In this paper we consider some basic questions regarding the extensions of modal logics with bisimulation quantifiers. In particular, we consider the relation between bisimualtion quantifiers and uniform interpolation for modal logic and the μ-calculus. We first consider these questions over the whole class of frames, and then we restrict to specific classes, where we see that the results obtained before can be easily falsified. Finally, we introduce classes of frames where we found the same good behaviour than in the whole class of frames. The results presented in this paper have been obtained in collaboration with other authors during the last years; in alphabetical order: Tim French, Marco Hollenberg, and Giacomo Lenzi.
