Taking dimension seriously in qualitative spatial reasoning

Antony Galton

In W. Wahlster (editor), Proceedings of the 12th European Conference on Artificial Intelligence, John Wiley & Sons, Ltd, 1996, pages 501-505.
ISBN 0-471-96809-9

Abstract

Space has a key role to play in the description of the physical world, and an important subgoal of AI is to provide a sound theoretical foundation for its qualitative description. The central notion of much recent work is that of a region, and the emphasis has been on the systematic description of qualitative properties of regions, relations amongst regions, and relations amongst these relations. Such work has tended to downplay dimensional issues, which tend to fall foul of the bewitchment of our spatial intuition brought about by point-set topology. In this paper we attempt to emancipate qualitative spatial reasoning from this bewitchment by taking dimension more seriously. A preliminary discussion in general terms is followed by an attempt to axiomatise the required notions, taking as our basis a restricted version of Classical Extensional Mereology, enriched by a topological notion of bounding.

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