We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. We assume that integrity-restoration actions are limited to tuple deletions. We identify two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers [ABC99] (is a tuple an answer to a given query in every repair of a given database?). We study the computational complexity of both problems, delineating the boundary between the tractable and the intractable. We consider denial constraints, general functional and inclusion dependencies, as well as key and foreign key constraints. Our results shed light on the computational feasibility of minimal-change integrity maintenance. The tractable cases should lead to practical implementations. The intractability results highlight the inherent limitations of any integrity enforcement mechanism, e.g., triggers or referential constraint actions, as a way of performing minimal-change integrity maintenance.Given a database instance r, the set Σ(r) of facts of r is the set of ground atomic formulas {P (ā) | r P (ā)}, where P is a relation name andā a ground tuple. Definition 2The distance ∆ − (r, r ′ ) between data-base instances r and r ′ is defined as ∆ − (r, r ′ ) = (Σ(r) − Σ(r ′ )).Definition 3 For the instances r, r ′ , r ′′ , r ′ ≤ r r ′′ if ∆ − (r, r ′ ) ⊆ ∆ − (r, r ′′ ), i.e., if the distance between r and r ′ is less than or equal to the distance between r and r ′′ .Definition 4 Given a set of integrity constraints IC and database instances r and r ′ , we say that r ′ is a repair of r w.r.t. IC if r ′ IC and r ′ is ≤ r -minimal in the class of database instances that satisfy IC.If r ′ is a repair of r, then Σ(r ′ ) is a maximal consistent subset of Σ(r). We denote by Repairs IC (r) the set of repairs of r w.r.t. IC. This set is nonempty, since the empty database instance satisfies every set of FDs and INDs.

A consistent query answer in an inconsistent database is an answer obtained in every (minimal) repair. The repairs are obtained by resolving all conflicts in all possible ways. Often, however, the user is able to provide a preference on how conflicts should be resolved. We investigate here the framework of preferred consistent query answers, in which user preferences are used to narrow down the set of repairs to a set of preferred repairs. We axiomatize desirable properties of preferred repairs. We present three different families of preferred repairs and study their mutual relationships. Finally, we investigate the complexity of preferred repairing and computing preferred consistent query answers.

A consistent query answer in a possibly inconsistent database is an answer which is true in every (minimal) repair of the database. We present here a practical framework for computing consistent query answers for large, possibly inconsistent relational databases. We consider relational algebra queries without projection, and denial constraints. Because our framework handles union queries, we can effectively (and efficiently) extract indefinite disjunctive information from an inconsistent database. We describe a number of novel optimization techniques applicable in this context and summarize experimental results that validate our approach.

Abstract. We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. Using the framework proposed by Arenas, Bertossi, and Chomicki [4], we focus on two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers (is a tuple an answer to a given query in every repair of a given database?). We study the computational complexity of both problems, delineating the boundary between the tractable and the intractable. We review relevant semantical issues and survey different computational mechanisms proposed in this context. Our analysis sheds light on the computational feasibility of minimal-change integrity maintenance. The tractable cases should lead to practical implementations. The intractability results highlight the inherent limitations of any integrity enforcement mechanism, e.g., triggers or referential constraint actions, as a way of performing minimal-change integrity maintenance.

Abstract-We solve a well known, long-standing open problem in relational databases theory, showing that the conjunctive query determinacy problem (in its "unrestricted" version) is undecidable.