Schema Mappings: A Case of Logical Dynamics in Database Theory

Abstract

A schema mapping is a high-level specification of the structural relationships between two database schemas. This specification is expressed in a schema-mapping language, which is typically a fragment of first-order logic or second-order logic. Schema mappings have played an essential role in the study of important data-interoperability tasks, such as data integration and data exchange. In this chapter, we examine schema mappings as a case of logical dynamics in action. We provide a self-contained introduction to this area of research in the context of logic and databases, and focus on some of the concepts and results that may be of particular interest to the readers of this volume. After a basic introduction to schema mappings and schema-mapping languages, we discuss a series of results concerning fundamental structural properties of schema mappings. We then show that these structural properties can be used to obtain characterizations of various schema-mapping languages, in the spirit of abstract model theory. We conclude this chapter by highlighting the surprisingly subtle picture regarding compositions of schema mappings and the languages needed to express them.