Showing papers by "Phokion G. Kolaitis published in 2012"

Learning schema mappings

Abstract: A schema mapping is a high-level specification of the relationship between a source schema and a target schema. Recently, a line of research has emerged that aims at deriving schema mappings automatically or semi-automatically with the help of data examples, i.e., pairs consisting of a source instance and a target instance that depict, in some precise sense, the intended behavior of the schema mapping. Several different uses of data examples for deriving, refining, or illustrating a schema mapping have already been proposed and studied.In this paper, we use the lens of computational learning theory to systematically investigate the problem of obtaining algorithmically a schema mapping from data examples. Our aim is to leverage the rich body of work on learning theory in order to develop a framework for exploring the power and the limitations of the various algorithmic methods for obtaining schema mappings from data examples. We focus on GAV schema mappings, that is, schema mappings specified by GAV (Global-As-View) constraints. GAV constraints are the most basic and the most widely supported language for specifying schema mappings.We present an efficient algorithm for learning GAV schema mappings using Angluin's model of exact learning with membership and equivalence queries. This is optimal, since we show that neither membership queries nor equivalence queries suffice, unless the source schema consists of unary relations only. We also obtain results concerning the learnability of schema mappings in the context of Valiant's well known PAC (Probably-Approximately-Correct) learning model. Finally, as a byproduct of our work, we show that there is no efficient algorithm for approximating the shortest GAV schema mapping fitting a given set of examples, unless the source schema consists of unary relations only.

On the data complexity of consistent query answering

Abstract: The framework of database repairs is a principled approach to managing inconsistency in databases. In particular, the consistent answers of a query on an inconsistent database provide sound semantics and the guarantee that the values obtained are those returned by the query on every repair of the given inconsistent database. In this paper, we carry out a systematic investigation of the data complexity of the consistent answers of conjunctive queries for set-based repairs and with respect to classes of constraints that, in recent years, have been extensively studied in the context of data exchange and data integration. Our results, which range from polynomial-time computability to undecidability, complement or improve on earlier work, and provide a fairly comprehensive picture of the data complexity of consistent query answering. We also address the problem of finding a "representative" or "useful" repair of an inconsistent database. To this effect, we introduce the notion of a universal repair, as well as relaxations of it, and then apply it to the investigation of the data complexity of consistent query answering.

Local transformations and conjunctive-query equivalence

Abstract: Over the past several decades, the study of conjunctive queries has occupied a central place in the theory and practice of database systems. In recent years, conjunctive queries have played a prominent role in the design and use of schema mappings for data integration and data exchange tasks. In this paper, we investigate several different aspects of conjunctive-query equivalence in the context of schema mappings and data exchange.In the first part of the paper, we introduce and study a notion of a local transformation between database instances that is based on conjunctive-query equivalence. We show that the chase procedure for GLAV mappings (that is, schema mappings specified by source-to-target tuple-generating dependencies) is a local transformation with respect to conjunctive-query equivalence. This means that the chase procedure preserves bounded conjunctive-query equivalence, that is, if two source instances are indistinguishable using conjunctive queries of a sufficiently large size, then the target instances obtained by chasing these two source instances are also indistinguishable using conjunctive queries of a given size. Moreover, we obtain polynomial bounds on the level of indistinguishability between source instances needed to guarantee indistinguishability between the target instances produced by the chase. The locality of the chase extends to schema mappings specified by a second-order tuple-generating dependency (SO tgd), but does not hold for schema mappings whose specification includes target constraints.In the second part of the paper, we take a closer look at the composition of two GLAV mappings. In particular, we break GLAV mappings into a small number of well-studied classes (including LAV and GAV), and complete the picture as to when the composition of schema mappings from these various classes can be guaranteed to be a GLAV mapping, and when they can be guaranteed to be conjunctive-query equivalent to a GLAV mapping.We also show that the following problem is decidable: given a schema mapping specified by an SO tgd and a GLAV mapping, are they conjunctive-query equivalent? In contrast, the following problem is known to be undecidable: given a schema mapping specified by an SO tgd and a GLAV mapping, are they logically equivalent?