Interpreting disjunctive logic programs based on a strong sense of disjunction

This paper studies a strong form of disjunctive information in deductive databases. The basic idea is that a disjunction A ∨B should be considered true only in the case when neither A nor B can be inferred, but the disjunction A ∨B is true. Under this interpretation, databases may be inconsistent. For those databases that are consistent, it is shown that a unique minimal model exists. We study a fixpoint theory and present a sound and complete proof procedure for query processing in consistent databases. For a class of inconsistent databases, we obtain a declarative semantics by selecting an interpretation that maximizes satisfaction, and minimizes indefiniteness. Two notions of negation are introduced.