Qualitative Reasoning about Convex Relations

Abstract

Various calculi have been designed for qualitative constraint-based representation and reasoning. Especially for orientation calculi, it happens that the well-known method algebraic closure cannot decide consistency constraint networks, even when considering networks over base relations (= scenarios) only. We show that this is the case for all relative orientation calculi capable 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 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 i¾?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 algebraic closure which can identify a subset inconsistent scenarios.