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).
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Truszczyński, M. (2009). Trichotomy Results on the Complexity of Reasoning with Disjunctive Logic Programs. In: Erdem, E., Lin, F., Schaub, T. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2009. Lecture Notes in Computer Science(), vol 5753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04238-6_26
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DOI: https://doi.org/10.1007/978-3-642-04238-6_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04237-9
Online ISBN: 978-3-642-04238-6
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