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

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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.

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References

  • Benferhat, S., & Kaci, S. (2001). A possibilistic logic handling of strong preferences. In International Fuzzy Systems Association (IFSA’01) (pp. 962–967).

  • 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).

  • Benferhat, S., Dubois, D., & Prade, H. (1999). Possibilistic and standard probabilistic semantics of conditional knowledge bases. Logic and Computation, 9(6), 873–895.

    Article  Google Scholar 

  • Benferhat, S., Dubois, D., & Prade, H. (2001). Towards a possibilistic logic handling of preferences. Applied Intelligence, 14(3), 303–317.

    Article  Google Scholar 

  • 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).

  • 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).

  • 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 

  • 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.

    Article  Google Scholar 

  • Bosi, G., Brafman, R. I., Chomicki, J., & Kießling, W. (Eds.) (2004). Preferences: specification, inference, applications, Dagstuhl Seminar Proceedings 04271.

  • 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).

  • 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 

  • Brafman, R., & Junker, U. (Eds.) (2005). Advances in preference handling, workshop of the international joint conference on artificial intelligence (IJCAI’05).

  • Cacioppo, J. T., & Bernston, G. G. (1999). The affect system: Architecture and operating characteristics. Current Directions in Psychological Science, 8(5), 133–137.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

  • 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).

  • Doyle, J., & Thomason, R. H. (1999). Background to qualitative decision theory. AI Magazine, 20(2), 55–68.

    Google Scholar 

  • 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).

  • 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).

  • 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).

  • Fishburn, P. C. (1999). Preference structures and their numerical representations. Theoretical Computer Science, 217, 359–383.

    Article  Google Scholar 

  • Halpern, J. Y. (1997). Defining relative likelihood in partially ordered preferential structures. Journal of Artificial Intelligence Research, 7, 1–24.

    Google Scholar 

  • Hansson, S. O. (1996). What is ceteris paribus preference? Journal of Philosophical Logic, 25, 307–332.

    Article  Google Scholar 

  • Special issue on preferences of computational intelligence. (2004). Computational Intelligence, 20(2).

  • 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.

  • 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.

  • Kaci, S., & van der Torre, L. (2005b). Nonmonotonic reasoning with various kinds of preferences. In ijcai’05 workshop on preferences (page to appear).

  • 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 

  • Lang, J., van der Torre, L., & Weydert, E. (2002). Utilitarian desires. Autonomous Agents and Multi-Agent Systems, 5, 329–363.

    Article  Google Scholar 

  • 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).

  • 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.

  • 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 

  • Rolls, E. T. (2000). Precis of “brain and emotion”. Behavioral and Brain Sciences, 23(2), 177–234.

    Article  Google Scholar 

  • Roubens, M., & Vincke, Ph. (1985). Preference modeling. LNEMS 250. Berlin: Springer.

  • Shoham, Y. (1987). Nonmonotonic logics: meaning and utility. In Proceedings of IJCAI 1987 (pp. 388–393).

  • Tan, S., & Pearl, J. (1994). Qualitative decision theory. In Proceedings of the national conference on artificial intelligence (AAAI’94) (pp. 928–933).

  • 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).

  • van der Torre, L., & Weydert, E. (2001). Parameters for utilitarian desires in a qualitative decision theory. Applied Intelligence, 14, 285–301.

    Article  Google Scholar 

  • von Wright, G. H. (1963). The logic of preference. University of Edinburgh Press.

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Authors and Affiliations

  1. Centre de Recherche en Informatique de Lens (C.R.I.L.), C.N.R.S., Rue de l’Université SP 16, 62307, Lens Cedex, France

    Souhila Kaci

  2. Department of Computer Science, University of Luxembourg, Luxembourg, Luxembourg

    Leendert van der Torre

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  1. Souhila Kaci
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  2. Leendert van der Torre
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Correspondence to Souhila Kaci.

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Kaci, S., van der Torre, L. Reasoning with various kinds of preferences: logic, non-monotonicity, and algorithms. Ann Oper Res 163, 89–114 (2008). https://doi.org/10.1007/s10479-008-0331-4

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  • DOI: https://doi.org/10.1007/s10479-008-0331-4

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