Annals of Operations Research

, Volume 163, Issue 1, pp 89–114 | Cite as

Reasoning with various kinds of preferences: logic, non-monotonicity, and algorithms

Article

Abstract

As systems dealing with preferences become more sophisticated, it becomes essential to deal with various kinds of preference statements and their interaction. We introduce a non-monotonic logic distinguishing sixteen kinds of preferences, ranging from strict to loose and from careful to opportunistic, and two kinds of ways to deal with uncertainty, either optimistically or pessimistically. The classification of the various kinds of preferences is inspired by a hypothetical agent comparing the two alternatives of a preference statement. The optimistic and pessimistic way of dealing with uncertainty correspond on the one hand to considering either the best or the worst states in the comparison of the two alternatives of a preference statement, and on the other hand to the calculation of least or most specific “distinguished” preference orders from a set of preference statements. We show that each way to calculate distinguished preference orders is compatible with eight kinds of preferences, in the sense that it calculates a unique distinguished preference order for a set of such preference statements, and we provide efficient algorithms that calculate these unique distinguished preference orders. In general, optimistic kinds of preferences are compatible with optimism in calculating distinguished preference orders, and pessimistic kinds of preferences are compatible with pessimism in calculating distinguished preference orders. However, these two sets of eight kinds of preferences are not exclusive, such that some kinds of preferences can be used in both ways to calculate distinguished preference orders, and other kinds of preferences cannot be used in either of them. We also consider the merging of optimistically and pessimistically constructed distinguished preferences orders.

