Qualitative triangulation for spatial reasoning

Abstract

This paper presents a systematic way of defining qualitative calculi for spatial reasoning. These calculi, which derive from the concept of qualitative triangulation, allow inference about the relative relationships of punctual objects in two-dimensional space. After introducing the general concept of qualitative triangulation, we discuss the main aspects of some important members of this family of calculi, including the so-called flipflop calculus, which subsumes the relative calculus in dimension one, and the calculus introduced by Freksa (orientation-based spatial inference). This allows us to present in a general setting the notions of coarse and fine inference, as well as the conceptual neighborhood properties of sets of spatial relations. We also show how these calculi can be used for actual inference, and how switching from a particular calculus to a refinement of it can be used to strengthen the inference.