Qualitative Reasoning about Convex Relations

  • Authors:

  • Dominik Lücke;Till Mossakowski;Diedrich Wolter

  • Affiliations:

  • SFB/TR 8 Spatial Cognition Dept. of Computer Science, University of Bremen, Bremen, D-28334;SFB/TR 8 Spatial Cognition Dept. of Computer Science, University of Bremen, Bremen, D-28334 and DFKI Lab Bremen, Safe & Secure Cognitive Systems, Bremen, D-28359;SFB/TR 8 Spatial Cognition Dept. of Computer Science, University of Bremen, Bremen, D-28334

  • Venue:
  • Proceedings of the international conference on Spatial Cognition VI: Learning, Reasoning, and Talking about Space
  • Year:
  • 2008

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Abstract

Various calculi have been designed for qualitative constraint-based representation and reasoning. Especially for orientation calculi, it happens that the well-known method of algebraic closure cannot decide consistency of constraint networks, even when considering networks over base relations (= scenarios) only. We show that this is the case for all relative orientation calculi capable of distinguishing between "left of" and "right of". Indeed, for these calculi, it is not clear whether efficient (i.e. polynomial) algorithms deciding scenario-consistency exist.As a partial solution of this problem, we present a technique to decide global consistency in qualitative calculi. It is applicable to all calculi that employ convex base relations over the real-valued space 茂戮驴nand it can be performed in polynomial time when dealing with convex relations only. Since global consistency implies consistency, this can be an efficient aid for identifying consistent scenarios. This complements the method of algebraic closure which can identify a subset of inconsistent scenarios.