Establishing local consistency is one of the main algorithmic techniques in temporal and spatial reasoning. A central question 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"

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... y by making use of a recently established connection of this property with universal algebra. Roughly speaking, the connection shows that this property is equivalent to the presence of a so-called quasi nearunanimity 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, Allen's interval algebra, and the spatial reasoning language RCC-5.