Cognitive spatial concepts are qualitative in nature, i.e., they are based not so much on exact quantities but on comparisons between perceived magnitudes. We develop a qualitative model for the representation of spatial knowledge (in particular, of positional information about 2-dimensional projections) that is based only on locative relations between the objects involved, does not need a global scale, and takes different kinds of reference frames into consideration. The resulting model is both cognitively plausible and computationally efficient.

The core of the book is the study of qualitative inference methods. We extend constraint reasoning mechanisms to take the rich structure of physical space into consideration, and describe methods to transform among reference frames and for the composition of relations. We also sketch extensions of the qualitative approach to represent positional information in 3-D scenes, as well as other spatial concepts such as size, shape, and distance.

Qualitative representations make only as many distinctions as necessary to identify objects, events, situations, etc. in a given context (recognition task) as opposed to those needed to fully reconstruct a situation (reconstruction task). Thus, they can be used in many application areas from everyday life in which spatial knowledge plays a role, particularly in those that are characterized by uncertain and incomplete knowledge, such as computer aided systems for ar chitectural design, geographical information systems, but also robot control or natural language information systems to give directions.

This book is a revised version of a dissertation submitted to the Institut fur Informatik (Department of Computer Science) of the Technische Universitat Munchen (Munich, Germany) in December of 1992. In the meantime, inter est in qualitative models of space has multiplied as reflected by several recent workshops and conference sections on the subject (QUARDET 93, COSIT 93, IJCAI 93, KI-93).1 Taking all of these new developments fully into account is impossible within the time allotted for revision, and without a complete rewrite of several parts of the text. However, I have tried to compile the references to newer published work in the bibliography, and to point to them in the appropri ate sections.