Topological reasoning between complex regions in databases with frequent updates

Reasoning about space has been a considerable field of study both in Artificial Intelligence and in spatial information theory. Many applications benefit from the inference of new knowledge about the spatial relationships between spatial objects on the basis of already available and explicit spatial relationship knowledge that we call spatial (relationship) facts. Hence, the task is to derive new spatial facts from known spatial facts. A considerable amount of work has focused on reasoning about topological relationships (as a special and important subset of spatial relationships) between simple spatial objects like simple regions. There is a common consensus in the GIS and spatial database communities that simple regions are insufficient to model spatial reality and that complex region objects are needed that allow multiple components and holes. Models for topological relationships between complex regions have already been developed. Hence, as the next logical step, the goal of this paper is to develop a reasoning model for them. Further, no reasoning model considers changes of the spatial fact basis stored in a database between consecutive queries. We show that conventional modeling suffers from performance degradation when the database is frequently changing. Our model does not assume any geometric representation model or data structure for the regions. The model is also backward compatible, i.e., it is also applicable to simple regions.