Local and Global Relational Consistency

Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new de nition of local consistency, called relational consistency. The new de nition is relation-based, in contrast with the previous de nition of local consistency, which we characterize as variable-based. We show the conceptual power of the new de nition by showing how it uni es known elimination operators such as resolution in theorem proving, joins in relational databases, and variable elimination for solving linear inequalities. Algorithms for enforcing various levels of relational consistency are introduced and analyzed. We also show the usefulness of the new de nition in characterizing relationships between properties of constraint networksand the level of local consistency needed to ensure global consistency.