Qualitative Spatial Reasoning Using Constraint Calculi

1. Introduction Qualitative reasoning is an approach for dealing with commonsense knowledge without using numerical computation. Instead, one tries to represent knowledge using a limited vocabulary such as qualitative relationships between entities or qualitative categories of numerical values, for instance, using {+, −, 0} for representing real values. An important motivation for using a qualitative approach is that it is considered to be closer to how humans represent and reason about commonsense knowledge. Another motivation is that it is possible to deal with incomplete knowledge. Qualitative reasoning, however, is different from fuzzy computation. While fuzzy categories are approximations to real values, qualitative categories make only as many distinctions as necessary—the granularity depends on the corresponding application. Two very important concepts of commonsense knowledge are time and space. Time, being a scalar entity, is very well suited for a qualitative approach and, thus, qualitative temporal reasoning has early emerged as a lively sub-field of qualitative reasoning which has generated a lot of research effort and important results. Space, in turn, is much more com