Abstract

This paper gives a general definition of a “kind of schema” along with general definitions for the schemas of a species, and for the databases, constraints, and queries over a given schema of a species. This leads naturally to a general theory of data translation and integration over arbitrary schemas of arbitrary species, based on schema morphisms, and to a similar general theory of ontology translation and integration over arbitrary logics. Institutions provide a general notion of logic, and Grothendieck flattening provides a general tool for integrating heterogeneous schemas, species and logics, as well as theories, such as ontologies, over different logics. Many examples of our novel concepts are included, some rather detailed. An initial section introduces data integration and ontologies for readers who are not specialists, with some emphasis on challenges. A brief review of universal algebra is also given, though some familiarity with category theory is assumed in later sections