Erratum to “Reformulating table constraints using functional dependencies—an application to explanation generation”

We had claimed that arc-consistency is preserved in a constraint reformulation relying on functional dependencies (Theorem 2 of Cambazard and O’Sullivan Constraints 13(3):385–406 ( 2008 )). 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.