Abstract
Schema mappings are high-level specifications that describe the relationship between two database schemas. As such, they constitute the essential building blocks in formalizing the main data inter-operability tasks, including data exchange and data integration. Several different operators on schema mappings have been introduced and studied in considerable depth. Among these, the composition operator is arguably the most fundamental and prominent one. The aim of this talk is to present an overview of results about the composition of schema mappings with emphasis on the interplay between first-order logic and second-order logic in expressing the composition.