Qualitative Representation and Reasoning over Direction Relations across Different Frames of Reference.

Direction relations are some of the most commonly used spatial relations in human communication. A number of formalisms have been proposed to capture direction information, but all of them suffer from the same problem: people use direction relations as if they are binary relations (e.g. A is to the left of B) when they are in fact ternary relations (e.g. A is to the left of B when viewed from C). This implicit third piece of information that is required, but typically missing, is often referred to as the frame of reference (FoR). Given only binary direction relations without knowing the FoR means that we cannot do proper spatial reasoning (e.g. A is to the left of B and A is to the right of B are both consistent), we cannot integrate direction information from different sources, not even from the same source, and it can be difficult to understand what exactly someone means. In this paper we provide 1) the spatial constraint language DAF(m) that can represent and compose direction relations across different FoRs; and 2) the foundations for deciding the overall consistency. We hope our model of representing and reasoning can bring research on direction relations to another level and will finally make it possible to properly use them in a comprehensive way.