Data integration is the problem of combining data residing at different sources, and providing the user with a unified view of these data. The problem of designing data integration systems is important in current real world applications, and is characterized by a number of issues that are interesting from a theoretical point of view. This document presents on overview of the material to be presented in a tutorial on data integration. The tutorial is focused on some of the theoretical issues that are relevant for data integration. Special attention will be devoted to the following aspects: modeling a data integration application, processing queries in data integration, dealing with inconsistent data sources, and reasoning on queries.

In this chapter, we summarize the research on querying inconsistent databases we have been conducting over the last five years. The formal framework 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.

In databases with integrity constraints, data may not satisfy the constraints. In this paper, we address the problem of obtaining consistent answers in such a setting, when key and inclusion dependencies are expressed on the database schema. We establish decidability and complexity results for query answering under different assumptions on data (soundness and/or completeness). In particular, after showing that the problem is in general undecidable, we identify the maximal class of inclusion dependencies under which query answering is decidable in the presence of key dependencies. Although obtained in a single database context, such results are directly applicable to data integration, where multiple information sources may provide data that are inconsistent with respect to the global view of the sources. 1.

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

In this paper we address the problem of query answering and rewriting in global-as-view data integration systems, when key and inclusion dependencies are expressed on the global integration schema. In the case of sound views, we provide sound and complete rewriting techniques for a maximal class of constraints for which decidability holds. Then, we introduce a semantics which is able to cope with violations of constraints, and present a sound and complete rewriting technique for the same decidable class of constraints. Finally, we consider the decision problem of query answering and give decidability and complexity results. 1

We solve the problem of obtaining answers to queries posed to a mediated integration system under the local-as-view paradigm that are consistent wrt to certain global integrity constraints. For this, the query program is combined with logic programming specifications under the stable model semantics of the class of minimal global instances, and of

Census data provide valuable insights on the economic, social and demographic conditions and trends occurring in a country. Census data is collected by means of millions of questionnaires, each one including the details of the persons living together in the same house. Before the data from the questionnaires is sent to the statisticians to be analysed, a cleaning phase (called \imputation") is performed, in order to eliminate consistency problems, missing answers, or errors. It is important that the imputation step is done without altering the statistical validity of the collected data. The contribution of this paper is twofold. On the one hand, it provides a clear and well-founded declarative semantics to questionnaires and to the imputation problem. On the other hand, a correct modular encoding of the problem in the disjunctive logic programming language DLP w , supported by the DLV system is shown. It turns out that disjunctive logic programming is very well-suited for this goal. Census data repair appears a challenging application area for disjunctive logic programming. Keywords: Nonmonotonic Reasoning, Disjunctive Logic Programming, Knowledge Representation. 1

Many data integration systems provide transparent access to heterogeneous data sources through a unified view of all data in terms of a global schema, which may be equipped with integrity constraints on the data. Since these constraints might be violated by the data retrieved from the sources, methods for handling such a situation are needed. To this end, recent approaches model query answering in data integration systems in terms of nonmonotonic logic programs.

When data sources are integrated into a single global system, inconsistencies wrt global integrity constraints are likely to occur. In this paper, the notion of consistent answer to a global query in the context of the local-as-view model of data integration is characterized. Furthermore, a methodology for generating query plans for retrieving consistent answer to global queries is introduced. For this purpose, an extension of the inverse-rules algorithm for deriving query plans is presented. It can be used to answer first order queries posed to data sources integrated according to the local-as-view.

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.