Multidimensional Mereotopology with Betweenness ? Torsten Hahmann Michael Gru?ninger
Abstract
Qualitative reasoning about commonsense space often involves entities of different dimensions. We present a weak axiomatization of multidimensional qualitative space based on ‘relative dimension’ and dimension-independent ‘containment’ which suf?ce to de?ne basic dimension-dependent mereotopological relations. We show the relationships to other meoreotopologies and to incidence geometry. The extension with betweenness, a primitive of relative position, results in a ?rst-order theory that qualitatively abstracts ordered incidence geometry.