Computing Intensions of Digital Library Collections

We model a Digital Library as a formal context in which objects are documents and attributes are terms describing documents contents. A formal concept is very close to the notion of a collection: the concept extent is the extension of the collection; the concept intent consists of a set of terms, the collection intension. The collection intension can be viewed as a simple conjunctive query which evaluates precisely to the extension. However, for certain collections no concept may exist, in which case the concept that best approximates the extension must be used. In so doing, we may end up with a too imprecise concept, in case too many documents denoted by the intension are outside the extension. We then look for a more precise intension by exploring 3 different query languages: conjunctive queries with negation; disjunctions of negationfree conjunctive queries; and disjunctions of conjunctive queries with negation. We show that a precise description can always be found in one of these languages for any set of documents. However, when disjunction is introduced, uniqueness of the solution is lost. In order to deal with this problem, we define a preferential criterion on queries, based on the conciseness of their expression. We then show that minimal queries are hard to find in the last 2 of the three languages above.