Logics expressing spatial properties go back to Tarksi. Often their semantics is based on topological spaces. Cianza et al. propose to use instead so-called closure spaces as underlying mathematical structure, because closure spaces comprise topological spaces as well as standard Kripke frames.

In this talk we exploit the fact that finite Kripke frames induce quasi-discrete closure spaces, strengthening the connection of the closure operator and the accessibility relation. For the corresponding Kripke models we relate a strong and a weak notion of bisimulation to equivalence w.r.t. to a logic with a forward and a backward modality of “being near” and a forward and a backward path modality, respectively.