A hybrid logic of knowledge supporting topological reasoning

We consider a certain, in a way hybrid extension of a system called topologic, which has been designed for reasoning about the spatial content of the idea of knowledge. What we add to the language of topologic are names of both points and neighbourhoods of points. Due to the special semantics of topologic these names do not quite behave like nominals in hybrid logic. Nevertheless, corresponding satisfaction operators can be simulated with the aid of the global modality, which becomes, therefore, another means of expression of our system. In this paper we put forward an axiomatization of the set of formulas valid in all such hybrid scenarios, and we prove the decidability of this logic. Moreover, we argue that the present approach to hybridizing modal concepts for knowledge and topology is not only much more powerful but also much more natural than a previous one.