Trichotomy and Dichotomy Results on the Complexity of Reasoning with Disjunctive Logic Programs

TL;DR

This paper characterizes the computational complexity of reasoning tasks in disjunctive logic programs, identifying classes where these tasks are tractable or easier, based on rule arities and semantics.

Contribution

It introduces a schema for classifying disjunctive logic programs and provides a detailed complexity analysis for various reasoning problems within these classes.

Findings

Certain classes of programs have polynomial-time reasoning algorithms.

Many classes are NP-complete, explaining the inherent difficulty.

Some classes are identified where reasoning is computationally easier.

Abstract

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. On 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). We obtain similar results for the complexity of reasoning with disjunctive programs under the supported-model semantics. To appear in Theory and Practice of Logic Programming (TPLP)