Abstract

In this paper we develop a hybrid logic of a simply structured class of set spaces, viz linear ones. In general, set spaces are used as semantic domains in a couple of modal approaches to modelling knowledge and reasoning about topology, respectively. It is, therefore, desirable to get to know and be able to handle the modal theory of the classes of spaces relevant for such applications. Just the fact that the set of actual knowledge states of an agent gaining knowledge constitutes a linear set space, makes this class interesting. However, it turned out that linear set spaces could not be dealt with purely modally. This is why we hybridize the underlying logical language. And in this way we can get to grips with the logic of linear set spaces. Subsequently we prove both a corresponding completeness and a decidability result. Afterwards we discuss these topics for a natural variant of our system