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.
The static semantics has both of these nice structural properties. Minker et al. A Compositional Semantics for Logic Programs and Deductive Databases. Proc. of the Joint International Conference and Symposium on Logic Programming. Doc 153 Foundations of Disjunctive Logic Programming - Lobo, Minker et al.