Structural characterizations of schema-mapping languages

Schema mappings are declarative specifications that describe the relationship between two database schemas. In recent years, there has been an extensive study of schema mappings and of their applications to several different data inter-operability tasks, including applications to data exchange and data integration. Schema mappings are expressed in some logical formalism that is typically a fragment of first-order logic or a fragment of second-order logic. These fragments are chosen because they possess certain desirable structural properties, such as existence of universal solutions or closure under target homomorphisms. In this paper, we turn the tables and focus on the following question: can we characterize the various schema-mapping languages in terms of structural properties possessed by the schema mappings specified in these languages? We obtain a number of characterizations of schema mappings specified by source-to-target (s-t) dependencies, including characterizations of schema mappings specified by LAV (local-as-view) s-t tgds, schema mappings specified by full s-t tgds, and schema mappings specified by arbitrary s-t tgds. These results shed light on schema-mapping languages from a new perspective and, more importantly, demarcate the properties of schema mappings that can be used to reason about them in data inter-operability applications.