A Compositional Semantics for Logic Programs and Deductive Databases.
François Bry · 1996
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. Finally, a (nonclassical) model theory is proposed for generalized programs, which is based on a weakening of the usual notion of model inspired from (but not corresponding to) minimal logic. This model theory allows local inconsistencies. The proposed model theory naturally extends the minimal model, stable, and completion semantics of positive programs. The proposed semantics is shown to be "compositional" in th...