Computational techniques for a simple theory of conditional preferences

A simple logic of conditional preferences is defined, with a language that allows the compact representation of certain kinds of conditional preference statements, a semantics and a proof theory. CP-nets and TCP-nets can be mapped into this logic, and the semantics and proof theory generalise those of CP-nets and TCP-nets. The system can also express preferences of a lexicographic kind. The paper derives various sufficient conditions for a set of conditional preferences to be consistent, along with algorithmic techniques for checking such conditions and hence confirming consistency. These techniques can also be used for totally ordering outcomes in a way that is consistent with the set of preferences, and they are further developed to give an approach to the problem of constrained optimisation for conditional preferences.

[1]  G. Wright.  The logic of preference reconsidered , 1972 .

[2]  Johan van Benthem,et al.  Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences , 2009, J. Philos. Log..

[3]  Sven Ove Hansson,et al.  The Structure of Values and Norms , 2007, Cambridge Studies in Probability, Induction and Decision Theory.

[4]  Nic Wilson,et al.  From Preference Logics to Preference Languages, and Back , 2010, KR.

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

[6]  Ronen I. Brafman,et al.  Graphically structured value-function compilation , 2008, Artif. Intell..

[7]  N. Rescher.  The Logic of Preference , 1968 .

[8]  Nic Wilson,et al.  Consistency and Constrained Optimisation for Conditional Preferences , 2004, ECAI.

[9]  Sven Ove Hansson.  What is ceteris paribus preference? , 1996, J. Philos. Log..

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

[11]  Ronen I. Brafman,et al.  On Graphical Modeling of Preference and Importance , 2011, J. Artif. Intell. Res..

[12]  Ronen I. Brafman,et al.  Extended Semantics and Optimization Algorithms for CP‐Networks , 2004, Comput. Intell..

[13]  E. Szpilrajn.  Sur l'extension de l'ordre partiel , 1930 .

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

[15]  Jon Doyle,et al.  Utility Functions for Ceteris Paribus Preferences , 2004, Comput. Intell..

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

[17]  Henri Prade,et al.  Relaxing Ceteris Paribus Preferences with Partially Ordered Priorities , 2007, ECSQARU.

[18]  Ronen I. Brafman,et al.  CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements , 2011, J. Artif. Intell. Res..

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

[20]  Jérôme Lang,et al.  Logical Preference Representation and Combinatorial Vote , 2004, Annals of Mathematics and Artificial Intelligence.

[21]  Jérôme Lang,et al.  From Preference Representation to Combinatorial Vote , 2002, KR.

[22]  Ronen I. Brafman,et al.  Qualitative decision making in adaptive presentation of structured information , 2004, TOIS.

[23]  Ronen I. Brafman,et al.  CP-nets: Reasoning and Consistency Testing , 2002, KR.

[24]  Ronen I. Brafman,et al.  UCP-Networks: A Directed Graphical Representation of Conditional Utilities , 2001, UAI.

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

[26]  Dov M. Gabbay,et al.  Handbook of Philosophical Logic , 2002 .

[27]  Carmel Domshlak,et al.  Modeling and Reasoning about Preferences with CP-nets , 2002 .

[28]  J. Doyle,et al.  Representing Preferences as Ceteris Paribus Comparatives , 1994 .

[29]  Ronen I. Brafman,et al.  Preference‐Based Constrained Optimization with CP‐Nets , 2004, Comput. Intell..

[30]  Vincent Conitzer,et al.  Voting on Multiattribute Domains with Cyclic Preferential Dependencies , 2008, AAAI.

[31]  Nic Wilson,et al.  An Efficient Upper Approximation for Conditional Preference , 2006, ECAI.

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

[33]  Nic Wilson,et al.  Lexicographically-ordered constraint satisfaction problems , 2009, Constraints.