Multidimensional Mereotopology with Betweenness ∗
Torsten Hahmann, Michael Grüninger · 2012
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 suffice to define 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 first-order theory that qualitatively abstracts ordered incidence geometry. 1