Trichotomy Results on the Complexity of Reasoning with Disjunctive Logic Programs

We present trichotomy results characterizing the complexity of reasoning with disjunctive logic programs. To this end, we introduce a certain definition schema for classes of programs based on a set of allowed arities of rules. We show that each such class of programs has a finite representation, and for each of the classes definable in the schema we characterize the complexity of the existence of an answer set problem. Next, we derive similar characterizations of the complexity of skeptical and credulous reasoning with disjunctive logic programs. Such results are of potential interest. Oil the one hand, they reveal some reasons responsible for the hardness of computing answer sets. On the other hand. they identify classes of problem instances, for which the problem is "easy" (in P) or "easier than in general" (in NP).