Expressive power and complexity of partial models for disjunctive deductive databases

Abstract

This paper investigates the expressive power and complexity of partial model semantics for disjunctive deductive databases. In particular, partial stable, regular model, maximal stable (M-stable), and least undefined stable (L-stable) semantics for function-free disjunctive logic programs are considered, for which the expressiveness of queries based on possibility and certainty inference is determined. On the complexity side, we determine the data and expression complexity of query evaluation. The analysis pays particular attention to the impact of syntactical restrictions on programs in the form of limited use of disjunction and negation. It appears that the considered semantics capture complexity classes at the lower end of the polynomial hierarchy. In fact, each class ∑ i P , Π i P , 1 ⩽ i⩽ 3 is captured by some semantics using appropriate syntactical restrictions. Partial stable models have exactly the same expressive power and complexity as total stable models (∑ 2 P resp. Π 2 P ), while a higher degree of expressiveness is obtained by the semantics which minimize undefinedness (M-stable, regular, and L-stable semantics). In particular, L-stable semantics has the highest expressive power (∑ 3 P resp. Π 3 P ). An interesting result in this course is that, in contrast with total stable models, negation is for partial stable models more expressive than disjunction. For the data complexity of queries, we obtain completeness results for the classes ∑ i P , Π i P , i⩽3, and, for the expression complexity, completeness results for the analogous classes at the lower end of the weak exponential hierarchy. The results of this paper complement and extend previous results, and contribute to a more complete picture of the computational aspects of disjunctive logic programming and databases, which supports in choosing an appropriate setting that fits the needs in practice.