Integrating a Spatial Reasoner with a Resolution Theorem-Prover

Abstract

Some spatial reasoning systems use images to solve problems, rather than making formal logical inferences. However, an open question is how to use these systems in contexts where some nonspatial information is also involved. We present a hybrid reasoning method in which we extend the capabilities of a spatial reasoner by integrating it with a resolution theorem-prover. We prove that the hybrid system is refutation-complete, in the sense that, if a domain theory is unsatisfiable, perhaps only because all of its models entail unrealizable images, then our algorithm will halt. We discuss how our approach differs from other hybrid reasoning algorithms in the way it manages the interaction between sub-systems. Introduction Recently there has been a resurgence of interest in spatial or diagrammatic reasoning (Glasgow, Narayanan, & Chandrasekaran 1995). Among the various spatial reasoning systems that have been proposed, there are two basic types of approaches: axiomatic and image-based. In ...