Considering integrity constraints and program composition, it is first argued that a semantics for logic programs and deductive databases should not accommodate inconsistencies globally like in classical logic, but locally. It is then shown that minimal logic, a natural deduction style weakening of classical logic, is sufficient to provide for a proof theory for a generalization of logic programs corresponding to deductive databases with integrity constraints and disjunctive logic programs.
Minimal logic differs from classical logic inasmuch as it precludes refutation proofs.
This model theory allows local inconsistencies. The proposed model theory naturally extends the minimal model, stable, and completion semantics of positive programs. Arguably, it appropriately conveys a practician's intuition.