Qualitative Temporal and Spatial Reasoning Revisited

Abstract

Establishing local consistency is one of the main algorithmic techniques in temporal and spatial reasoning. In this area, one of the central questions for the various proposed temporal and spatial constraint languages is whether local consistency implies global consistency. Showing that a constraint language Γ has this “local-to-global” property implies polynomial-time tractability of the constraint language, and has further pleasant algorithmic consequences.In the present paper, we study the “local-to-global” property by making use of a recently established connection of this property with universal algebra. Specifically, the connection shows that this property is equivalent to the presence of a so-called quasi near-unanimity polymorphism of the constraint language. We obtain new algorithmic results and give very concise proofs of previously known theorems. Our results concern well-known and heavily studied formalisms such as the point algebra and its extensions, Allen’s interval algebra, and the spatial reasoning language RCC-5.KeywordsConstraint SatisfactionConstraint Satisfaction ProblemRelation AlgebraSpatial ReasoningRelation SymbolThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.