On the Translation of Qualitative Spatial Reasoning Problems into Modal Logics

Authors:
Werner Nutt
Affiliations:
-
Venue:
KI '99 Proceedings of the 23rd Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Year:
1999

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Abstract

We introduce topological set constraints that express qualitative spatial relations between regions. The constraints are interpreted over topological spaces. We show how to translate our constraints into formulas of a multimodal propositional logic and give a rigorous proof that this translation preserves satisfiability. As a consequence, the known algorithms for reasoning in modal logics can be applied to qualitative spatial reasoning. Our results lay a formal foundation to previous work by Bennett, Nebel, Renz, and others on spatial reasoning in the RCC8 formalism.