Erratum to "Reformulating table constraints using functional dependencies - an application to explanation generation"

Abstract. We had claimed that arc-consistency is preserved in a constraint reformulation relying on functional dependencies (Theorem 2 of [2]). We show that the statement of this theorem was too strong by providing a counter-example. However, the result holds for dependencies between pairs of variables, and more generally in restricted settings. 1 Reformulation of Positive Table Constraints We consider the setting in which a constraint c is defined over a subset of the variables in the problem, scope(c). The set of assignments to the variables in scope(c) that satisfy the constraint are specified as an extensionally defined relation, rel(c). A functional dependency in a relation rel(c) is written as F : X y, where X is a set of variables in the scope of c and y is a single variable in the scope of c, i.e. X {y} scope(c). Informally, a functional dependency states that if a pair of tuples in the relation take the same values for the variables in X, they must also take the same value ...

• Type: Journal
• Year: 2010
• Where: CONSTRAINTS
• Authors: Hadrien Cambazard, Barry O'Sullivan
• Keywords: Constraint Reformulation, CONSTRAINTS 2010, Functional Dependencies, Positive Table Constraints