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 wellknown and heavily studied formalisms such as the point algebra and its extensions, A...

• Type: Conference
• Year: 2007
• Where: CSL
• Authors: Manuel Bodirsky, Hubie Chen
• Keywords: Constraint Language, CSL 2007, Local Consistency, Spatial Reasoning