Leopoldo E. Bertossi

Consistent query answers in inconsistent databases

In this paper we consider the problem of the logical characterization of the notion of consistent answer in a relational database that may violate given integrity constraints. This notion is captured in terms of the possible repaired versions of the database. A method for computing consistent answers is given and its soundness and completeness (for some classes of constraints and queries) proved. The method is based on an iterative procedure whose termination for several classes of constraints is proved as well.

Answer sets for consistent query answering in inconsistent databases

A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on answer sets to the problem of retrieving consistent information from a possibly inconsistent database. Since consistent information persists from the original database to every of its minimal repairs, the approach is based on a specification of database repairs using disjunctive logic programs with exceptions, whose answer set semantics can be represented and computed by systems that implement stable model semantics. These programs allow us to declare persistence by default of data from the original instance to the repairs; and changes to restore consistency, by exceptions. We concentrate mainly on logic programs for binary integrity constraints, among which we find most of the integrity constraints found in practice.

Consistent query answering in databases

For several reasons databases may become inconsistent with respect to a given set of integrity constraints (ICs): (a) The DBMS have no mechanism to maintain certain classes of ICs. (b) New constraints are imposed on preexisting, legacy data. (c) The ICs are soft, user, or informational constraints that are considered at query time, but without being necessarily enforced. (d) Data from different and autonomous sources are being integrated, in particular in mediator-based approaches.

Database Repairing and Consistent Query Answering

Integrity constraints are semantic conditions that a database should satisfy in order to be an appropriate model of external reality. In practice, and for many reasons, a database may not satisfy those integrity constraints, and for that reason it is said to be inconsistent. However, and most likely, a large portion of the database is still semantically correct, in a sense that has to be made precise. After having provided a formal characterization of consistent data in an inconsistent database, the natural problem emerges of extracting that semantically correct data, as query answers. The consistent data in an inconsistent database is usually characterized as the data that persists across all the database instances that are consistent and minimally differ from the inconsistent instance. Those are the so-called repairs of the database. In particular, the consistent answers to a query posed to the inconsistent database are those answers that can be simultaneously obtained from all the database repairs. As expected, the notion of repair requires an adequate notion of distance that allows for the comparison of databases with respect to how much they differ from the inconsistent instance. On this basis, the minimality condition on repairs can be properly formulated. In this monograph we present and discuss these fundamental concepts, different repair semantics, algorithms for computing consistent answers to queries, and also complexity-theoretic results related to the computation of repairs and doing consistent query answering. Table of Contents: Introduction / The Notions of Repair and Consistent Answer / Tractable CQA and Query Rewriting / Logically Specifying Repairs / Decision Problems in CQA: Complexity and Algorithms / Repairs and Data Cleaning

Query Answering in Inconsistent Databases

In this chapter, we summarize the research on querying inconsistent databases that we have been conducting during the last five years. The formal framework that we have used is based on two concepts: repair and consistent query answer. We describe different approaches to the issue of computing consistent query answers: query transformation, logic programming, inference in annotated logics, and specialized algorithms. We also characterize the computational complexity of this problem. Finally, we discuss related research in artificial intelligence, databases, and logic programming.

Scalar aggregation in inconsistent databases

We consider here scalar aggregation queries in databases that may violate a given set of functional dependencies. We define consistent answers to such queries to be greatest-lowest/least-upper bounds on the value of the scalar function across all (minimal) repairs of the database. We show how to compute such answers. We provide a complete characterization of the computational complexity of this problem. We also show how tractability can be improved in several special cases (one involves a novel application of Boyce-Codd Normal Form) and present a practical hybrid query evaluation method.

Complexity of consistent query answering in databases under cardinality-based and incremental repair semantics

A database D may be inconsistent wrt a given set IC of integrity constraints. Consistent Query Answering (CQA) is the problem of computing from D the answers to a query that are consistent wrt IC. Consistent answers are invariant under all the repairs of D, i.e. the consistent instances that minimally depart from D. Three classes of repair have been considered in the literature: those that minimize set-theoretically the set of tuples in the symmetric difference; those that minimize the changes of attribute values, and those that minimize the cardinality of the set of tuples in the symmetric difference. The latter class has not been systematically investigated. In this paper we obtain algorithmic and complexity theoretic results for CQA under this cardinality-based repair semantics. We do this in the usual, static setting, but also in a dynamic framework where a consistent database is affected by a sequence of updates, which may make it inconsistent. We also establish comparative results with the other two kinds of repairs in the dynamic case.

Specifying and Querying Database Repairs using Logic Programs with Exceptions

Databases may be inconsistent with respect to a given set of integrity constraints. Nevertheless, most of the data may be consistent. In this paper we show how to specify consistent data and how to query a relational database in such a way that only consistent data is retrieved. The specification and queries are based on disjunctive extended logic programs with positive and negative exceptions that generalize those previously introduced by Kowalski and Sadri.

Logic Programs for Querying Inconsistent Databases

Consistent answers from a relational database that violates a given set of integrity constraints (ICs) are characterized as ordinary answers that can be obtained from every minimally repaired version of the database (a repair). Repairs can be specified and interpreted as the stable models of a simple disjunctive normal logic program with database predicates extended with appropriate annotation arguments. In consequence, consistent query answers can be obtained by running a query program in combination with the repair program under the cautious or skeptical stable model semantics. In this paper we show how to write repair programs for universal and referential ICs; we establish their correctness and show how to run them on top of the DLV system.

Data cleaning and query answering with matching dependencies and matching functions

Matching dependencies were recently introduced as declarative rules for data cleaning and entity resolution. Enforcing a matching dependency on a database instance identifies the values of some attributes for two tuples, provided that the values of some other attributes are sufficiently similar. Assuming the existence of matching functions for making two attributes values equal, we formally introduce the process of cleaning an instance using matching dependencies, as a chase-like procedure. We show that matching functions naturally introduce a lattice structure on attribute domains, and a partial order of semantic domination between instances. Using the latter, we define the semantics of clean query answering in terms of certain/possible answers as the greatest lower bound/least upper bound of all possible answers obtained from the clean instances. We show that clean query answering is intractable in some cases. Then we study queries that behave monotonically w.r.t. semantic domination order, and show that we can provide an under/over approximation for clean answers to monotone queries. Moreover, non-monotone positive queries can be relaxed into monotone queries.