Determining Consistency of Topological Relations

Abstract

This paper examines the problem of testing consistency of sets of topological relations which are instances of the RCC-8 relation set Leeds92a. Representations of these relations as constraints within a number of logical frameworks are considered. It is shown that, if the arguments of the relations are interpreted as non-empty open sets within an arbitrary topological space, a complete consistency checking procedure can be provided by means of a composition table. This result is contrasted with the case where regions are required to be planar and bounded by Jordan curves, for which the consistency problem is known to be NP-hard. In order to investigate the completeness of compositional reasoning, the notion of k-compactness of a set of relations w.r.t. a theory is introduced. This enables certain consistency properties of relational networks to be examined independently of any specific interpretation of the domain of entities constrained by the relations.