Beginnings of a Theory of General Database Completions

Ordinary logical implication is not enough for answering queries in a logic database, since especially negative information is only implicitly represented in the database state. Many database completions have been proposed to remedy this problem, but a clear understanding of their properties and differences is still needed. In this paper, a general framework is proposed for studying database completions, which reveals an interesting and fruitful relation to social choice theory. We apply our framework to parameterized forms of the minimal model approach and the closed world assumption, as well as to two versions of the default logic: simple defaults with constraints and normal defaults. Thereby the relationship between these important classes of database completions is clarified. In particular, it is shown that the GCWA cannot be simulated by any of the other three approaches. We also give a characterization of those completions which can be represented as a form of minimal implication. The whole discussion is based on various properties of database completions which have proven useful as a means for classifying the proposed approaches. Finally, we illustrate the applicability of general database completions to conventional deductive databases by means of transformation.