Skip to main content
SpringerLink
Log in

Abstracting Soft Constraints

  • Conference paper
  • First Online:
New Trends in Constraints (WC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1865))

Included in the following conference series:

Abstract

We propose an abstraction scheme for soft constraint problems and we study its main properties. Processing the abstracted version of a soft constraint problem can help us in many ways: for example, to find good approximations of the optimal solutions, or also to provide us with information that can make the subsequent search for the best solution easier. The results of this paper show that the proposed scheme is promising; thus they can be used as a stable formal base for any experimental work specific to a particular class of soft constraint problems.

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. G. Birkhoff and S. MacLane. A Survey of Modern Algebra. MacMillan, 1965.

    Google Scholar 

  2. S. Bistarelli, H. Fargier, U. Montanari, F. Rossi, T. Schiex, and G. Verfaillie. Semiring-based CSPs and valued CSPs: Basic properties and comparison. In Over-Constrained Systems. Springer-Verlag, LNCS 1106, 1996.

    Google Scholar 

  3. S. Bistarelli, U. Montanari, and F. Rossi. Constraint Solving over Semirings. In Proc. IJCAI95. Morgan Kaufman, 1995.

    Google Scholar 

  4. S. Bistarelli, U. Montanari, and F. Rossi. Semiring-based Constraint Solving and Optimization. Journal of the ACM, 44(2):201–236, March 1997.

    Google Scholar 

  5. P. Cousot and R. Cousot. Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In Fourth ACM Symp. Principles of Programming Languages, pages 238–252, 1977.

    Google Scholar 

  6. P. Cousot and R. Cousot. Systematic design of program analyis. In Sixth ACM Symp. Principles of Programming Languages, pages 269–282, 1979.

    Google Scholar 

  7. S. de Givry, G. Verfaille, and T. Schiex. Bounding The Optimum of Constraint Optimization Problems. In G. Smolka, editor, Proc. CP97, pages 405–419. Springer-Verlag, LNCS 1330, 1997.

    Chapter  Google Scholar 

  8. D. Dubois, H. Fargier, and H. Prade. The calculus of fuzzy restrictions as a basis for flexible constraint satisfaction. In Proc. IEEE International Conference on Fuzzy Systems, pages 1131–1136. IEEE, 1993.

    Google Scholar 

  9. Thomas Ellman. Synthesis of abstraction hierarchies for constraint satisfaction by clustering approximately equivalent objects. In Proceedings of International Conference on Machine Learning, pages 104–111, 1993.

    Google Scholar 

  10. H. Fargier and J. Lang. Uncertainty in constraint satisfaction problems: a probabilistic approach. In Proc. European Conference on Symbolic and Qualitative Approaches to Reasoning and Uncertainty (ECSQARU), pages 97–104. Springer-Verlag, LNCS 747, 1993.

    Chapter  Google Scholar 

  11. E. C. Freuder. Eliminating interchangeable values in constraint satisfaction subproblems. In Proc. AAAI-91, 1991.

    Google Scholar 

  12. E. C. Freuder and D Sabin. Interchangeability supports abstraction and reformulation for constraint satisfaction. In Proceedings of Symposium on Abstraction, Reformulation and Approximation (SARA’95), 1995. http://www.cs.unh.edu/csprojects/csp/csp.html.

  13. E. C. Freuder and R. J. Wallace. Partial constraint satisfaction. AI Journal, 58, 1992.

    Google Scholar 

  14. Y. Georget and P. Codognet. Compiling semiring-based constraints with clp(fd,s). In M. Maher and J-F. Puget, editors, Proc. CP98. Springer-Verlag, LNCS 1520, 1998.

    Google Scholar 

  15. F. Giunchiglia, A. Villafiorita, and T. Walsh. Theories of abstraction. AI Communication, 10(3–4):167–176, 1997.

    Google Scholar 

  16. F. Giunchiglia and T. Walsh. A theory of abstraction. Artificial Intelligence, 56(2–3):323–390, 1992.

    Article  MathSciNet  Google Scholar 

  17. A.K. Mackworth. Consistency in networks of relations. Artificial Intelligence, 8(1):99–118, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  18. A.K. Mackworth. Constraint satisfaction. In Stuart C. Shapiro, editor, Encyclopedia of AI (second edition), volume 1, pages 285–293. John Wiley & Sons, 1992.

    Google Scholar 

  19. Zs. Ruttkay. Fuzzy constraint satisfaction. In Proc. 3rd IEEE International Conference on Fuzzy Systems, pages 1263–1268, 1994.

    Google Scholar 

  20. T. Schiex. Possibilistic constraint satisfaction problems, or “how to handle soft constraints?”. In Proc. 8th Conf. of Uncertainty in AI, pages 269–275, 1992.

    Google Scholar 

  21. T. Schiex, H. Fargier, and G. Verfaille. Valued Constraint Satisfaction Problems: Hard and Easy Problems. In Proc. IJCAI95, pages 631–637. Morgan Kaufmann, 1995.

    Google Scholar 

  22. R. Schrag and D. Miranker. An evaluation of domain reduction: Abstraction for unstructured csps. In Proceedings of the Symposium on Abstraction, Reformulation, and Approximation, pages 126–133, 1992. http://www.cs.utexas.edu/users/schrag/SARA.ps.

  23. M. Wallace. Practical applications of constraint programming. Constraints: An International Journal, 1, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universitá di Pisa, Corso Italia 40, 56125, Pisa, Italy

    S. Bistarelli

  2. University of Paris 6, LIP6 case 169, 4, Place Jussieu, 75 252, Paris, Cedex 05, France

    P. Codognet

  3. INRIA Roquencourt, BP 105, 78153, Le Chesnay, France

    Y. Georget

  4. Dipartimento di Matematica, Universitá di Padova, Via Belzoni 7, 35131, Padova, Italy

    F. Rossi

Authors
  1. S. Bistarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Codognet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Georget
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CWI, Kruislaan 413, 1090, GB Amsterdam, The Netherlands

    Krzysztof R. Apt  & Eric Monfroy  & 

  2. Department of Computer Science, University of Cyprus, 75 Kallipoleos Str., 1678, Nicosia, Cyprus

    Antonis C. Kakas

  3. Department of Pure and Applied Mathematics, University of Padua, Via G. B. Belzoni 7, 35131, Padua, Italy

    Francesca Rossi

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bistarelli, S., Codognet, P., Georget, Y., Rossi, F. (2000). Abstracting Soft Constraints. In: Apt, K.R., Monfroy, E., Kakas, A.C., Rossi, F. (eds) New Trends in Constraints. WC 1999. Lecture Notes in Computer Science(), vol 1865. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44654-0_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-44654-0_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67885-4

  • Online ISBN: 978-3-540-44654-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation