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Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs

Published online by Cambridge University Press:  08 October 2010

MIROSŁAW TRUSZCZYŃSKI
MIROSŁAW TRUSZCZYŃSKI*
Affiliation:
Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA (mirek@cs.uky.edu)
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Abstract

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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.

Keywords

answer setssupported modelscomplexity of reasoning

Information

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 11 , Issue 6 , November 2011, pp. 881 - 904
Copyright
Copyright © Cambridge University Press 2010

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