Disjunctive Rules and Null Values: Logic Programs with Incomplete Information

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 well-founded 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.