Timed Contact Algebras

Timed contact algebras constitute an approach to a temporal version of a region based theory of space. The general theory does not provide a notion of an underlying static world, i.e. it does not explicitly contain a set of non moving regions. Furthermore, the model of time does not have any structure, i.e. time is neither ordered nor required to be discrete or continuous. In this paper we want to investigate two extensions of the basic theory. The first extension considers grounded timed contact algebras that make the underlying static world explicit. In this context we introduce the Axiom of Construction that relates the existence of certain regions and the time structure for the first time. The second addition is given by a betweenness relation on the set of time. In this context we introduce the Axiom of Continuity (CONT), ensuring "smooth'' movement of regions through time. Last but not least, we show that both axioms together do not allow finite models.