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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

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
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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References

Ben-Eliyahu, R. and Dechter, R. 1997. Propositional semantics for disjunctive logic program. Annals of Mathematics and Artificial Intelligence 12, 53–87.CrossRefGoogle Scholar
Brass, S. and Dix, J. 1997. Characterizations of the disjunctive stable semantics by partial evaluation. Journal of Logic Programming 32, 3, 207–228.CrossRefGoogle Scholar
Bulatov, A. A., Jeavons, P. and Krokhin, A. A. 2005. Classifying the complexity of constraints using finite algebras. SIAM J. Comput. 34, 3, 720–742.CrossRefGoogle Scholar
Cadoli, M. 1992. The complexity of model checking for circumscriptive formulae. Information Processing Letters 44, 3, 113–118.CrossRefGoogle Scholar
Cadoli, M. and Lenzerini, M. 1994. The complexity of propositional closed world reasoning and circumscription. Journal of Computer and System Sciences 48, 255–310.CrossRefGoogle Scholar
Chapdelaine, P., Hermann, M. and Schnoor, I. 2007. Complexity of default logic on generalized conjunctive queries. In Proc. of 9th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR '07, Baral, C., Brewka, G. and Schlipf, J., Eds. Lecture Notes in Computer Science, vol. 4483. Springer, Heidelberg, 58–70.CrossRefGoogle Scholar
Creignou, N., Khanna, S. and Sudan, M. 2001. Complexity Classifications of Boolean Constraint Satisfaction Problems. SIAM, London, UK.CrossRefGoogle Scholar
Dantsin, E., Eiter, T., Gottlob, G. and Voronkov, A. 2001. Complexity and expressive power of logic programming. ACM Computing Surveys 33, 3, 374–425.CrossRefGoogle Scholar
Dowling, W. and Gallier, J. 1984. Linear-time algorithms for testing the satisfiability of propositional Horn formulae. Journal of Logic Programming 1, 3, 267–284.CrossRefGoogle Scholar
Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: propositional case. Annals of Mathematics and Artificial Intelligence 15, 3–4, 289–323.CrossRefGoogle Scholar
Ferraris, P. and Lifschitz, V. 2005. Mathematical foundations of answer set programming. In We Will Show Them! Essays in Honour of Dov Gabbay, Artëmov, S., Barringer, H., d'Avila Garcez, A., Lamb, L. C. and Woods, J., Eds. College Publications, Philadelphia, USA, 615–664.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385.CrossRefGoogle Scholar
Inoue, K. and Sakama, C. 1998. Negation as failure in the head. Journal of Logic Programming 35, 39–78.CrossRefGoogle Scholar
Marek, W. and Truszczyński, M. 1991. Autoepistemic logic. Journal of the ACM 38, 3, 588–619.CrossRefGoogle Scholar
Marek, W. and Subrahmanian, V. S. 1992. The relationship between stable, supported, default and autoepistemic semantics for general logic programs. Theoretical Computer Science 103, 2, 365–386.CrossRefGoogle Scholar
Nordh, G. and Zanuttini, B. 2008. What makes propositional abduction tractable. Artificial Intelligence 172, 10, 1245–1284.CrossRefGoogle Scholar
Schaefer, T. 1978. The complexity of satisfiability problems. In Proceedings of the 10th Annual ACM Symposium on Theory of Computing, STOC '78. 216–226.Google Scholar
Truszczyński, M. 2009. Trichotomy results on the complexity of reasoning with disjunctive logic programs. In Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR '09, Erdem, E., Lin, F. and Schaub, T., Eds. Lecture Notes in Computer Science, vol. 5753. Springer, Heidelberg, 303–315.CrossRefGoogle Scholar