Explicit Negation in Relational

Negative facts in relational databases have traditionally been inferred using the closed world assumption. There are situations where this is not appropriate. We need to resort to the open world assumption, where the negative facts are sometimes explicitly stated. We present a formalism which is capable of answering queries in the relational database context under the open world assumption. We introduce partial relations, which are extensions of relations. We deene the information content of partial relations as the set of all possible ordinary relations that are represented by a partial relation. We then deene algebraic operators over partial relations. The correctness of the algebraic operations on partial relations is established with respect to their information content. Finally, we present an application of the extended relational model, in which we show how the formalism introduced in this paper can be used to compute the semantics of general deductive databases.