The semantics of disjunctive deductive databases

Abstract

The problem of determining the correct declarative semantics for generalized logic programs is still open. In generalized logic programs the body of a rule may contain negated goals. Using a logical equivalence these programs may be viewed as disjunctive logic programs where the head of a rule may contain a disjunction of goals. We hope that a careful study of the declarative semantics of disjunctive logic programs will produce criteria for evaluating the different candidates for the semantics of generalized logic programs.

A conceptual analysis leads to a semantical definition of the notion of a disjunctive deductive database as a generalization of the notion of a deductive database. It will be shown that the notion of a disjunctive deductive database is equivalent to the syntactical definition of a disjunctive logic program. We have characterized disjunctive deductive databases, i. e. theories which admit in each irreducible component a minimal Herbrand model and for which this property is preserved under the addition of new facts, as disjunctive logic programs. As a special case the result yields the known characterization of deductive databases, i. e. theories which admit a minimal Herbrand model and for which this property is preserved under the addition of new facts, as logic programs. In the presence of equations term structures i. e. extended Herbrand structures replace the Herbrand structures and h-core models replace the minimal models. Actually, the results could be proved in a more general context where pseudo term structures replace the term structures. In addition, there is an intermediate case where the irreducible components coincide with the connected components. Moreover, there are characterization results for the cases where the uniformity condition is not present.