Royer, Y., The semantics of incomplete databases as an expression of preferences, Theoretical Computer Science 78 (1991) 113-136. We address the problem of incomplete information in deductive databases from a semantic point of view. We want to treat the problem in a homogeneous way, using a formalism which can handle different types of incompleteness. We argue that it is convenient to define an incomplete database as a double entity: an underlying incomplete database together with selection

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... eria, formally some preference relation on the set of models of the underlying database, intended to reduce the incompleteness. Such an idea has been already exploited in the Perfect Model semantics of Negation as Failure in the stratified databases. We propose another notion of preference which induces a stronger selection of models and captures an intuitive process of "making choices" in disjunctive databases. We study both the declarative and the operational semantics for this notion of preference. is by some triple (L, T, F=) where L is a (first-order) logical language, T a set of formulas of Land F= a particular entailment relation I defined on the formulas of L. In this setting, a knowledge base is incomplete if there is some formula 4> of L such that T I;e 4> and T I;e ,4>. \I It means r is a complete reduction order for Char(DDB) with respect to <*. 12 Closure by the law: if B