modal Logic, an Introduction

Modal logics are applied in diverse areas to reason about properties of systems. In computer science, some of the best known examples include Hennessy-Milner logic, temporal logic, and the modal mu-calculus.

Coalgebraic modal logic is a general framework for studying modal logics for systems viewed as coalgebras. In particular, basic modal logic (with box and diamond) is an instance of this framework when viewing Kripke frames as coalgebras for the powerset functor. In fact, the relationship between coalgebra and modal logic is so fundamental that it is often captured by the slogan: Modal logics are coalgebraic.

In this talk I will give a basic introduction to coalgebraic modal logic where modalities are obtained as predicate liftings for a functor. I will show basic results such as invariance for bisimulation and how to find modalities for a given type of coalgebra. Time permitting, I will state some of the general theorems concerning expressivity, duality and completeness that show how well-known properties of basic modal logic turn out to hold at the more general level of coalgebra.