Data Exchange: Semantics and Query Answering

Abstract

Abstract. 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.

Exchange-Repairs: Managing Inconsistency in Data Exchange

“…Detailed information about schema mappings and certain answers can be found in [3,19], and about repairs and consistent answers in [4,7].…”

“…However, if Σ t is the union of a weakly acyclic set of target tgds and a set of egds, then a solution exists if and only if a universal solution exists. Moreover, the chase procedure can be used to determine if, given a source instance I, a solution for I exists and, if it does, to actually construct a universal solution chase(I, M) for I in time polynomial in the size of I (see [19] for details). The definition of weak acyclicity is given next, followed by the definition of the chase procedure.…”

“…Data exchange is a ubiquitous data inter-operability task that has been explored in depth during the past decade (see [3]). This task is formalized with the aid of schema mappings M = (S, T, Σ st , Σ t ), where S is the source schema, T is the target schema, Σ st is a set of constraints between S and T, and Σ t is a set of constraints on T. The most thoroughly investigated schema mappings are the ones in which Σ st is a set of source-to-target tuplegenerating dependencies (s-t tgds) and Σ t is a set of target tuple-generating dependencies (target tgds) and target equality-generating dependencies (target egds) [19]. An example of such a schema mapping, along with a target query, follows: Every schema mapping M = (S, T, Σ st , Σ t ) gives rise to two distinct algorithmic problems.…”

“…For arbitrary schema mappings specified by s-t tgds and target tgds and egds, both these problems can be undecidable [26]. However, as shown in [19], if the set Σ t of target tgds obeys a mild structural condition, called weak acyclicity, then both these problems can be solved in polynomial time using the chase procedure. Given a source instance I, the chase procedure attempts to build a "most general" solution J for I by generating facts that satisfy each s-t tgd and each target tgd as needed, and by equating two nulls or equating a null to a constant, as dictated by the egds.…”

Defining and Using Schematic Correspondences for Automatically Generating Schema Mappings

“…A data integration system can play a central role in multiple applications, e.g., it can be used for cross-querying of data stored in databases that belong to independent companies, or to promote collaboration in large scientific projects by providing investigators with a means for querying and combining results produced by multiple research labs [21]. The components at the heart of a data integration system are: the schemas of the sources, the data sets to be integrated, an integration schema over which users pose queries, and mappings that specify how data structured under the schemas of the sources can be transformed and combined into data structured according to the integration schema [6].…”