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Logic programs with monotone abstract constraint atoms*

  • VICTOR W. MAREK (a1), ILKKA NIEMELÄ (a2) and MIROSŁAW TRUSZCZYŃSKI (a3)

Abstract

We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the generalization involves nondeterminism. Our main results demonstrate that our formalism is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with weight atoms lparse programs) with the semantics of stable models, as defined by Niemelä, Simons and Soininen, and (3) of disjunctive logic programming with the possible-model semantics of Sakama and Inoue.

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Aloul, F., Ramani, A., Markov, I. and Sakallah, K. 2002. PBS: a backtrack-search pseudo-boolean solver and optimizer. In Proceedings of the 5th International Symposium on Theory and Applications of Satisfiability, (SAT-02), pp. 346–353.
Apt, K. 1990. Logic programming. In Handbook of theoretical computer science, Leeuven, J. van, Ed. Elsevier, pp. 493574.
Babovich, Y. & Lifschitz, V. 2002. Cmodels package. http://www.cs.utexas.edu/users/tag/cmodels.html.
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.
Barth, P. 1995. A Davis-Putnam based elimination algorithm for linear pseudo-boolean optimization. Tech. Rep., Max-Planck-Institut für Informatik. MPI-I-95-2-003.
Calimeri, F., Faber, W., Leone, N. and Perri, S. Declarative and Computational Properties of Logic Programs with Aggregates. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI-05), pp. 406–411.
Clark, K. 1978. Negation as failure. In Logic and data bases, Gallaire, H. & Minker, J., Eds. Plenum Press, pp. 293322.
Dell'Armi, T., Faber, W., Ielpa, G., Leone, N. & Pfeifer, G. 2003. Aggregate functions in disjunctive logic programming: semantics, complexity, and implementation in DLV. In Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI-2003). Morgan Kaufmann, pp. 847–852.
Denecker, M., Marek, V. & Truszczyński, M. 2000. Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning. In Logic-Based Artificial Intelligence, Minker, J., Ed. Kluwer Academic Publishers, pp. 127144.
Denecker, M., Marek, V. & Truszczyński, M. 2004. Ultimate approximation and its application in nonmonotonic knowledge representation systems. Information and Computation 192, 84121.
Denecker, M., Pelov, N., & Bruynooghe, M. 2001. Ultimate well-founded and stable semantics for logic programs with aggregates. In Logic Programming, Proceedings of the 2001 International Conference on Logic Programming (ICLP-01). LNCS 2237. Springer, pp. 212226.
East, D. & Truszczyński, M. 2006. Predicate-calculus based logics for modeling and solving search problems. ACM Transactions on Computational Logic 7, 38–83.
Faber, W., Leone, N. & Pfeifer, G. 2004. Recursive aggregates in disjunctive logic programs: Semantics and complexity. In Proceedings of the 9th European Conference on Artificial Intelligence (JELIA-04). LNAI 3229. Springer, pp. 200212.
Fages, F. 1994. Consistency of Clark's completion and existence of stable models. Journal of Methods of Logic in Computer Science 1, 5160.
Fitting, M. C. 2002. Fixpoint semantics for logic programming – a survey. Theoretical Computer Science 278, 2551.
Gelfond, M. & Leone, N. 2002. Logic programming and knowledge representation – the A-prolog perspective. Artificial Intelligence 138, 338.
Gelfond, M. & Lifschitz, V. 1988. The stable semantics for logic programs. In Proceedings of the 5th International Conference on Logic Programming (ICLP-88). MIT Press, pp. 10701080.
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases, New Generation Computing 9, 365385.
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S. & Scarcello, F. 2006. The dlv system for knowledge representation and reasoning. ACM Transactions on Computational Logic. To appear, available at http://xxx.lanl.gov/abs/cs.AI/0211004.
Lifschitz, V. 1996. Foundations of logic programming. In Principles of Knowledge Representation, pp. 69127. CSLI Publications.
Lin, F. & Zhao, Y. 2002. ASSAT: Computing answer sets of a logic program by SAT solvers. In Proceedings of the 18th National Conference on Artificial Intelligence (AAAI-02). AAAI Press, pp. 112117.
