Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T01:42:28.092Z Has data issue: false hasContentIssue false
  • English
  • Français

Logic programs with monotone abstract constraint atoms*

Published online by Cambridge University Press:  01 March 2008

VICTOR W. MAREK ,
ILKKA NIEMELÄ  and
MIROSŁAW TRUSZCZYŃSKI
VICTOR W. MAREK
Affiliation:
Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA (e-mail: [email protected])
ILKKA NIEMELÄ
Affiliation:
Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, FI-02015 TKK, Finland (e-mail: [email protected])
MIROSŁAW TRUSZCZYŃSKI
Affiliation:
Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Logic programsstable modelsconstraints
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 8 , Issue 2 , March 2008 , pp. 167 - 199
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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.Google Scholar
Apt, K. 1990. Logic programming. In Handbook of theoretical computer science, Leeuven, J. van, Ed. Elsevier, pp. 493–574.Google Scholar
Babovich, Y. & Lifschitz, V. 2002. Cmodels package. http://www.cs.utexas.edu/users/tag/cmodels.html.Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.Google Scholar
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.Google Scholar
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.Google Scholar
Clark, K. 1978. Negation as failure. In Logic and data bases, Gallaire, H. & Minker, J., Eds. Plenum Press, pp. 293–322.CrossRefGoogle Scholar
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.Google Scholar
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. 127–144.CrossRefGoogle Scholar
Denecker, M., Marek, V. & Truszczyński, M. 2004. Ultimate approximation and its application in nonmonotonic knowledge representation systems. Information and Computation 192, 84–121.Google Scholar
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. 212–226.Google Scholar
East, D. & Truszczyński, M. 2006. Predicate-calculus based logics for modeling and solving search problems. ACM Transactions on Computational Logic 7, 38–83.Google Scholar
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. 200–212.Google 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
Fitting, M. C. 2002. Fixpoint semantics for logic programming – a survey. Theoretical Computer Science 278, 25–51.Google Scholar
Gelfond, M. & Leone, N. 2002. Logic programming and knowledge representation – the A-prolog perspective. Artificial Intelligence 138, 3–38.Google Scholar
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. 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases, New Generation Computing 9, 365–385.Google Scholar
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.Google Scholar
Lifschitz, V. 1996. Foundations of logic programming. In Principles of Knowledge Representation, pp. 69–127. CSLI Publications.Google Scholar
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. 112–117.Google Scholar
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. 495–509.Google Scholar
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. 410–415.Google Scholar
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. 701–706.Google Scholar
Marek, V. W. 2005. Mathematics of Satisfiability http://www.cs.uky.edu/marek/book.pdf.Google Scholar
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. 154–166.Google Scholar
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. 154–167.Google Scholar
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. 86–91.Google Scholar
Minker, J. 1982. On indefinite databases and the closed world assumption. In Proceedings of the 6th conference on automated deduction. LNCS 138. Springer, pp. 292–308.Google Scholar
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. 420–429.Google Scholar
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. 317–331.Google Scholar
Pelov, N. 2004. Semantics of logic programs with aggregates. PhD Dissertation. Department of Computer Science, K.U. Leuven, Leuven, Belgium.Google Scholar
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. 207–219.Google Scholar
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.Google Scholar
Przymusinski, T. 1990. The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae 13 (4), 445–464.Google Scholar
Przymusinski, T. 1991. Stable semantics for disjunctive programs, New Generation Computing 9, 401–424.Google Scholar
Sakama, C. & Inoue, K. 1994. An alternative approach to the semantics of disjunctive logic programs and deductive databases. Journal of Automated Reasoning 13, 145–172.Google Scholar
Sakama, C. & Inoue, K. 1995. Paraconsistent Stable Semantics for Extended Disjunctive Programs. Journal of Logic and Computation 5, 265–285.Google Scholar
Simons, P., Niemelä, I., & Soininen, T. 2002. Extending & implementing the stable model semantics. Artificial Intelligence 138, 181–234.Google Scholar
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. 129–134.Google Scholar
vanEmden, M. Emden, M. & Kowalski, R. 1976. The semantics of predicate logic as a programming language. Journal of the ACM 23, 4, 733–742.Google Scholar
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. 269–274.Google Scholar