The Mathematical Morpho-Logical view on Reasoning about Space

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 morphologic operators as the inspiration for a new language and inference mechanism to reason about space. Interestingly, the proposed morphologic 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.