Abstract
This paper argues for the use of conceptual spaces in qualitative spatial and temporal reasoning. Conceptual spaces provide a natural framework for enriching the purely combinatorial and symbolic calculi such as Allen's calculus with a geometrical or topological structure. Recent work has shown that such enrichments are useful, since they provide simpler ways of characterizing tractable subclasses of the calculi. Hence part of the computational properties can be related to geometrical properties. The paper discusses a family of calculi (including Allen's calculus) for which substantial results have been obtained using this approach. It then examines other instances of calculi where the relationship has not yet been fully investigated and lists the main open questions which arise in this context.
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