Keywords

Logic of preferences Preference logic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benferhat, S., & Kaci, S. (2001). A possibilistic logic handling of strong preferences. In International Fuzzy Systems Association (IFSA’01) (pp. 962–967). Google Scholar
  2. Benferhat, S., Dubois, D., & Prade, H. (1992). Representing default rules in possibilistic logic. In Proceedings of 3rd international conference of principles of knowledge representation and reasoning (KR’92) (pp. 673–684). Google Scholar
  3. Benferhat, S., Dubois, D., & Prade, H. (1999). Possibilistic and standard probabilistic semantics of conditional knowledge bases. Logic and Computation, 9(6), 873–895. CrossRefGoogle Scholar
  4. Benferhat, S., Dubois, D., & Prade, H. (2001). Towards a possibilistic logic handling of preferences. Applied Intelligence, 14(3), 303–317. CrossRefGoogle Scholar
  5. Benferhat, S., Dubois, D., Kaci, S., & Prade, H. (2002a). Bipolar possibilistic representations. In 18th international conference on uncertainty in artifcial intelligence (UAI’02) (pp. 45–52). Google Scholar
  6. Benferhat, S., Dubois, D., Kaci, S., & Prade, H. (2002b). Bipolar representation and fusion of preferences in the possibilistic logic framework. In 8th international confenrence on principle of knowledge representation and reasoning (KR’02) (pp. 421–432). Google Scholar
  7. Benferhat, S., Dubois, D., Kaci, S., & Prade, H. (2006). Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions. International Journal on Multi-Sensor, Multi-Source Information Fusion, 7, 135–150. Google Scholar
  8. Booth, R., & Paris, J. (1998). A note on the rational closure of knowledge bases with both positive and negative knowledge. Journal of Logic, Language and Information, 7(2), 165–190. CrossRefGoogle Scholar
  9. Bosi, G., Brafman, R. I., Chomicki, J., & Kießling, W. (Eds.) (2004). Preferences: specification, inference, applications, Dagstuhl Seminar Proceedings 04271. Google Scholar
  10. Boutilier, C. (1994). Toward a logic for qualitative decision theory. In Proceedings of the 4th international conference on principles of knowledge representation (KR’94) (pp. 75–86). Google Scholar
  11. Boutilier, C., Brafman, R., Domshlak, C., Hoos, H., & Poole, D. (2004). CP-nets: A tool for representing and reasoning with conditional ceteris paribus preference statements. Journal of Artificial Intelligence Research, 21, 135–191. Google Scholar
  12. Brafman, R., & Junker, U. (Eds.) (2005). Advances in preference handling, workshop of the international joint conference on artificial intelligence (IJCAI’05). Google Scholar
  13. Cacioppo, J. T., & Bernston, G. G. (1999). The affect system: Architecture and operating characteristics. Current Directions in Psychological Science, 8(5), 133–137. CrossRefGoogle Scholar
  14. Cacioppo, J. T., Gardner, W. L., & Bernston, G. G. (1997). Beyond bipolar conceptualizations and measures: The case of attitudes and evaluative space. Personality and Social Psychology Review, 1(1), 3–25. CrossRefGoogle Scholar
  15. de Saint-Cyr, D.F., Lang, J., & Schiex, T. (1994). Penalty logic and its link with dempster-shafer theory. In Proceedings of 10th international conference on uncertainty in artificial intelligence (UAI’94) (pp. 204–211). Google Scholar
  16. Domshlak, C., Venable, B., Rossi, F., & Walsh, T. (2003). Reasoning about soft constraints and conditional preferences. In International joint conference on artificial intelligence (IJCAI’03) (pp. 215–220). Google Scholar
  17. Doyle, J., & Thomason, R. H. (1999). Background to qualitative decision theory. AI Magazine, 20(2), 55–68. Google Scholar
  18. Doyle, J., & Wellman, M. (1994). Representing preferences as cetaris paribus comparatives. In Proceedings of the AAAI spring symposium on decision-theoretic planning, (pp. 69–75). Google Scholar
  19. Dubois, D., Kaci, S., & Prade, H. (2004a). Bipolarity in reasoning and decision – an introduction. the case of the possibility theory framework. In Proceedings of information processing and management of uncertainty in knowledge-based systems conference, IPMU’04 (pp. 959–966). Google Scholar
  20. Dubois, D., Kaci, S., & Prade, H. (2004b). Ordinal and absolute representations of positive information in possibilistic logic. In Proceedings of the International Workshop on Nonmonotonic Reasoning (NMR’ 2004), Whistler, June (pp. 140–146). Google Scholar
  21. Fishburn, P. C. (1999). Preference structures and their numerical representations. Theoretical Computer Science, 217, 359–383. CrossRefGoogle Scholar
  22. Halpern, J. Y. (1997). Defining relative likelihood in partially ordered preferential structures. Journal of Artificial Intelligence Research, 7, 1–24. Google Scholar
  23. Hansson, S. O. (1996). What is ceteris paribus preference? Journal of Philosophical Logic, 25, 307–332. CrossRefGoogle Scholar
  24. Special issue on preferences of computational intelligence. (2004). Computational Intelligence, 20(2). Google Scholar
  25. Junker, U. (Ed.) (2002). Preferences in AI and CP: symbolic approaches, workshop of the eighteenth national conference on artificial intelligence (AAAI02). Technical Report WS-02-13. AAAI. Google Scholar
  26. Kaci, S., & van der Torre, L. (2005a). Algorithms for a nonmonotonic logic of preferences. In Symbolic and quantitative approaches to reasoning with uncertainty, 8th European conference, ECSQARU 2005, LNCS 3571 (pp. 281–292), Springer. Google Scholar
  27. Kaci, S., & van der Torre, L. (2005b). Nonmonotonic reasoning with various kinds of preferences. In ijcai’05 workshop on preferences (page to appear). Google Scholar
  28. Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of measurement: Vol. 1 Additive and polynomial representations. New York: Academic Press. Google Scholar
  29. Lang, J., van der Torre, L., & Weydert, E. (2002). Utilitarian desires. Autonomous Agents and Multi-Agent Systems, 5, 329–363. CrossRefGoogle Scholar
  30. Lang, J., van der Torre, L., & Weydert, E. (2003). Hidden uncertainty in the logical representation of desires. In Proceedings of eighteenth international joint conference on artificial intelligence (IJCAI2003) (pp. 685–690). Google Scholar
  31. Neves, R., & Raufaste, E. (2004). A psychological study of bipolarity in the possibilistic framework. In 10th international conference on information processing and management of uncertainty in knowledge-based systems (IPMU’04), Perugia. Google Scholar
  32. Pearl, J. (1990). System Z: A natural ordering of defaults with tractable applications to default reasoning. In R. Parikh (Ed.), Proceedings of the 3rd conference on theoretical aspects of reasoning about knowledge (TARK’90) (pp. 121–135). San Mateo: Morgan Kaufmann. Google Scholar
  33. Rolls, E. T. (2000). Precis of “brain and emotion”. Behavioral and Brain Sciences, 23(2), 177–234. CrossRefGoogle Scholar
  34. Roubens, M., & Vincke, Ph. (1985). Preference modeling. LNEMS 250. Berlin: Springer. Google Scholar
  35. Shoham, Y. (1987). Nonmonotonic logics: meaning and utility. In Proceedings of IJCAI 1987 (pp. 388–393). Google Scholar
  36. Tan, S., & Pearl, J. (1994). Qualitative decision theory. In Proceedings of the national conference on artificial intelligence (AAAI’94) (pp. 928–933). Google Scholar
  37. Thomason, R. H., & Horty, J. F. (1996). Nondeterministic action and dominance: foundations for planning and qualitative decision. In Proceedings of TARK 1996 (pp. 229–250). Google Scholar
  38. van der Torre, L., & Weydert, E. (2001). Parameters for utilitarian desires in a qualitative decision theory. Applied Intelligence, 14, 285–301. CrossRefGoogle Scholar
  39. von Wright, G. H. (1963). The logic of preference. University of Edinburgh Press. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Centre de Recherche en Informatique de Lens (C.R.I.L.)C.N.R.S.Lens CedexFrance
  2. 2.Department of Computer ScienceUniversity of LuxembourgLuxembourgLuxembourg

Personalised recommendations