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The introduction of negation in rule bodies of logic programs may lead to semantic ambiguities: Normal programs can have more than one stable model and the three-valued well-founded model may leave the truth status of some ground atoms undetermined. We show that this kind of ambiguity can be naturally combined with ambiguities caused by incomplete information. We define generalized notions of stable and well-founded models which allow to combine recursion, negation and incomplete information within a uniform framework. The well-founded approximation is composed of two not necessarily identical anti-monotonic operators. A general characterization of the best wellfounded approximation is given. Programs with disjunctions, maybe tuples and null values are studied as examples of logic programs with incomplete information. What concerns null values, our approach can also be seen as a generalization of Biskup's proposal for relational databases. Advances in Databases and Information Systems, 1996 Disjunctive Rules and Null Values: Logic Programs with Incomplete Information In the same general setting well-founded approximations are defined by a pair of anti-monotonic operators. One could say that stable models are the semantic and well-founded approximations the operational side of our approach. Assumption functions admit of different pre-interpretations of negative literals in logic programs. Stable model semantic says which of these pre-interpretations are "reasonable". Analogously, incomplete data can be completed on a hypothetical basis, such that our uniform framework can be applied again. Stable models and well-founded approximations can thus be defined for logic programs with maybe tuples and null values. We believe that in order to make non-monotonic reasoning fit for applications it is imperative to further enhance expressiveness of logic programs and to combine the key notions of non-monotonic reasoning with representation features that have been proposed for or are in use with databases. Section 2 introduces the basic concepts and notation. Section 3 first defines assumption functions and a generalized notion of stable models. Then alternating operator pairs are introduced and some results are established which highlight the relationship between operator pairs and stable models. The remaining sections present instances of this general scheme. In Section 5 normal and disjunctive logic programs are discussed. In Section 7 relations with maybe tuples are considered. On this basis it will in Section 8 be possible to handle relations with null values.

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