Liu, L. & Truszczyński, M. 2003. Local-search techniques in propositional logic extended with cardinality atoms. In Proceedings of the 9th International Conference on Principles and Practice of Constraint Programming (CP-2003). LNCS 2833. Springer, pp. 495509.
Liu, L. & Truszczyński, M. 2005a. Pbmodels – software to compute stable models by pseudoboolean solvers. In Logic Programming and Nonmonotonic Reasoning, Proceedings of the 8th International Conference (LPNMR-05). LNAI 3662. Springer, pp. 410415.
Liu, L. & Truszczyński, M. 2005b. Properties of programs with monotone and convex constraints. In Proceedings of the 20th National Conference on Artificial Intelligence (AAAI-05). AAAI Press, pp. 701706.
Marek, V. W. 2005. Mathematics of Satisfiability http://www.cs.uky.edu/marek/book.pdf.
Marek, V., Niemelä, & Truszczyński, M. 2004. Characterizing stable models of logic programs with cardinality constraints. In Logic Programming and Nonmonotonic Reasoning, Proceedings of the 7th International Conference (LPNMR-04). LNAI 2923. Springer, pp. 154166.
Marek, V. W. & Remmel, J. B. 2004. Set Constraints in Logic Programming. In Logic Programming and Nonmonotonic Reasoning, Proceedings of the 7th International Conference (LPNMR-04). LNAI 2923. Springer, pp. 154167.
Marek, V. & Truszczyński, M. 2004. Logic programs with abstract constraint atoms. In Proceedings of the 19th National Conference on Artificial Intelligence (AAAI-04). AAAI Press, pp. 8691.
Minker, J. 1982. On indefinite databases and the closed world assumption. In Proceedings of the 6th conference on automated deduction. LNCS 138. Springer, pp. 292308.
Niemelä, I. & Simons, P. 1997. Smodels – an implementation of the stable model & well-founded semantics for normal logic programs. In Logic Programming and Nonmonotonic Reasoning, Proceedings of the 4th International Conference (LPNMR-97). LNAI 1265. Springer, pp. 420429.
Niemelä, I., Simons, P. & Soininen, T. 1999. Stable model semantics of weight constraint rules. In Logic Programming and Nonmonotonic Reasoning, Proceedings of the 5th International Conference (LPNMR-99). LNAI 1730. Springer, pp. 317331.
Pelov, N. 2004. Semantics of logic programs with aggregates. PhD Dissertation. Department of Computer Science, K.U. Leuven, Leuven, Belgium.
Pelov, N., Denecker, M. & Bruynooghe, M. 2004. Partial stable models for logic programs with aggregates. In Logic Programming and Nonmonotonic Reasoning, Proceedings of the 7th International Conference (LPNMR-04), LNAI 2923. Springer, pp. 207219.
Pelov, N. & Truszczynski, M. 2004. Semantics of disjunctive programs with monotone aggregates – an operator-based approach. In Proceedings of the 10th International Workshop on Non-Monotonic Reasoning (NMR-04), pp. 327–334.
Przymusinski, T. 1990. The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae 13 (4), 445464.
Przymusinski, T. 1991. Stable semantics for disjunctive programs, New Generation Computing 9, 401424.
Sakama, C. & Inoue, K. 1994. An alternative approach to the semantics of disjunctive logic programs and deductive databases. Journal of Automated Reasoning 13, 145172.
Sakama, C. & Inoue, K. 1995. Paraconsistent Stable Semantics for Extended Disjunctive Programs. Journal of Logic and Computation 5, 265285.
Simons, P., Niemelä, I., & Soininen, T. 2002. Extending & implementing the stable model semantics. Artificial Intelligence 138, 181234.
Son, C., Pontelli, E. & Tu, P. H. 2006. Answer sets for logic programs with arbitrary abstract constraint atoms. In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI-06). AAAI Press, pp. 129134.
vanEmden, M. Emden, M. & Kowalski, R. 1976. The semantics of predicate logic as a programming language. Journal of the ACM 23, 4, 733742.
Walser, J. 1997. Solving linear pseudo-boolean constraints with local search. In Proceedings of the 14th National Conference on Artificial Intelligence (AAAI-97). AAAI Press, pp. 269274.

Keywords

Logic programs with monotone abstract constraint atoms*

  • VICTOR W. MAREK (a1), ILKKA NIEMELÄ (a2) and MIROSŁAW TRUSZCZYŃSKI (a3)

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