A Theory for Qualitative Spatial Reasoning Based on Order Relations

Ralf Röhrig

What is needed for an analysis of the existing approaches to qualitative spatial reasoning and for a deeper understanding of the domain of space is a unifying theory that explains all of the concepts used for the representation of the different aspects of space by some primitive but well understood relations. In order to provide such primitive relations it will be shown that the concepts used in the existing approaches can be explained by simple order relations between points on some low-dimensional structures. One of the properties of an order relation is transitivity. It will be shown that this property alone is sufficient to explain all the inferences described in the various approaches to qualitative spatial reasoning.

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