Integrating Schema Integration Frameworks, Algebraically *

The paper presents a framework, in which the main concepts of schema and data integration can be specified both semantically and syntactically in an abstract data-model independent way. We first define what are schema matching and integration semantically, in terms of sets of instances and mappings between them. We also define a schema matching and integration syntactically, and introduce a procedure (the how) for computing the integration of matched schema according to the syntactical definition in fairly abstract terms. The main theorem of the paper states that the result of syntactical integration satisfies the semantic definition and, hence, does produce what we really need. We show how this framework unifies the approach taken in at least five other schema integration proposals and fills in some important gaps in these proposals. Viewed in a broader perspective, the framework developed in the paper integrates the syntactical and semantical sides of model management and, particularly, reveals a re∗Supported by Bell Canada through the Bell University Labs, NSERC and Ontario Centres Of Excellence markable duality between them. The results of the paper can then be seen as an (important yet) particular case of this general duality theory.