Viewing Collections as Abstractions

Digital Libraries collections are an abstraction mechanism, endowed with an extension and an intension, similarly to predicates in logic. The extension of a collection is the set of objects that are members of the collection at a given point in time, while the intension is a description of the meaning of the collection, that is the peculiar property that the members of the collection possess and that distinguishes the collection from other collections. This view reconciles the many types of collections found in Digital Library systems, but raises several problems, among which how to automatically derive the intension from a given extension. This problem must be solved e.g. for the creation of a collection from a set of documents. We outline basic results on the problem and then show how intensions can be exploited for carrying out basic tasks on collections, establishing a connection between Digital Library management and data integration.