Describing Rigid Body Motions in a Qualitative Theory of Spatial Regions

Abstract

We explore the expressive power of a recently developed qualitative region-based geometry and apply it to the problem of representing and reasoning about the motion of rigid bodies within a confining environment. Introduction This paper is an investigation of the expressive power of Region-Based Geometry (RBG) (Bennett et al. 2000). This is a qualitative theory of spatial information based on the primitive relation of parthood (P) and a sphere predicate (S). The domain of the theory is that of spatial regions. This theory builds on the earlier work of (Tarski 1929), (Randell, Cui, & Cohn 1992) and (Borgo, Guarino, & Masolo 1996). We show that the framework is expressive enough to formulate a `qualitative kinematics' capable of describing the possible movements of systems of rigid objects in a far more general way than previous theories (Davis 1987; Faltings 1987; Davis 1988; Mukerjee & Bhatia 1995). Moreover, our work provides a rigorous formal ontology (as advocated by e.g. (Len...