Imprecise Qualitative Spatial Reasoning

Abstract

This paper addresses the issue of qualitative reasoning in imprecise spatial domains. In particular, the uncertainty in the nature of the spatial relationships between objects in space is represented by a set of possibilities. The approach to spatial reasoning proposed here is carried out in three steps. First, a transformation is carried out on the disjunctive set of possible relationships to derive their corresponding set of spatial constraints. Reasoning formulae are developed to propagate the set of identified constraints and finally a transformation is carried out on the resulting constraints to map them back to the domain of spatial relations to identify the result of the spatial composition. Two general equations form the basis for the propagation of the spatial constraints. A major advantage of this method is that reasoning with incomplete knowledge can be done by direct application of the reasoning formulae on the spatial objects considered, and thus eliminates the need for utilising the inordinate number of composition tables which must be built for specific object types and topology. The method is applied on spatial objects of arbitrary complexity and in a finite definite number of steps controlled by the complexity needed in the representation of objects and the granularity of the spatial relations required.