Maintaining Qualitative Spatial Knowledge

We present mechanisms used to maintain the consistency of a knowledge base of spatial information based on a qualitative representation of 2-D positions. These include the propagation heuristics used when inserting new relations as well as the reason maintenance mechanisms necessary to undo the eeects of propagation when deleting a relation. Both take advantage of the rich structure of the spatial domain. 1 Introduction For a representation to be of any use, we have to consider not only its constituents and how they correspond to what is being represented, but also the mechanisms operating on them. In this paper we look into the mechanisms that allow us to reason with qualitative representations of 2-D positions. These mechanisms are determined in part by the tasks for which qualitative reasoning is used, such as: Inferring knowledge implicit in the knowledge base; answering queries given partial knowledge and a spe-ciic context; maintaining various types of consistency; acquiring new knowledge; and, particularly in the case of spatial knowledge, building cognitive maps and visualizing qualitatively represented spatial situations. Even though the qualitative approach has been extensively used for modeling physical phenomena (Bobrow 1984; Weld and de Kleer 1990), it is only recently that research on qualitative models of space has been undertaken. Allen (1983) introduced an interval-based temporal logic, in which knowledge about time is maintained qualitatively by storing comparative relations between intervals. Freksa (1992a) presents a generalization of Allen's temporal reasoning approach based on semi-intervals and