A Naive Theory of Dimension for Qualitative Spatial Relations

We present an ontology consisting of a theory of spatial dimension and a theory of dimension-independent mereological and topological relations in space. Though both are fairly weak axiomatizations, their interplay suffices to define various mereotopological relations and to make any necessary dimension constraints explicit. We show that models of the INCH Calculus and the Region-Connection Calculus (RCC) can be obtained from extensions of the proposed ontology.