9+-Intersection Calculi for Topological Reasoning on Heterogeneous Objects

This paper develops a series of qualitative spatial calculi that feature topological relations. While most qualitative spatial calculi have targeted spatial relations between single-type objects, our calculi support spatial relations between heterogeneous combinations of objects. Thus, with our calculi, we can disambiguate topological arrangements of objects without regard to the types of the objects. Topological relations between points, lines, regions, and their combinations are distinguished systematically by the 9+-intersection and assigned unique names that indicate their characteristics. The 9+-intersection is a refinement of the 9-intersection, which is has been frequently used in GIScience communities as a model of topological relations. Based on the 9+-intersection we can generalize the rules for deriving compositions and, accordingly, a variety of composition tables are generated systematically as a foundation of new calculi. By integrating all relevant sets of topological relations, composition tables, and lists of converse relations, the algebraic framework of ordinary spatial calculi is successfully reused in our new spatial calculi for conducting constraint-based spatial reasoning. We demonstrate that our 9+intersection calculi realize finer spatial reasoning than the former 9-intersection calculi.