On the Fusion of Coalgebraic Logics

Fusion is arguably the simplest way to combine modal logics. For normal modal logics with Kripke semantics, many properties such as completeness and decidability are known to transfer from the component logics to their fusion. In this paper we investigate to what extent these results can be generalised to the case of arbitrary coalgebraic logics. Our main result generalises a construction of Kracht and Wolter and confirms that completeness transfers to fusion for a large class of logics over coalgebraic semantics. This result is independent of the rank of the logics and relies on generalising the notions of distance and box operator to coalgebraic models.