A pointless theory of space based on strong connection and congruence

Abstract

We present a logical theory of space where only tridimensional regions are assumed in the domain. Three distinct primitives are used to describe their mereological, topological and morphological properties: mereology is described by a parthood relation satisfying the axioms of Closed Extensional Mereology; topology is described by means of a "simple region" predicate, by which a relation of "strong connection" between regions having at least a surface in common is defined; morphology is described by means of a "congruence" primitive, whose axioms exploit Tarski's analogy between points and spheres. 1 INTRODUCTION Various logical theories aimed at the representation of commonsense spatial knowledge have been proposed in the AI community in recent years. In the spirit of (Hayes 1985a), the goal has been that of establishing the logical basis of a "geometry of commonsense", intended to be used for tasks as disparate as robot navigation or natural language understanding. Besides specific p...