Defining a ‘Doughnut’ Made Difficult (1994) [7 citations — 0 self]
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Abstract:
Qualitative descriptions of spatial properties and relationships, and qualitative spatial reasoning, are of fundamental importance in human problemsolving: even where we use quantitative approaches, these depend on an accompanying qualitative representation. The work described is aimed at formalising 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 the `logic 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 primitive `C', where `C(x; y) ' indicates that regions x and y are `connected', meaning that their closures share at least one point. This is done by considering a specific 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 the `target', 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 definition of successive layers of terminology, all derived ultimately from `C', and providing a basis for successively broader taxonomies of topological properties and relationships. 1
