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.

Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema that reflects the source data as accurately as possible. In this paper, we address foundational and algorithmic issues related to the semantics of data exchange and to query answering in the context of data exchange. These issues arise because, given a source instance, there may be many target instances that satisfy the constraints of the data exchange problem. We give an algebraic specification that selects, among all solutions to the data exchange problem, a special class of solutions that we call universal. A universal solution has no more and no less data than required for data exchange and it represents the entire space of possible solutions. We then identify fairly general, and practical, conditions that guarantee the existence of a universal solution and yield algorithms to compute a canonical universal solution efficiently. We adopt the notion of "certain answers" in indefinite databases for the semantics for query answering in data exchange. We investigate the computational complexity of computing the certain answers in this context and also study the problem of computing the certain answers of target queries by simply evaluating them on a canonical universal solution.

We present a novel framework for mapping between any combination of XML and relational schemas, in which a high-level, userspecified mapping is translated into semantically meaningful queries that transform source data into the target representation. Our approach works in two phases. In the first phase, the high-level mapping, expressed as a set of inter-schema correspondences, is converted into a set of mappings that capture the design choices made in the source and target schemas (including their hierarchical organization as well as their nested referential constraints).

In this paper we study data complexity of answering conjunctive queries over Description Logic knowledge bases constituted by an ABox and a TBox. In particular, we are interested in characterizing the FOL-reducibility and the polynomial tractability boundaries of conjunctive query answering, depending on the expressive power of the Description Logic used to specify the knowledge base. FOL-reducibility means that query answering can be reduced to evaluating queries over the database corresponding to the ABox. Since firstorder queries can be expressed in SQL, the importance of FOL-reducibility is that, when query answering enjoys this property, we can take advantage of Data Base Management System (DBMS) techniques for both representing data, i.e., ABox assertions, and answering queries via reformulation into SQL. What emerges from our complexity analysis is that the Description Logics of the DL-Lite family are the maximal logics allowing conjunctive query answering through standard database technology. In this sense, they are the first Description Logics specifically tailored for effective query answering over very large ABoxes.

A schema mapping is a specification that describes how data structured under one schema (the source schema) is to be transformed into data structured under a di#erent schema (the target schema). Schema mappings play a key role in numerous areas of database systems, including database design, information integration, and model management. A fundamental problem in this context is composing schema mappings: given two successive schema mappings, derive a schema mapping between the source schema of the first and the target schema of the second that has the same e#ect as applying successively the two schema mappings.

Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema that reflects the source data as accurately as possible. Given a source instance, there may be many solutions to the data exchange problem, that is, many target instances that satisfy the constraints of the data exchange problem. In an earlier paper, we identified a special class of solutions that we call universal. A universal solution has homomorphisms into every possible solution, and hence is a "most general possible" solution. Nonetheless, given a source instance, there may be many universal solutions. This naturally raises the question of whether there is a "best" universal solution, and hence a best solution for data exchange. We answer this question by considering the well-known notion of the core of a structure, a notion that was first studied in graph theory, but has also played a role in conjunctive-query processing. The core of a structure is the smallest substructure that is also a homomorphic image of the structure. All universal solutions have the same core (up to isomorphism); we show that this core is also a universal solution, and hence the smallest universal solution. The uniqueness of the core of a universal solution together with its minimality make the core an ideal solution for data exchange. Furthermore, we show that the core is the best among all universal solutions for answering unions of conjunctive queries with inequalities. After this, we investigate the computational complexity of producing the core. Well-known results by Chandra and Merlin imply that, unless P = NP, there is no polynomial-time algorithm that, given a structure as input, returns the core of that structure as output. In contrast, in the context of data e...

Semantic mappings between data sources play a key role in several data sharing architectures. Mappings provide the relationships between data stored in different sources, and therefore enable answering queries that require data from other nodes in a data sharing network. Composing mappings is one of the core problems that lies at the heart of several optimization methods in data sharing networks, such as caching frequently traversed paths and redundancy analysis.

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.

Peer data management systems (PDMS) offer a flexible architecture for decentralized data sharing. In a PDMS, every peer is associated with a schema that represents the peer's domain of interest, and semantic relationships between peers are provided locally between pairs (or small sets) of peers. By traversing semantic paths of mappings, a query over one peer can obtain relevant data from any reachable peer in the network. Semantic paths are traversed by reformulating queries at a peer into queries on its neighbors. Naively following semantic paths...

Creating semantic matches between disparate data sources is fundamental to numerous data sharing efforts. Manually creating matches is extremely tedious and error-prone. Hence many recent works have focused on automating the matching process. To date, however, virtually all of these works deal only with one-to-one (1-1) matches, such as address = location. They do not consider the important class of more complex matches, such as address = concat(city,state) and room-price = room-rate * (1 + tax-rate). We describe the iMAP system which semi-automatically discovers both 1-1 and complex matches. iMAP reformulates schema matching as a search in an often very large or infinite match space. To search effectively, it employs a set of searchers, each discovering specific types of complex matches. To further improve matching accuracy, iMAP exploits a variety of domain knowledge, including past complex matches, domain integrity constraints, and overlap data. Finally, iMAP introduces a novel feature that generates explanation of predicted matches, to provide insights into the matching process and suggest actions to converge on correct matches quickly. We apply iMAP to several real-world domains to match relational tables, and show that it discovers both 1-1 and complex matches with high accuracy. 1.