Logical representation of preference: a brief survey

  • Jérôme Lang
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 482)


Specifying an individual or collective decision making problem requires agents’ preferences over the possible alternatives to be expressed. There exist various models for preference modelling; however, whatever model is chosen does not tell how the transition from the preferences, as they are expressed by the agent, to the preferential structure, is done. Logic plays an important role in designing preference representation languages, which are aimed at expressing preferences over very large, combinatorial sets of alternatives in a compact and structured way. This paper gives a brief survey on these languages.


Logical Representation Conjunctive Normal Form Deontic Logic Combinatorial Auction Propositional Formula 
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.


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  1. [1]
    F. Bacchus and A. Grove. Graphical models for preference and utility. In Uncertainty in Artificial Intelligence (UAI-95), pages 3–10, 1995.Google Scholar
  2. [2]
    N.D. Belnap. A useful four-valued logic. In Modern Uses of Multiple Valued Logic. D. Reidel, Dordrecht, 1977.Google Scholar
  3. [3]
    S. Benferhat, C. Cayrol, D. Dubois, J. Lang, and H. Prade. Inconsistency management and prioritized syntax-based entailment. In Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI’93), pages 640–645, 1993.Google Scholar
  4. [4]
    S. Benferhat, D. Dubois, S. Kaci, and H. Prade. Bipolar possibilistic representations. In Proceedings of UAI-02, 2002.Google Scholar
  5. [5]
    S. Benferhat, D. Dubois, S. Kaci, and H. Prade. Bipolar representation and fusion of preferences in the possibilistic logic framework. In Proceedings of KR2002, 2002.Google Scholar
  6. [6]
    S. Benferhat, D. Dubois, S. Kaci, and H. Prade. Possibilistic representation of preference: relating prioritized goals and satisfaction levels expressions. In Proceedings of KR2002, 2002.Google Scholar
  7. [7]
    S. Benferhat, D. Dubois, J. Lang, H. Prade, A. Saffiotti, and P. Smets. A general approach for inconsistency handling and merging information in prioritized knowledge bases. In Proceedings of the 6th International Conference on Knowledge Representation and Reasoning (KR’98), 1998.Google Scholar
  8. [8]
    S. Benferhat, D. Dubois, and H. Prade. Towards a possibilistic logic handling of preferences. Applied Intelligence, 14(3):403–417, 2001.CrossRefGoogle Scholar
  9. [9]
    C. Boutilier. Toward a logic for qualitative decision theory. In Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning (KR’94), pages 75–86, 1994.Google Scholar
  10. [10]
    C. Boutilier, R. Brafman, H. Hoos, and D. Poole. Reasoning with conditional ceteris paribus statements. In Proceedings of UAI-99, pages 71–80, 1999.Google Scholar
  11. [11]
    C. Boutilier and H. Hoos. Bidding languages for combinatorial auctions. In Proc. IJCA I-2001, pages 1211–1217. Morgan Kaufmann Publishers, 2001.Google Scholar
  12. [12]
    G. Brewka. Preferred subtheories: an extended logical framework for default reasoning. In Proceedings of the llth International Joint Conference on Artificial Intelligence (IJCAI’89), pages 1043–1048, 1989.Google Scholar
  13. [13]
    G. Brewka. Logic programming with ordered disjunction. In Proceedings of the 18th National Conference on Artificial Intelligence (AAAI-02), pages 100–105, 2002.Google Scholar
  14. [14]
    C. Cayrol. Un modèle logique pour le raisonnement révisable. Revue d’Intelligence Artificielle, 6:255–284, 1992.Google Scholar
  15. [15]
    Y. Chevaleyre, U. Endriss, S. Estivie, and N. Maudet. Welfare engineering in practice: On the variety of multiagent resource allocation problems. In Proceedings of the 5th International Workshop on Engineering Societies in the Agents World (ESAW-2004), October 2004.Google Scholar
  16. [16]
    L. Cholvy and Ch. Garion. An attempt to adapt a logic of conditional preferences for reasoning with contrary-to-duties. In Proceedings of the 5 th International Workshop on Deontic Logic In Computer Science (DEON’OO), pages 125–145, 2000.Google Scholar
  17. [17]
    S. Coste-Marquis, J. Lang, P. Liberatore, and P. Marquis. Expressive power and succinctness of propositional languages for preference representation. In Proceedings of KR-2004, pages 203–212, 2004.Google Scholar
  18. [18]
