Determining Consistency of Topological Relations

Authors:
Brandon Bennett
Affiliations:
School of Computer Studies, The University of Leeds, LS2 9JT, UK
Venue:
Constraints
Year:
1998

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Abstract

This paper examines the problem of testing consistencyof sets of topological relations which are instances of the RCC-8relation set Leeds92a. Representations of these relations asconstraints within a number of logical frameworks are considered.It is shown that, if the arguments of the relations are interpretedas non-empty open sets within an arbitrary topological space,a complete consistency checking procedure can be provided bymeans of a composition table. This result is contrasted withthe case where regions are required to be planar and boundedby Jordan curves, for which the consistency problem is knownto be NP-hard.In order to investigate the completeness of compositional reasoning,the notion of k-compactnessof a set of relations w.r.t. a theory is introduced. This enablescertain consistency properties of relational networks to be examinedindependently of any specific interpretation of the domain ofentities constrained by the relations.