Default Logic as a Query Language

Abstract

Research in NMR has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using non-monotonic formalisms as relational database query languages has been investigated to a much smaller extent. In this work we propose a novel application of default logic by introducing a default query language (DQL) for finite relational databases, which is based on default rules. The main result of this paper is that DQL is as expressive as SO∃∀, the existential universal fragment of second order logic. This result is not only of theoretical importance: We show queries -which are useful in practice- that can be expressed with DQL and cannot with other query languages based on non-monotonic logics such as DATALOGstable Another result in this paper concerns the combined complexity of DQL, i.e., when it is assumed that the query is part of the input; for this problem, NEXPTIMENP-completeness is shown.