Theoretical Foundations of Schema Restructuring in Heterogeneous Multidatabase Systems

Abstract

Previous work on schema integration typically has taken either a very ad-hoc approach of identifying a specific integration problem and providing a solution for it, or a very general approach of providing a rich integration facility, but one that requires writing rule-based, logic-based, or conventional programs to specify an integration. The latter approach is powerful, but places an undue burden on someone to verify the validity of an integration that is defined, as well as to write and maintain the program(s). Alternatively, one might follow a transformation-based approach where a collection of schema transformations is provided, together with a theoretical basis of validity in applying the transformations. This approach has been applied successfully to certain problem domains, such as the integration of relational schemas with referential integrity. However, one can encode information in arbitrary, complex ways with the relational model, including using non-First Normal Form encodings, and with the incorporation of object technology into the relational model, it is becoming increasingly common for users to create new data types that have their own special semantics. Thus, no specific theory of schema integration, no matter how complete, can ever account for all possible integration problem domains. To address this situation, we propose an extensible theory of schema integration that can serve as a framework for developing theories of schema integration in new problem areas. We then present some general theoretical results concerning schema equivalence that could be used to apply the theory to a number of problem domains.