Path Composition of Positional Relations Integrating Qualitative and Fuzzy Knowledge

Qualitative models of spatial knowledge concern the description of both objects and their relative position in space. In this context, fuzzy knowledge concerns the degree of likelihood with which a qualitative spatial relation can be mapped to a geometric counterpart. In this chapter, we argue that the integration of fuzzy knowledge into qualitative models allows us more effective spatial reasoning. In fact, the basic step of reasoning with positional relations, that is, the composition of two relations, if iterated over a path of several intermediate positions, introduces too much indeterminacy in the result. If the algorithms for composition take into account fuzzy knowledge, the latter effect is considerably reduced, obtaining an indication of the degree of likelihood of the result.