Brandon Bennett, Anthony G. Cohn, Paolo Torrini, Shyamanta M. Hazarika
We present a highly expressive logical language for describing qualitative configurations of spatial regions, based on Tarski's Geometry of Solids, in which the `parthood' relation and the concept of `sphere' are taken as primitive. We give a complete axiom system, whose models can be interpreted classically in terms of Cartesian spaces over R. We show that within this system the concept of sphere and the `congruence' relation are interdefinable. We investigate the 2nd-order character of the theory and prove incompletenss of some weaker 1st-order variants.
Keywords: Ontologies, Spatial Reasoning, Qualitative Reasoning, Representation
Citation: Brandon Bennett, Anthony G. Cohn, Paolo Torrini, Shyamanta M. Hazarika: A Foundation for Region-based Qualitative Geometry. In W.Horn (ed.): ECAI2000, Proceedings of the 14th European Conference on Artificial Intelligence, IOS Press, Amsterdam, 2000, pp.204-208.