Qualitative Reasoning about Imprecise Spatial Information

This paper investigates the problem of reasoning about imprecise spatial information. As a representation scheme we assume haze-points that are points surrounded by an area, the haze, denoting the imprecision that is associated with them. Haze-points are related by haze and precedence relations. Using these notions we can build higher dimension objects and relations Top94a]. This paper focuses on reasoning about spatial imprecision which is formalized as a constraint satisfaction problem over networks of constraints expressed in the language of haze-orders. The main contributions of this paper are (a) a set of preprocessing transformations that decrease the ambiguity which is introduced from unconditional transitivity over the haze relation, and (b) a graph-based data structure which is suitable for ee-cient inferencing of order relations. 1 Introduction It is generally accepted that neither human perception nor measurement instruments are precise in the information they provide. This is especially true for spatial knowledge. The position of objects in space and the spatial relations between objects are perceived in relation to the degree of detail with which the world is viewed. The ability to reason with knowledge that is imprecise or is speciied in various degrees of precision, is fundamental to human intelligence. Incorporating this ability into knowledge representation and reasoning models is a major issue for artiicial intelligence research. In this paper we investigate this problem focusing on spatial knowledge. The haze-space ontology introduced in Top94a] sets the formal framework for this work. In the haze-space ontology, space is viewed as a totality of spatial objects connected in terms of spatial relations. There are two types of objects: points and regions. In the proposed framework, a point is not a zero-sized object but has an associated haze area, anywhere inside which the point in question may be located. Consequently, points which are \very close" to each other are indistinguishable. The notion of haze can help