Formal Properties of Constraint Calculi for Qualitative Spatial Reasoning

In the previous two decades, a number of qualitative constraint calculi have been developed, which are used to represent and reason about spatial configurations. A common property of almost all of these calculi is that reasoning in them can be understood as solving a binary constraint satisfaction problem over infinite domains. The main algorithmic method that is used is constraint propagation in the form of the path-consistency method. This approach can be applied to a wide range of different aspects of spatial reasoning. We describe how to make use of this representation and reasoning technique and point out the possible problems one might encounter. 1 Qualitative Spatial Representation and Reasoning Representing spatial information and reasoning about this information is an important subproblem in many applications, such as geographical information systems (GIS), natural language understanding, robot navigation, and document interpretation. Often this information is only available qualitatively, for instance when a GIS query or integrity condition has to be specified (Sharma et al., 1994). Similarly, in document interpretation, the precise size and location of layout objects is not of interest, but the relative position of these objects matters (Walischewski, 1999). A number of approaches to representing qualitative spatial information and reasoning about it are possible. A very early attempt at qualitative spatial representation and reasoning is Kuipers’ (1978) TOUR model, which addresses the navigation problem using qualitative descriptions. Other approaches aim, for instance, to capture spatial notions using first-order logic (Randell and Cohn, 1989;