Skip to main content
SpringerLink
Log in

Enabling local computation for partially ordered preferences

  • Published:
Constraints Aims and scope Submit manuscript

Abstract

Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A major strength of this work is that it is based on an algebraic description: what is proved is the correctness of the local computation algorithm under a few axioms on the algebraic structure. The instantiations of the framework in practice make use of totally ordered scales. The present paper focuses on the use of partially ordered scales and examines how such scales can be cast in the Shafer–Shenoy framework and thus benefit from local computation algorithms. It also provides several examples of such scales, thus showing that each of the algebraic structures explored here is of interest.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Benferhat, S., Lagrue, S., & Papini, O. (2005). Revision of partially ordered information: Axiomatization, semantics and iteration. In IJCAI’05, proceedings of the nineteenth international joint conference on artificial intelligence (pp. 376–381).

  2. Bistarelli, S., Montanari, U., & Rossi, F. (1995). Constraint solving over semirings. In IJCAI’95 (pp. 624–630).

  3. Bistarelli, S., Montanari, U., & Rossi, F. (1997). Semiring-based constraint satisfaction and optimization. Journal of the ACM, 44(2), 201–236.

    Article  MATH  MathSciNet  Google Scholar 

  4. Boutilier, C., Brafman, R., Domshlak, C., Hoos, H., & Poole, D. (2004). CP-nets: A tool for representing and reasoning with conditional ceteris paribus statements. Journal of Artificial Intelligence Research, 21, 135–191.

    MATH  MathSciNet  Google Scholar 

  5. Brewka, G. (1989). Preferred subtheories: An extended logical framework for default reasoning. In IJCAI’89 (pp. 1043–1048).

  6. Dubois, D., & Fargier, H. (2006). Qualitative decision making with bipolar information. In KR’06 (pp. 175–186).

  7. Dubois, D., Lang, J., & Prade, H. (1991). Timed possibilistic logic. Fundamenta Informaticae, 15(3–4), 211–234.

    MATH  MathSciNet  Google Scholar 

  8. Dubus, J.-P., Gonzales, C., & Perny, P. (2009). Multiobjective optimization using GAI models. In IJCAI’09 (pp. 1902–1907).

  9. Fargier, H., & Wilson, N. (2009). Local computation schemes with partially ordered preferences. In ECSQARU’09 (pp. 34–45).

  10. Freuder, E., & Wallace, R. (1992). Partial constraint satisfaction. Artificial Intelligence, 58(1–3), 21–70.

    Article  MathSciNet  Google Scholar 

  11. Friedman, N., & Halpern, J. (1996). Plausibility measures and default reasoning. In AAAI’96 (pp. 1297–1304).

  12. Giunchiglia, E., & Maratea, M. (2007). Planning as satisfiability with preferences. In AAAI’07 (pp. 987–992).

  13. Henig, M. I. (1985). The shortest path problem with two objective functions. European Journal of Operational Research, 25, 281–291.

    Article  MathSciNet  Google Scholar 

  14. Kohlas, J. (2003). Information algebras: Generic structures for inference. New York: Springer (2003).

    MATH  Google Scholar 

  15. Kohlas, J., & Wilson, N. (2008). Semiring induced valuation algebras: Exact and approximate local computation algorithms. Artificial Intelligence, 172, 1360–1399.

    Article  MATH  MathSciNet  Google Scholar 

  16. Lindström, S., & Rabinowicz, W. (1989). Epistemic entrenchment with incomparabilities and relational belief revision. In The logic of theory change, workshop, Konstanz, FRG, 13–15 October 1989. Proceedings (pp. 93–126).

  17. Papadimitriou, C. H., & Yannakakis, M. (2000). On the approximability of trade-offs and optimal access of web sources (extended abstract). In FOCS’00 (pp. 86–92).

  18. Rollon, E. (2008). Multi-objective optimization for graphical models. Ph.D. thesis, Universitat Politècnica de Catalunya, Barcelona, Spain.

  19. Rollon, E., & Larrosa, J. (2006). Bucket elimination for multiobjective optimization problems. Journal of Heuristics, 12(4–5), 307–328.

    Article  MATH  Google Scholar 

  20. Roy, B. (1991). The outranking approach and the foundations of ELECTRE methods. Theory and Decision, 31(1), 49–73.

    Article  MathSciNet  Google Scholar 

  21. Schiex, T., Fargier, H., & Verfaillie, G. (1995). Valued constraint satisfaction problems: Hard and easy problems. In IJCAI’95 (pp. 631–637). Montreal.

  22. Shenoy, P. P. (1990). Valuation-based systems for discrete optimisation. In UAI’90 (pp. 385–400).

  23. Shenoy, P. P., & Shafer, G. (1988). Axioms for probability and belief-function propagation. In UAI’88 (pp. 169–198).

  24. Wilson, N. (1995). An order of magnitude calculus. In UAI’95 (pp. 548–555).

  25. Wilson, N. (2006). A logic of soft constraints based on partially ordered preferences. Journal of Heuristics, 12(4–5), 241–262.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRIT, 118 route de Narbonne, 31062, Toulouse Cedex, France

    Hélène Fargier

  2. Technical University of Catalonia, Jordi Girona 1–3, 08034, Barcelona, Spain

    Emma Rollon

  3. Cork Constraint Computation Centre, Department of Computer Science, University College Cork, Cork, Ireland

    Nic Wilson

Authors
  1. Hélène Fargier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emma Rollon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nic Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nic Wilson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fargier, H., Rollon, E. & Wilson, N. Enabling local computation for partially ordered preferences. Constraints 15, 516–539 (2010). https://doi.org/10.1007/s10601-010-9094-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10601-010-9094-z

Keywords

Search

Navigation