The paper investigates the question of whether a partially closed database has complete information to answer a query. In practice an enterprise often maintains master data Dm, a closed-world database. We say that a database D is partially closed if it satisfies a set V of containment constraints of the form q(D) p(Dm), where q is a query in a language LC and p is a projection query. The part of D not constrained by (Dm, V ) is open, from which some tuples may be missing. The database D is said to be complete for a query Q relative to (Dm, V ) if for all partially closed extensions D of D, Q(D ) = Q(D), i.e., adding tuples to D either violates some constraints in V or does not change the answer to Q. We first show that the proposed model can also capture the consistency of data, in addition to its relative completeness. Indeed, integrity constraints studied for consistency can be expressed as containment constraints. We then study two problems. One is to decide, given Dm, V , a query...