Skip to main content
SpringerLink
Log in

Answer Sets: From Constraint Programming Towards Qualitative Optimization

  • Conference paper
Logic Programming and Nonmonotonic Reasoning (LPNMR 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2923))

Abstract

One of the major reasons for the success of answer set programming in recent years was the shift from a theorem proving to a constraint programming view: problems are represented such that stable models, respectively answer sets, rather than theorems correspond to solutions. This shift in perspective proved extremely fruitful in many areas. We believe that going one step further from a “hard” to a “soft” constraint programming paradigm, or, in other words, to a paradigm of qualitative optimization, will prove equally fruitful. In this paper we try to support this claim by showing that several generic problems in logic based problem solving can be understood as qualitative optimization problems, and that these problems have simple and elegant formulations given adequate optimization constructs in the knowledge representation language.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baral, C.: Knowledge representation, reasoning and declarative problem solving. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  2. Baral, C., Uyan, C.: Declarativ specification and solution of combinatorial auctions using logic programming. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, p. 186. Springer, Heidelberg (2001)

    Google Scholar 

  3. Balduccini, M., Gelfond, M.: Logic Programs with Consistency-Restoring Rules. In: Doherty, P., McCarthy, J., Williams, M.-A. (eds.) International Symposium on Logical Formalization of Commonsense Reasoning, March 2003. AAAI 2003 Spring Symposium Series (2003)

    Google Scholar 

  4. Brewka, G.: Logic programming with ordered disjunction. In: Proc. AAAI 2002, pp. 100–105. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  5. Brewka, G., Eiter, T.: Preferred answer sets for extended logic programs. Artificial Intelligence 109, 297–356 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Brewka, G., Niemelä, I., Truszczynski, M.: Answer set optimization. In: Proc. IJCAI 2003, Acapulco, pp. 867–872 (2003)

    Google Scholar 

  7. Brewka, G., Niemelä, I., Syrjänen, T.: Implementing ordered disjunction using answer set solvers for normal programs. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, p. 444. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Buccafurri, F., Leone, N., Rullo, P.: Enhancing disjunctive datalog by constraints. IEEE Transactions on Knowledge and Data Engineering 12(5), 845–860 (2000)

    Article  Google Scholar 

  9. Console, L., Dupre, D.T., Torasso, P.: On the relatio between abduction and deduction. Journal of Logic and Computation 1(5), 661–690 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  10. Damasio, C.V., Pereira, L.M.: A Survey on Paraconsistent Semantics for Extended Logic Programas. In: Gabbay, D.M., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 2, pp. 241–320. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  11. Dressler, O., Struss, P.: The consistency-based approach to automated diagnosis of devices. In: Brewka, G. (ed.) Principles of Knowledge Representation. CSLI Publications, Stanford (1996)

    Google Scholar 

  12. Eiter, T., Leone, N., Mateis, C., Pfeifer, G., Scarcello, F.: The kr system dlv: Progress report, comparisons and benchmarks. In: Proc. Principles of Knowledge Representation and Reasoning, KR 1998. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  13. Eiter, T., Faber, W., Leone, N., Pfeifer, G.: The Diagnosi Frontend of the dlv System. AI Communications 12(1-2), 99–111 (1999)

    MathSciNet  Google Scholar 

  14. Eiter, T., Fink, M., Sabbatini, G., Tompits, H.: A generic approach for knowledgebased information-site selection. In: Proc. Principles of Knowledge Representation and Reasoning, KR 2002, Toulouse. Morgan Kaufman, San Francisco (2002)

    Google Scholar 

  15. Eiter, T., Faber, W., Leone, N., Pfeifer, G., Polleres, A.: Answer se planning under action costs. In: Proc. JELIA 2002, Springer, Heidelberg (2002); extended version to appear in Journal of Artificial Intelligence Research

    Google Scholar 

  16. Konolige, K.: Abduction versus closure in causal theories. Artificial Intelligence 53, 255–272 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)

    Article  Google Scholar 

  18. Lifschitz, V.: Answer set programming and plan generation. Artificial Intelligence 138(1-2), 39–54 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Marek, V., Truszczynski, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective (1999)

    Google Scholar 

  20. Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25(3,4), 241–273 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  21. Niemelä, I., Simons, P.: Efficient implementation of the stable model and wellfounded semantics for normal logic programs. In: Proc. 4th Intl. Conference on Logic Programming and Nonmonotonic Reasoning. Springer, Heidelberg (1997)

    Google Scholar 

  22. Peng, Y., Reggia, J.: Abductive inference models for diagnostic problem solving. In: Symbolic Computation - Artificial Intelligence. Springer, Heidelberg (1990)

    Google Scholar 

  23. Pereira, L.M., Alferes, J.J., Aparicio, J.: Contradiction Removal within Well Founded Semantics. In: Nerode, A., Marek, W., Subrahmanian, V.S. (eds.) Logic Programming and Nonmonotonic Reasoning, pp. 105–119. MIT Press, Cambridge (1991)

    Google Scholar 

  24. Poole, D.: An architecture for default and abductive reasoning. Computational Intelligence 5(1), 97–110 (1989)

    Article  MathSciNet  Google Scholar 

  25. Sakama, C., Inoue, K.: Prioritized logic programming and its application to commonsense reasoning. Artificial Intelligence 123(1-2), 185–222 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  26. Schaub, T., Wang, K.: A comparative study of logic programs with preference. In: Proc. Intl. Joint Conference on Artificial Intelligence, IJCAI 2001 (2001)

    Google Scholar 

  27. Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138(1-2), 181–234 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  28. Soininen, T.: An Approach to Knowledge Representation and Reasoning for Product Configuration Tasks. PhD thesis, Helsinki University of Technology, Finland (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Leipzig, Augustusplatz 10-11, 04109, Leipzig, Germany

    Gerhard Brewka

Authors
  1. Gerhard Brewka
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Sciences, University of Texas at Austin, USA

    Vladimir Lifschitz

  2. Department of Information and Computer Science, Helsinki University of Technology TKK,  

    Ilkka Niemelä

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brewka, G. (2003). Answer Sets: From Constraint Programming Towards Qualitative Optimization. In: Lifschitz, V., Niemelä, I. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2004. Lecture Notes in Computer Science(), vol 2923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24609-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24609-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20721-4

  • Online ISBN: 978-3-540-24609-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation