Consistency and Set Intersection

Abstract

We propose a new framework to study properties of consistency in a Constraint Network from the perspective of properties of set intersection. Our framework comes with a proof schema which gives a generic way of lifting a set intersection property to one on consistency. Various well known results can be derived with this framework. More importantly, we use the framework to obtain a number of new results. We identify a new class of tree convex constraints where local consistency ensures global consistency. Another result is that in a network of arbitrary constraints, local consistency implies global consistency whenever there are certain m-tight constraints. The most interesting result is that when the constraint on every pair of variables is properly m-tight in an arbitrary network, global consistency can be achieved by enforcing relational m+ !-consistency. These results significantly improve our understanding of convex and tight constraints. This demonstrates that our framework is a promising and powerful tool for studying consistency.