Reasoning with Qualitative Representations: Exploiting the Structure of Space

We present a variety of mechanisms to reason with qualitative representations in general, and qualitative representations of 2-D positional information in particular. One of the simplest is transforming between explicit reference frames (intrinsic, extrinsic, deictic) and a canonical implicit one. Another is computing the composition of spatial relations. Constraint propagation and constraint relaxation form the core of the qualitative inference system. All of them exploit the rich structure of space to reduce the complexity of the algorithms involved. In some cases we even use analogical data structures (abstract maps) that allow us to reason diagrammatically.

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