Translating Logics for Coalgebras

This paper shows, that three di erent types of logics for coalgebras are institutions. The logics di er regarding the presentation of their syntax. In the rst framework, abstract behavioural logic, one has a syntax-free representation of behavioural properties. We then turn to coalgebraic logic, the syntax of which is given as an initial algebra. The last framework, which we consider, is coalgebraic modal logic, the syntax of which is concretely given.