ar X iv : 0 91 0 . 33 72 v 4 [ cs . D B ] 4 M ar 2 01 0 Composition and Inversion of Schema Mappings

A schema mapping is a specification that describes how data from a source schema is to be mapped to a target schema. Schema mappings have proved to be essential for data-interoperability tasks such as data exchange and data integration. The research on this area has mainly focused on performing these tasks. However, as Bernstein pointed out [7], many information-system problems involve not only the design and integration of complex application artifacts, but also their subsequent manipulation. Driven by this consideration, Bernstein proposed in [7] a general framework for managing schema mappings. In this framework, mappings are usually specified in a logical language, and high-level algebraic operators are used to manipulate them [7, 17, 34, 13, 8]. Two of the most fundamental operators in this framework are the composition and inversion of schema mappings. Intuitively, the composition can be described as follows. Given a mapping M1 from a schema A to a schema B, and a mapping M2 from B to a schema E, the composition of M1 and M2 is a new mapping that describes the relationship between schemas A and E. This new mapping must be semantically consistent with the relationships previously established by M1 and M2. On the other hand, an inverse of M1 is a new mapping that describes the reverse relationship from B to A, and is semantically consistent with M1. In practical scenarios, the composition and inversion of schema mappings can have several applications. In a data exchange context [14], if a mapping M is used to exchange data from a source to a target schema, an inverse of M can be used to exchange the data back to the source, thus reversing the application of M. As a second application, consider a peer-data management system (PDMS) [10, 25]. In a PDMS, a peer can act as a data source, a mediator, or both, and the system relates peers