Abstract
Answer set programming has emerged as a new important paradigm for declarative problem solving. It relies on algorithms that compute the stable models of a logic program, a problem that is, in the worst-case, intractable. Although, local search procedures have been successfully applied to a variety of hard computational problems, the idea of employing such procedures in answer set programming has received very limited attention.
This paper presents several local search algorithms for computing the stable models of a normal logic program. They are all based on the notion of a conflict set, but use it in different ways, resulting in different computational behaviors. The algorithms are inspired from related work in solving propositional satisfiability problems, suitably adapted to the stable model semantics. The paper also discusses how the heuristic equivalence method, that has been proposed in the context of propositional satisfiability, can be used in systematic search procedures that compute the stable models of logic programs.
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References
A. Bertoni, G. Grossi, A. Provetti, V. Kreinovich, and L. Tari. The prospect for answer sets computation by a genetic model. In Proc. of the AAAI Spring 2001 Symposium on Answer Set Programming. http://www.cs.nmsu.edu/~tson/ASP2001/, 2001.
T. Dell’Armi, W. Faber, G. Ielpa, C. Koch, N. Leone, S. Perri, and G. Pfeifer. System description: DLV. In Proc. of the 6th Intern. Conf. on Logic Programming and Nonmonotonic Reasoning, LPNMR-01, LNCS 2173, pages 424–428. Springer Verlag, 2001.
Y. Dimopoulos, B. Nebel, and J. Koehler. Encoding planning problems in nonmonotonic logic programs. In Proc. of the 4th European Conference on Planning, ECP’97, LNCS 1348, pages 169–181. Springer Verlag, 1997.
T. Eiter, W. Faber, N. Leone, and G. Pfeifer. The diagnosis frontend of the dlv system. AI Communications, 12(1/2):99–111, 1999.
J. Frank. Learning short-term weights for GSAT. In Proc. 15h Intern. Joint Conference on AI, IJCAI-97, pages 384–391, 1997.
M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proc. of the 5th Intern. Conf. and Symp. on Logic Programming, ICSLP-88, pages 1070–1080, 1988.
M. Gelfond and V. Lifschitz. Classical negation in logic programs and disjunctive databases. New Generation Computing, 9(3/4):365–386, 1991.
C. Gomes, B. Selman, and H. Kautz. Boosting combinatorial search through randomization. In Proc. of the 15th National Conference on AI, AAAI-98, pages 431–437, 1998.
K. Heljanko and I. Niemela. Bounded LTL model checking with stable models. In Proc. of the 6th Intern. Conf. on Logic Programming and Nonmonotonic Reasoning, LPNMR’01, LNCS 2173, pages 200–212. Springer Verlag, 2001.
H. Hoos and T. Stutzle. Local search algorithms for SAT: An empirical evaluation. Journal of Automated Reasoning, 24(4):421–481, 2000.
N. Jussien and O. Lhomme. Local search with constraint propagation and conflictbased heuristics. In Proc. of the 17th National Conference on AI, AAAI-00, pages 169–174, 2000.
N. Leone, S. Perri, and P. Rullo. Local search techniques for disjunctive logic programs. In 6th Congress of the Italian Association for Artificial Intelligence, AI*IA 99, LNCS 1792, pages 107–118. Springer Verlag, 2000.
B. Mazure, L. Sais, and E. Gregoire. Tabu search for SAT. In Proc. of the 14th National Conference on AI, AAAI-97, pages 281–285, 1997.
D. McAllester, B. Selman, and H. Kautz. Evidence for invariants in local search. In Proc. of the 14th National Conference on AI, AAAI-97, pages 321–326, 1997.
P. Nicolas, F. Saubion, and I. Stephan. GADEL: a genetic algorithm to compute default logic extensions. In Proc. of the 14th European Conference on AI, ECAI’00, pages 484–488. IOS Press, 2000.
P. Nicolas, F. Saubion, and I. Stephan. New generation systems for non-monotonic reasoning. In Proc. of the 6th Intern. Conf. on Logic Programming and Nonmonotonic Reasoning, LPNMR’01, LNCS 2173, pages 309–321. Springer Verlag, 2001.
D. Schuurmans and F. Southey. Local search characteristics of incomplete SAT procedures. In Proc. of the 17th National Conference on AI, AAAI-00, pages 297–302, 2000.
B. Selman, H. Kautz, and B. Cohen. Noise strategies for improving local search. In Proc. of the 12th National Conference on AI, AAAI-94, pages 337–343, 1994.
B. Selman, H. Levesque, and D. Mithcell. A new method for solving hard satisfiability porblems. In Proc. of the 10th National Conference on AI, AAAI-92, pages 440–446, 1992.
P. Simons. Extending the stable model semantics with more expressive rules. In Proc. of the 5th Intern. Conf. on Logic Programming and Nonmonotonic Reasoning, LPNMR-99, LNCS 1730, pages 305–316. Springer Verlag, 1999.
P. Simons. Extending and implementing the stable model semantics. Ph.D. Thesis, Research Report 58, Helsinki University of Technology, 2000.
T. Surjanen and I. Niemela. The Smodels system. In Proc. of the 6th Intern. Conf. on Logic Programming and Nonmonotonic Reasoning, LPNMR-01, LNCS 2173, pages 434–438. Springer Verlag, 2001.
A. Van Gelder, K. Ross, and J. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620–650, 1991.
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Dimopoulos, Y., Sideris, A. (2002). Towards Local Search for Answer Sets. In: Stuckey, P.J. (eds) Logic Programming. ICLP 2002. Lecture Notes in Computer Science, vol 2401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45619-8_25
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DOI: https://doi.org/10.1007/3-540-45619-8_25
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