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 focus on two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers [3] (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 cases. 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. 1

www.elsevier.com/locate/jcss We consider the problem of retrieving consistent answers over databases that might be inconsistent with respect to a set of integrity constraints. In particular, we concentrate on sets of constraints that consist of key dependencies, and we give an algorithm that computes the consistent answers for a large and practical class of conjunctive queries. Given a query q, the algorithm returns a first-order query Q (called a query rewriting) such that for every (potentially inconsistent) database I, the consistent answers for q can be obtained by evaluating Q directly on I. © 2006 Published by Elsevier Inc.

When data sources are virtually integrated there is no common and centralized mechanism for maintaining global consistency. In consequHHj9 it is likely that inconsistencies with respect to certain global integrity constraints (ICs)will occu; In this chapter we consider the problem of defining andcompu2;) those answers that are consistent wrt the global ICs when global qubal) are posed tovirtuM data integration systems whosesou)33 are specified following the local-as-view approach.

Abstract. The problem of answering queries posed to a peer who is a member of a peer-to-peer data exchange system is studied.The answers have to be consistent wrt to both the local semantic constraints and the data exchange constraints with other peers; and must also respect certain trust relationships between peers. A semantics for peer consistent answers under exchange constraints and trust relationships is introduced and some techniques for obtaining those answers are presented. 1

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.

c ○ Copyright by Loreto Bravo, 2007 For several reasons a database may not satisfy certain integrity constraints (ICs), for example, when it is the result of integrating several independent data sources. However, most likely, information in it is still consistent with the ICs; and could be retrieved when queries are answered. Consistent answers with respect to a set of ICs have been characterized as answers that can be obtained from every possible minimal repair of the database. The goal of this research is to develop methods to retrieve consistent answers for a wide and practical class of constraints and queries from relational databases and from data integration systems. We will put special interest on databases with null values. We will give a semantics of satisfaction of constraints in the presence of null that generalizes the one used in commercial DBMS. Since there are interesting connections between the area of consistently querying virtual data integration systems and other areas, like querying incomplete databases, merging inconsistent theories, semantic reconciliation of data, schema mapping, data exchange, and query answering in peer data management systems, the results of this research could also be applied to them. In our research, we explore in more depth the connection with virtual data integration systems and peer data management systems. ii To my husband

Abstract. Consistent answers to a query from an inconsistent database are answers that can be simultaneously retrieved from every possible repair; and repairs are consistent instances that minimally differ from the original instance. Database repairs can be specified as the stable models of a disjunctive logic program. In this paper we show how to use the repair programs to transform the problem of consistent query answering into a problem of reasoning wrt a concrete theory written in second-order predicate logic. It also investigated how a first-order theory can be obtained instead, by applying second-order quantifier elimination techniques. 1