The Mathematical Morpho-Logical view on Reasoning about Space

Marco Aiello, Brammert Ottens

Qualitative reasoning about mereotopological relations has been extensively investigated, while more recently geometrical and spatio-temporal reasoning are gaining increasing attention. We propose to consider mathematical morphology operators as the inspiration for a new language and inference mechanism to reason about space. Interestingly, the proposed morpho-logic captures not only traditional mereotopological relations, but also notions of relative size and morphology. The proposed representational framework is a hybrid arrow logic theory for which we define a resolution calculus which is, to the best of our knowledge, the first such calculus for arrow logics.

Subjects: 3.2 Geometric Or Spatial Reasoning; 15.9 Theorem Proving

Submitted: Oct 13, 2006


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