Multidimensional mereotopology with betweenness

Authors:
Torsten Hahmann;Michael Grüninger
Affiliations:
Department of Computer Science, University of Toronto;Department of Mechanical and Industrial Engineering, University of Toronto
Venue:
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Year:
2011

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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 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.