Semantic schema refinements for multilevel schema integration

Within the database field, schema refinements have been proved useful for documentation and maintenance purposes; moreover, schemata describing the reality of interest at different levels of abstraction are extensively used in Computer Aided Software Engineering tools and visual query languages. So, much effort has been spent in analyzing schema transformations and schema refinements. Till now, however, while the syntax of schema transformations has been deeply investigated, the semantics has been very often neglected. In this paper we present a full formal framework, supporting both the syntax and the semantics of schema refinements. Such a formal framework is used to support a methodology able to merge a set of schemata and the top-down chains of refinement planes produced during their design. The result of this kind of integration, that we call multilevel integration, is an integrated schema plus an associated top-down chain of schemata. The integrated schema and the chain are related to the input schemata by interesting properties, giving rise to a two-dimensional structure useful for exploring the data content of complex information systems.