Approximation of Conditional Preferences Networks fiCP-netsfl in Possibilistic Logic

This paper proposes a first comparative study of the expressive power of two approaches to the representation of preferences: conditional preferences networks (CP-nets) and a logical preference representation framework, namely possibilistic logic. It is shown that possibilistic logic, using a method for handling symbolic priority weights, can always provide complete preorders compatible with the partial CP-net order. Although CP-nets provide an intuitive appealing setting for expressing preferences, possibilistic logic appears to be somewhat more flexible for that purpose.

[1]  Ronen I. Brafman,et al.  Introducing Variable Importance Tradeoffs into CP-Nets , 2002, UAI.

[2]  Craig Boutilier,et al.  CP-nets: a tool for represent-ing and reasoning with conditional ceteris paribus state-ments , 2004 .

[3]  Didier Dubois,et al.  Ordinal and absolute representations of positive information in possibilistic logic , 2004, NMR.

[4]  Carmel Domshlak,et al.  Hard and soft constraints for reasoning about qualitative conditional preferences , 2006, J. Heuristics.

[5]  Thomas Schiex,et al.  Penalty Logic and its Link with Dempster-Shafer Theory , 1994, UAI.

[6]  Gerhard Brewka,et al.  Answer Sets and Qualitative Optimization , 2006, Log. J. IGPL.

[7]  Souhila Kaci,et al.  A possibilistic logic handling of strong preferences , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[8]  Didier Dubois,et al.  Expressing Preferences from Generic Rules and Examples - A Possibilistic Approach Without Aggregation Function , 2005, ECSQARU.

[9]  Didier Dubois,et al.  Possibilistic Merging and Distance-Based Fusion of Propositional Information , 2002, Annals of Mathematics and Artificial Intelligence.

[10]  Henri Prade,et al.  A Theoretical Framework for Possibilistic Independence in a Weakly Ordered Setting , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[11]  H. Prade,et al.  Possibilistic logic , 1994 .

[12]  Souhila Kaci,et al.  Non-monotonic reasoning with various kinds of preferences , 2005 .

[13]  Didier Dubois,et al.  Bridging Logical, Comparative, and Graphical Possibilistic Representation Frameworks , 2001, ECSQARU.

[14]  Carmel Domshlak,et al.  Reasoning about soft constraints and conditional preferences: complexity results and approximation techniques , 2003, IJCAI.

[15]  Jérôme Lang,et al.  Expressive Power and Succinctness of Propositional Languages for Preference Representation , 2004, KR.

[16]  Jürg Kohlas,et al.  Handbook of Defeasible Reasoning and Uncertainty Management Systems , 2000 .

[17]  J. Lang.  Possibilistic Logic: Complexity and Algorithms , 2000 .

[18]  Didier Dubois,et al.  Bipolar Possibilistic Representations , 2002, UAI.

[19]  Toby Walsh,et al.  Constraint-Based Preferential Optimization , 2005, AAAI.

[20]  Leon van der Torre,et al.  Algorithms for a Nonmonotonic Logic of Preferences , 2005, ECSQARU.

[21]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[22]  Ronen I. Brafman,et al.  Reasoning With Conditional Ceteris Paribus Preference Statements , 1999, UAI.

[23]  Miroslaw Truszczynski,et al.  The computational complexity of dominance and consistency in CP-nets , 2005, IJCAI.

[24]  Didier Dubois,et al.  Towards a Possibilistic Logic Handling of Preferences , 1999, Applied Intelligence.

[25]  Didier Dubois,et al.  Representing Default Rules in Possibilistic Logic , 1992, KR.

[26]  Leon van der Torre,et al.  Parameters for Utilitarian Desires in a Qualitative Decision Theory , 2001, Applied Intelligence.

[27]  Nic Wilson,et al.  Extending CP-Nets with Stronger Conditional Preference Statements , 2004, AAAI.

[28]  Miroslaw Truszczynski,et al.  Answer Set Optimization , 2003, IJCAI.

[29]  Jon Doyle,et al.  Efficient utility functions for ceteris paribus preferences , 2002, AAAI/IAAI.