A Compositional Semantics for Logic Programs and Deductive Databases

Considering integrity constraints and program composition, it is argued that a semantics for logic programs and deductive databases should not accommodate inconsistencies globally like in classical logic, but locally. It is shown that minimal logic, a weakening of classical logic which precludes refutation proofs, is sufficient to provide for a proof theory for generalized programs corresponding to deductive databases and disjunctive logic programs. A (nonclassical) model theory is proposed for these programs, which allows local inconsistencies. The proposed semantics naturally extends the minimal model and completion semantics of positive programs and is compositional. Arguably, it appropriately conveys a practician's intuition.