Singularities in Qualitative Reasoning

Qualitative Reasoning is characterised by making knowledge explicit in order to arrive at efficient reasoning techniques. It contrasts with often intractable quantitative models. Whereas quantitative models require computations on continuous spaces, qualitative models work on discrete spaces. A problem arises in discrete spaces concerning transitions between neighbouring qualitative concepts. A given arrangement of objects may comprise relations which correspond to such transitions, e.g. an object may be neither left of nor right of another object but precisely aligned with it. Such singularities are sometimes undesirable and influence underlying reasoning mechanisms. We shall show how to deal with singular relations in a way that is more closely related to commonsense reasoning than treating singularities as basic qualitative concepts.