    C. Domshlak. Modelling and reasoning about preferences with CP-nets. PhD thesis, Ben-Gurion University, 2002.Google Scholar
  19. [19]
    C. Domshlak and R. Brafman. CP-nets: reasoning and consistency testing. In Proceedings of KR2002, pages 121–132, 2002.Google Scholar
  20. [20]
    J. Doyle, Y. Shoham, and M. P. Wellman. A logic of relative desire. In Proceedings of ISMIS-91, pages 16–31, 1991.Google Scholar
  21. [21]
    J. Doyle and M. P. Wellman. Preferential semantics for goals. In AAAI-91, pages 698–703, 1991.Google Scholar
  22. [22]
    D. Dubois, H. Fargier, and H. Prade. Ordinal and probabilistic representations of acceptance. Journal of Artificial Intelligence Research, 22, 2004.Google Scholar
  23. [23]
    D. Dubois, J. Lang, and H. Prade. Inconsistency in possibilistic knowledge bases-to live or not live with it. Fuzzy logic for the management of uncertainty, pages 335–351, 1992.Google Scholar
  24. [24]
    D. Dubois, J. Lang, and H. Prade. Possibilistic logic. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, editors, Handbook of logic in Artificial Intelligence and logic programming, volume 3, pages 439–513. Clarendon Press Oxford, 1994.Google Scholar
  25. [25]
    D. Dubois and H. Prade. Conditionals: from Philosophy to Computer Science (G. Crocco, L. Farinas del Cerro, A. Herzig, eds.), chapter Conditional objects, possibility theory and default rules, pages 301–336. Oxford University Press, 1995.Google Scholar
  26. [26]
    D. Dubois and H. Prade. Possibilistic logic in decision. Fuzzy Logic and Soft Computing, 1999.Google Scholar
  27. [27]
    F. Dupin de Saint-Cyr, J. Lang, and T. Schiex. Penalty logic and its link with Dempster-Shafer theory. In Proceedings of UAI’94, pages 204–211. Morgan Kaufmann, 1994.Google Scholar
  28. [28]
    J. Fodor, S.A. Orlovski, P. Perny, and M. Roubens. The use of fuzzy preference models in multiple criteria: choice, ranking and sorting. Chapter 3 of volume 5 (Operations Research and Statistics) edited by Slowinski R. in: Handbooks of Fuzzy Sets, eds. Dubois D. and Prade H., 1998.Google Scholar
  29. [29]
    H. Geffner. Default reasoning: causal and conditional theories. MIT Press, 1992.Google Scholar
  30. [30]
    M. L. Ginsberg, A. J. Parkes, and Amitabha Roy. Supermodels and robustness. In Proceedings of AAAI’98, pages 334–339, 1998.Google Scholar
  31. [31]
    C. Gonzales and P. Perny. Gai networks for utility elicitation. In Proceedings of KR-2004, pages 224–233, 2004.Google Scholar
  32. [32]
    P. Haddawy and S. Hanks. Representations for decision theoretic planning: utility functions for deadline goals. In Proceedings of KR’92, pages 71–82, 1992.Google Scholar
  33. [33]
    J. Halpern. Defining relative likelihood in partially-ordered preferential structures. Journal of Artificial Intelligence Research, 7:1–24, 1997.zbMATHMathSciNetGoogle Scholar
  34. [34]
    S. O. Hansson. Preference logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, pages 319–393. Kluwer, 2001.Google Scholar
  35. [35]
    S. O. Hansson. The structure of values and norms. Cambridge University Press, 2001.Google Scholar
  36. [36]
    H. Katsuno and A.O. Mendelzon. On the difference between updating a knowledge base and revising it. In Proceedings of KR’ 91, pages 387–394, 1991.Google Scholar
  37. [37]
    H. Katsuno and A.O. Mendelzon. Propositional knowledge base revision and minimal change. Artificial Intelligence, 52(3):263–294, 1992.CrossRefMathSciNetGoogle Scholar
  38. [38]
    S. Konieczny, J. Lang, and P. Marquis. Distance-based merging: a general framework and some complexity results. In Proceedings of KR2002, pages 97–108, 2002.Google Scholar
  39. [39]
    S. Konieczny and R. Pino-Pérez. On the logic of merging. In Proc. of KR’98, pages 488–498, 1998.Google Scholar
  40. [40]
    C. Lafage and J. Lang. Logical representation of preferences for group decision making. In KR-00, pages 457–468, 2000.Google Scholar
  41. [41]
    C. Lafage and J. Lang. Propositional distances and preference representation. In Proceedings of ECSQARU-2001, pages 48–59, 2001.Google Scholar
  42. [42]
    J. Lang. Possibilistic logic as a logical framework for min-max discrete optimization and prioritized constraints. In Procedings of the International Workshop on Fundamentals of Artificial Intelligence Research, pages 113–125, 1991.Google Scholar
  43. [43]
