Deening a `doughnut' Made Diicult

Qualitative descriptions of spatial properties and relationships, and qualitative spatial reasoning, are of fundamental importance in human problem-solving: even where we use quantitative approaches, these depend on an accompanying qualitative representation. The work described is aimed at for-malising some topological aspects of qualitative spatial description and reasoning. The paper continues the work of Randell, Cohn and Cui on region-based qualitative representations of spatial properties and relations, built on thèlogic of connection' developed by Clarke. It is shown how taxonomies of the topological properties and relationships of spatial regions can be developed, using the single primitivèC', wherèC(x; y)' indicates that regions x and y arèconnected', meaning that their closures share at least one point. This is done by considering a speciic task: deciding whether or not a region has the topology of a `doughnut', or solid torus. A range of`near misses' and doubtful cases is discussed, and ways of distinguishing these from thètarget', the solid torus, are considered. It is shown how the task could be performed given certain assumptions about the target region and about regions in general. These assumptions are then progressively relaxed; as this is done, the task requires the deenition of successive layers of terminology, all derived ultimately from`C', and providing a basis for successively broader taxonomies of topological properties and relationships.