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Abstract answer set solvers with backjumping and learning

Published online by Cambridge University Press:  22 February 2011

YULIYA LIERLER
YULIYA LIERLER*
Affiliation:
Department of Computer Science, University of Kentucky, 773C Anderson Hall, Lexington, USA (e-mail: yuliya@cs.uky.edu)
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Abstract

Nieuwenhuis et al. (2006. Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53(6), 937977 showed how to describe enhancements of the Davis–Putnam–Logemann–Loveland algorithm using transition systems, instead of pseudocode. We design a similar framework for several algorithms that generate answer sets for logic programs: smodels, smodelscc, asp-sat with Learning (cmodels), and a newly designed and implemented algorithm sup. This approach to describe answer set solvers makes it easier to prove their correctness, to compare them, and to design new systems.

Keywords

answer set programminginferencelearning
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 11 , Special Issue 2-3: The 24th International Conference on Logic Programming (ICLP 2008) , March 2011 , pp. 135 - 169
Copyright
Copyright © Cambridge University Press 2011

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References

Clark, K. 1978. Negation as failure. In Logic and Data Bases, Gallaire, H. and Minker, J., Eds. Plenum Press, New York, NY, USA, 293–322.CrossRefGoogle Scholar
Davis, M., Logemann, G. and Loveland, D. 1962. A machine program for theorem proving. Communications of the ACM 5 (7), 394–397.CrossRefGoogle Scholar
Fages, F. 1994. Consistency of Clark's completion and existence of stable models. Journal of Methods of Logic in Computer Science 1, 51–60.Google Scholar
Gebser, M., Kaufmann, B., Neumann, A. and Schaub, T. 2007. Conflict-driven answer set solving. In Proceedings of 20th International Joint Conference on Artificial Intelligence (IJCAI'07). MIT Press, Cambridge, MA, USA, 386–392.Google Scholar
Gebser, M. and Schaub, T. 2006. Tableau calculi for answer set programming. In Proceedings of 22nd International Conference on Logic Programming (ICLP'06). Springer, New Mexico, USA, 11–25.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proceedings of International Logic Programming Conference and Symposium, Kowalski, R. and Bowen, K., Eds. MIT Press, Cambridge, MA, USA, 1070–1080.Google Scholar
Giunchiglia, E., Lierler, Y. and Maratea, M. 2006. Answer set programming based on propositional satisfiability. Journal of Automated Reasoning 36, 345–377.CrossRefGoogle Scholar
Giunchiglia, E. and Maratea, M. 2005. On the relation between answer set and SAT procedures (or, between smodels and cmodels). In Proceedings of 21st International Conference on Logic Programming (ICLP'05). Springer, New Mexico, USA, 37–51.Google Scholar
Gomes, C. P., Kautz, H., Sabharwal, A. and Selman, B. 2008. Satisfiability solvers. In Handbook of Knowledge Representation, van Harmelen, F., Lifschitz, V. and Porter, B., Eds. Elsevier, Missouri, USA, 89–134.CrossRefGoogle Scholar
Lee, J. 2005. A model-theoretic counterpart of loop formulas. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI). Professional Book Center, Denver CO, USA, 503–508.Google Scholar
Lierler, Y. 2008. Abstract answer set solvers. In Proceedings of International Conference on Logic Programming (ICLP'08). Springer, New Mexico, USA, 377–391.Google Scholar
Lierler, Y. 2010. Abstract answer set solvers with learning (long version). arxiv:1001.0820v1 [cs.ai].Google Scholar
Lifschitz, V. 2008. What is answer set programming? In Proceedings of the AAAI Conference on Artificial Intelligence. MIT Press, Cambridge, MA, USA, 1594–1597.Google Scholar
Lin, F. and Zhao, Y. 2002. ASSAT: Computing answer sets of a logic program by SAT solvers. In Proceedings of National Conference on Artificial Intelligence (AAAI). MIT Press, Cambridge, MA, USA, 112–117.Google Scholar
Lin, F. and Zhao, Y. 2004. ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157, 115–137.CrossRefGoogle Scholar
Lin, Z., Zhang, Y. and Hernandez, H. 2006. Fast SAT-based answer set solver. In Proceedings of National Conference on Artificial Intelligence (AAAI). MIT Press, Cambridge, MA, USA, 92–97.Google Scholar
Marques-Silva, J. P. and Sakallah, K. A. 1996. Conflict analysis in search algorithms for propositional satisfiability. In Proceedings of 8th International Conference on Tools with Artificial Intelligence (ICTAI'96). IEEE Computer Society, Toulouse, France, 467–469.Google Scholar
Mitchell, D. G. 2005. A SAT solver primer. EATCS Bulletin (The Logic in Computer Science Column) 85, 112–133.Google Scholar
Nieuwenhuis, R., Oliveras, A. and Tinelli, C. 2006. Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53 (6), 937–977.CrossRefGoogle Scholar
Ricca, F., Faber, W. and Leone, N. 2006. A backjumping technique for disjunctive logic programming. AI Communications 19 (2), 155–172.Google Scholar
Saccá, D. and Zaniolo, C. 1990. Stable models and non-determinism in logic programs with negation. In Proceedings of ACM Symposium on Principles of Database Systems (PODS), April 2–4, Nashville, TN, USA. ACM Press, 205–217.Google Scholar
Simons, P. 2000. Extending and Implementing the Stable Model Semantics. Ph.D. thesis, Helsinki University of Technology, Adviser-Niemelä, Ilkka.Google Scholar
Van Gelder, A., Ross, K. and Schlipf, J. 1991. The well-founded semantics for general logic programs. Journal of ACM 38 (3), 620–650.CrossRefGoogle Scholar
Ward, J. 2004. Answer Set Programming with Clause Learning. Ph.D. thesis, The University of Cincinnati, Cincinnati, OH, USA. URL: http://www.nku.edu/~wardj1RresearchTthesis.pd, accessed 10 January 2010.Google Scholar
Ward, J. and Schlipf, J. 2004. Answer set programming with clause learning. In Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'04), Fort Lauderdale, FL, USA, January 6-8, 302–313.Google Scholar
Zhang, L., Madigan, C. F., Moskewicz, M. W. and Malik, S. 2001. Efficient conflict driven learning in a Boolean satisfiability solver. In Proceedings of International Conference on Computer-Aided Design (ICCAD-01), November 2001, 279–285.Google Scholar