    J. Lang. Conditional desires and utilities-an alternative logical approach to qualitative decision theory. In Proceedings of ECAI-96, pages 318–322, 1996.Google Scholar
  44. [44]
    J. Lang. From preference representation to combinatorial vote. In Proceedings of KR2002, pages 277–288, 2002.Google Scholar
  45. [45]
    J. Lang. Logical preference representation and combinatorial vote. Annals of Mathematics and Artificial Intelligence, 42(1):37–71, 2004.zbMATHCrossRefMathSciNetGoogle Scholar
  46. [46]
    J. Lang, L. van der Torre, and E. Weydert. Utilitarian desires. International Journal on Autonomous Agents and Multi-Agent Systems, 5:329–363, 2002.CrossRefGoogle Scholar
  47. [47]
    D. Lehmann. Another perspective on default reasoning. Annals of Mathematics and Artificial Intelligence, 15(l):61–82, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  48. [48]
    D. Lewis. Counterfactuals. Blackwell, 1973.Google Scholar
  49. [49]
    D. Makinson. Five faces of minimality. Studio, Logica, 52:339–379, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  50. [50]
    M. McGeachie and J. Doyle. Efficient utility functions for ceteris paribus preferences. In Proceedings of AAAI-02, 2002.Google Scholar
  51. [51]
    B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In Proceedings of the 2nd International Conference on Knowledge Representation and Reasoning (KR’91), pages 417–428, 1991.Google Scholar
  52. [52]
    N. Nisan. Bidding and allocation in combinatorial auctions. In 2nd ACM Conf on Electronic Commerce, 2000.Google Scholar
  53. [53]
    N. Nisan. Combinatorial auctions, chapter Bidding languages. MIT Press, 2005.Google Scholar
  54. [54]
    S.A. Orlovsky. Decision making with a fuzzy preference relation. Fuzzy Sets and Systems, 1:155–167, 1978.zbMATHCrossRefMathSciNetGoogle Scholar
  55. [55]
    J. Pearl. System Z: a natural ordering of defaults with tractable applications for default reasoning. In Proceedings of TARK-90, pages 121–135, 1990.Google Scholar
  56. [56]
    G. Pinkas. Propositional nonmonotonic reasoning and inconsistency in symmetric neural networks. In Proceedings of IJCAI’91, pages 525–530. Morgan-Kaufmann, 1991.Google Scholar
  57. [57]
    P.Z. Revesz. On the semantics of arbitration, Int, Journal of Algebra and Computation, pages 133–160, 1997.Google Scholar
  58. [58]
    B. Roy. Partial preference analysis and decision aid: the fuzzy outranking relation concept. Conflicting objectives in decision, pages 40–75, 1977.Google Scholar
  59. [59]
    R. Sabbadin. Decision as abduction. In Proceedings of ECAI-98, 1998.Google Scholar
  60. [60]
    T. Sandholm. An algorithm for optimal winner determination in combinatorial auctions. In Proceedings of IJCAI’99, pages 452–547, 1999.Google Scholar
  61. [61]
    T. Schiex, H. Fargier, and G. Verfaillie. Valued constraint satisfaction problems: hard and easy problems. In Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI’95), pages 631–637, 1995.Google Scholar
  62. [62]
    S.O. Hansson. What is ceteris paribus preference? Journal of Philosophical Logic, 425:307–332, 1996.MathSciNetGoogle Scholar
  63. [63]
    S.W. Tan and J. Pearl. Specification and evaluation of preferences for planning under uncertainty. In Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning (KR’ 94), pages 530–539, 1994.Google Scholar
  64. [64]
    A. Tsoukiàs. A first-order, four valued, weakly paraconsistent logic and its relation to rough sets semantics. Foundations of Computing and Decision Sciences, 27:77–96, 2002.MathSciNetGoogle Scholar
  65. [65]
    A. Tsoukiàs and P. Vincke. A survey on non conventional preference modelling. Ricerca Operativa, 61:5–49, 1992.Google Scholar
  66. [66]
    L. van der Torre. Reasoning about obligations. PhD thesis, Erasmus University Rotterdam, 1997.Google Scholar
  67. [67]
    L. van der Torre and E. Weydert. Parameters for utilitarian desires in a qualitative decision theory. Applied Intelligence, 14(3):285–302, 2001.zbMATHCrossRefGoogle Scholar
  68. [68]
    G. H. von Wright. The logic of preference. Edinburgh University Press, 1963.Google Scholar
  69. [69]
    N. Wilson. Extending CP-nets with stronger conditional preference statements. In Proceedings of AAAI-04, pages 735–741, 2004.Google Scholar

Copyright information

© CISM, Udine 2006

Authors and Affiliations

  • Jérôme Lang
    • 1
  1. 1.Institut de Recherche en Informatique de ToulouseToulouse CedexFrance

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