Hypothesis-founded semantics for datalog programs with negation

A precise meaning or semantics must be associated with any logic program or deductive database, and that even in presence of incomplete information. The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well-founded semantics corresponds to the assumption that every such atom is false, while the Kripke-Kleene semantics corresponds to the assumption that every such atom is unknown. However, these assumptions are uniform in the sense that they always assign the same default value to all atoms: either everything is supposed to be false by default (closed world assumption) or everything is supposed to be unknown by default (open world assumption). In several application environments, however, including information retrieval and information integration, such uniformity is not realistic. In this paper, we propose to unify and extend the assumption-based approaches by allowing assumptions to be non-uniform. To deal with such assumptions, we extend the concept of unfounded set of Van Gelder to the notion of support of a hypothesis. Based on the support of a hypothesis, we define our hypothesis-founded semantics and show that this semantics generalizes both the Kripke-Kleene semantics and the well-founded semantics of Datalog programs with negation.