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

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. We propose a generalization of the well-known Magic Sets technique to Datalog ¬ programs with (possibly unstratified) negation under stable model semantics. Our technique produces a new program whose evaluation is generally more efficient (due to a smaller instantiation), while preserving soundness under cautious reasoning. Importantly, if the original program is consistent, then full query-equivalence is guaranteed for both brave and cautious reasoning, which turn out to be sound and complete. In order to formally prove the correctness of our Magic Sets transformation, we introduce a novel notion of modularity for Datalog ¬ under the stable model semantics, which is relevant per se. We prove that a module can be evaluated independently from the rest of the program, while preserving soundness under cautious reasoning. For consistent programs, both soundness and completeness are guaranteed for brave reasoning and cautious reasoning as well. Our Magic Sets optimization constitutes an effective method for enhancing the performance of data-integration systems in which query-answering is carried out by means of cautious reasoning over Datalog ¬ programs. In fact, preliminary results of experiments in the EU project INFOMIX, show that Magic Sets are fundamental for the scalability of the system. 1

We address the problem of retrieving certain and consistent answers to queries posed to a mediated data integration system with open sources under the local-as-view paradigm using conjunctive and disjunctive view definitions. For obtaining certain answers a query program is run on top of a normal deductive database with choice that defines the class of minimal legal instances of the integration system under the cautious stable model semantics. This methodology works for all monotone Datalog queries. To compute answers to queries that are consistent wrt given global integrity constraints, the specification of minimal legal instances is combined with another disjunctive deductive database that specifies the repairs of those legal instances. This allows to retrieve the consistent answers to any Datalog query, for any set of universal and acyclic referential integrity constraints.

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.

The task of an information integration system is to combine data residing at different sources, providing the user with a unified view of them, called global schema. Users formulate queries over the global schema, and the system

We describe the Consistency Extractor System (ConsEx) that computes consistent answers to Datalog queries with negation posed to relational databases that may be inconsistent with respect to certain integrity constraints. In order to solve this task, ConsEx uses answers set programming. More precisely, ConsEx uses disjunctive logic programs with stable models semantics to specify and reason with the repairs, i.e. with the consistent virtual instances that minimally depart from the original database. The consistent information is invariant under all repairs. ConsEx achieves efficient query evaluation by implementing magic sets techniques. We describe the general methodology, its optimizations for query answering, and the architecture of the system. We also present encouraging experimental results.

Abstract. We present the Consistency Extractor System (ConsEx) that uses answer set programming to compute consistent answers to first-order queries posed to relational databases that may be inconsistent wrt their integrity constraints. Among other features, ConsEx implements a magic sets technique to evaluate queries via disjunctive logic programs with stable model semantics that specify the repair of the original database. We describe the methodology and the system; and also present some experimental results. 1

Query answering from inconsistent databases amounts to finding “meaningful” answers to queries posed over database instances that do not satisfy integrity constraints specified over their schema. A declarative approach to this problem relies on the notion of repair, i.e., a database that satisfies integrity constraints and is obtained from the original inconsistent database by “minimally” adding and/or deleting tuples. Consistent answers to a user query are those answers that are in the evaluation of the query over each repair. Motivated by the fact that computing consistent answers from inconsistent databases is in general intractable, the present paper investigates techniques that allow to localize the difficult part of the computation on a small fragment of the database at hand, called “affected ” part. Based on a number of localization results, an approach to query answering from inconsistent data is presented, in which the query is evaluated over each of the repairs of the affected part only, augmented with the part that is not affected. Single query results are then suitably recombined. For some relevant classes of queries and constraints, techniques are also discussed to factorize repairs into components that can be processed independently of one another, thereby guaranteeing exponential gain w.r.t. the basic approach, which is not based on localization. The effectiveness of the results is demonstrated for consistent query answering over expressive schemas,

Databases may not always satisfy their integrity constraints (ICs) and a number of different reasons can be held accountable for this. However, in most cases an important part of the data is still consistent with the ICs, and can still be retrieved through queries posed to the database. Consistent query answers are characterized as ordinary answers obtained from every minimally repaired and consistent version of the database. Database repairs wrt a wide class of ICs can be specified as stable models of disjunctive logic programs. Thus, Consistent Query Answering (CQA) for first-order queries is translated into cautious reasoning under the stable models semantics. The use of logic programs does not exceed the intrinsic complexity of CQA. However, using them in a straightforward manner is usually inefficient. The goal of this thesis is to develop optimized techniques to evaluate queries over inconsistent