A Representation Theorem for Spatial Relations

Spatial relations have been investigated in various inter-related areas such as qualitative spatial reasoning (for agents moving in an environment), geographic information science, general topology, and others. Most of the results are specific constructions of spatial relations that fulfill some required properties. Results on setting up axioms that capture the desired properties of the relations are rare. And results that characterize spatial relations in the sense that they give a complete set of axioms for the intended spatial relations still have to be presented. This paper aims at filling the gap by providing a representation theorem: It shows that there is a finite set of axioms that are fulfilled by a binary relation if and only if it can be constructed as a binary spatial relation based on a nested partition chain.