Advertisement

Extending the Notion of Preferred Explanations for Quantified Constraint Satisfaction Problems

  • Deepak Mehta
  • Barry O’Sullivan
  • Luis QuesadaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9399)

Abstract

The Quantified Constraint Satisfaction Problem (QCSP) is a generalization of classical constraint satisfaction problem in which some variables can be universally quantified. This additional expressiveness can help model problems in which a subset of the variables take value assignments that are outside the control of the decision maker. Typical examples of such domains are game-playing, conformant planning and reasoning under uncertainty. In these domains decision makers need explanations when a QCSP does not admit a winning strategy. We extend our previous approach to defining preferences amongst the requirements of a QCSP by considering more general relaxation schemes. We also present key complexity results on the hardness of finding preferred conflicts of QCSPs under this extension of the notion of preference. This paper unifies work from the fields of constraint satisfaction, explanation generation, and reasoning under preferences and uncertainty.

Keywords

Consistency Check Total Order Relaxation Function Universal Quantifier Equivalent Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowldedgement

This material is based upon work supported by the Science Foundation Ireland under Grant No.10/CE/I1853 and the FP7 Programme (FP7/2007–2013) under grant agreement No. 318137 (DISCUS). The Insight Centre for Data Analytics is also supported by Science Foundation Ireland under Grant No. SFI/12/RC/2289.

References

  1. 1.
    Chen, H.: The Computational Complexity of Quantified Constraint Satisfaction. Ph.D. thesis, Cornell, August 2004Google Scholar
  2. 2.
    Junker, U.: Quickxplain: preferred explanations and relaxations for over-constrained problems. In: Proceedings of AAAI 2004, pp. 167–172 (2004)Google Scholar
  3. 3.
    Verger, G., Bessière, C.: : A bottom-up approach for solving quantified csps. In: Proceedings of CP, pp. 635–649 (2006)Google Scholar
  4. 4.
    Gent, I.P., Nightingale, P., Stergiou, K.: QCSP-solve: a solver for quantified constraint satisfaction problems. In: Proceedings of IJCAI, pp. 138–143 (2005)Google Scholar
  5. 5.
    Mehta, D., O’Sullivan, B., Quesada, L.: Preferred explanations for quantified constraint satisfaction problems. In: 22nd IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2010, Arras, France, 27–29 October 2010, vol. 1, pp. 275–278. IEEE Computer Society (2010)Google Scholar
  6. 6.
    Bordeaux, L., Monfroy, E.: Beyond NP: arc-consistency for quantified constraints. In: Proceedings of CP 2002, pp. 371–386 (2002)Google Scholar
  7. 7.
    Stynes, D., Brown, K.N.: Realtime online solving of quantified CSPs. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 771–786. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  8. 8.
    Ferguson, A., O’Sullivan, B.: Quantified constraint satisfaction problems: from relaxations to explanations. In: Proceedings of IJCAI-2007, pp. 74–79 (2007)Google Scholar
  9. 9.
    Brafman, R.I., Domshlak, C.: Introducing variable importance tradeoffs into CP-Nets. In: UAI, pp. 69–76 (2002)Google Scholar
  10. 10.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the The Theory of NP-Completeness. W. H Freeman and Company, New York (1979) zbMATHGoogle Scholar
  11. 11.
    Scholl, C., Becker, B.: Checking equivalence for partial implementations. In: Proceedings of the 38th Design Automation Conference, DAC 2001, Las Vegas, NV, USA, June 18–22, pp. 238–243. ACM (2001)Google Scholar
  12. 12.
    Miller, C., Kupferschmid, S., Lewis, M., Becker, B.: Encoding Techniques, craig interpolants and bounded model checking for incomplete designs. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 194–208. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  13. 13.
    Benedetti, M., Lallouet, A., Vautard, J.: QCSP made practical by virtue of restricted quantification. In: Veloso, M.M. (ed.) IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, January 6–12 2007, pp. 38–43 (2007)Google Scholar
  14. 14.
    Brewka, G.: Answer sets and qualitative optimization. Log. J IGPL 14(3), 413–433 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Confalonieri, R., Nieves, J.C., Osorio, M., Vázquez-Salceda, J.: Dealing with explicit preferences and uncertainty in answer set programming. Ann. Math. Artif. Intell. 65(2–3), 159–198 (2012)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Deepak Mehta
    • 1
  • Barry O’Sullivan
    • 1
  • Luis Quesada
    • 1
    Email author
  1. 1.Insight Centre for Data AnalyticsUniversity College CorkCorkIreland

Personalised recommendations