Disjunctive datalog

We consider disjunctive Datalog, a powerful database query language based on disjunctive gic programming. Briefly, disjunctive Datalog is a variant of Datalog where disjunctions may appear in the rule heads; advanced versions also allow for negation in the bodies, which can be handled according to a semantics for negation in disjunctive logic programming. In particular, we investigate three different semantics for disjunctive Datalog: the minimal model semantics, the perfect model semantics, and the stable model semantics. For each of these semantics, the expressive power and complexity are studied. We show that the possibility variants of these semantics express the same set of queries. In fact, they precisely capture the complexity class Sigma(2)(p). Thus, unless the Polynomial Hierarchy collapses, disjunctive Datalog is more expressive than normal logic programming with negation. These results are not only of theoretical interest; we demonstrate that problems relevant in practice such as computing the optimal tour value in the Traveling Salesman Problem and eigenvector computations can be handled in disjunctive Datalog, but not Datalog with negation (unless the Polynomial Hierarchy collapses). In addition, we study modularity properties of disjunctive Datalog and investigate syntactic restrictions of the formalisms.