Using topology for spatial reasoning

Several formalisms have been proposed for qualitative reasoning about regions and their topological relations in space. These formalisms, based on pairwise relations, do not allow sufficiently powerful inferences to be used for spatial reasoning tasks such as planning a collision-free path. In this paper, I show how considering relations between region triples, much more powerful reasoning techniques become possible. I show in particular that in two dimensions, purely topological reasoning is sufficient to compute a minimal place graph which represents all minimal and maximal region combinations, as well as all minimal paths between them. I illustrate how this could be applied to motion planning, showing that in spite of its qualitative nature, the formalism is powerful enough to solve problems of pratical interest.

• Type: Conference
• Year: 2000
• Where: AMAI
• Authors: Boi Faltings
• Keywords: AMAI 2000, Artificial Intelligence, Powerful Reasoning Techniques, Reasoning, Spatial Reasoning Tasks