A Theory of Multidimensional Qualitative Space : Semantic Integration of Spatial Theories that Distinguish Interior from Boundary Contact ( Extended

We extend our multidimensional qualitative theory of space based on relative dimension and containment by closures under intersections and differences and by a new primitive relation of boundary containment, a special kind of incidence. We provide a descriptions of the intended structures which ensure that boundary and interior are always clearly distinguishable. The resulting theory can define all the mereotopological relations from previous accounts of areas, lines, and points in a general multidimensional setting and is thus capable of semantically integrating those accounts of space.