A Knowledge Compilation Map for Conditional Preference Statements-based Languages

Conditional preference statements have been used to compactly represent preferences over combinatorial domains. They are at the core of CP-nets and their generalizations, and lexicographic preference trees. Several works have addressed the complexity of some queries (optimization, dominance in particular). We extend in this paper some of these results, and study other queries which have not been addressed so far, like equivalence, thereby contributing to a knowledge compilation map for languages based on conditional preference statements. We also introduce a new parameterised family of languages, which enables to balance expressiveness against the complexity of some queries.

[1]  Bruno Zanuttini,et al.  Learning conditional preference networks , 2010, Artif. Intell..

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

[3]  Yann Chevaleyre,et al.  Learning various classes of models of lexicographic orderings , 2009 .

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

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

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

[7]  Michael Schmitt,et al.  On the Complexity of Learning Lexicographic Strategies , 2006, J. Mach. Learn. Res..

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

[9]  Bart Selman,et al.  The Comparative Linguistics of Knowledge Representation , 1995, IJCAI.

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

[11]  Francesco M. Donini,et al.  Space Efficiency of Propositional Knowledge Representation Formalisms , 2000, J. Artif. Intell. Res..

[12]  Pierre Marquis,et al.  A Knowledge Compilation Map , 2002, J. Artif. Intell. Res..

[13]  Patrice Perny,et al.  GAI Networks for Utility Elicitation , 2004, KR.

[14]  Thomas Schiex,et al.  Valued Constraint Satisfaction Problems: Hard and Easy Problems , 1995, IJCAI.

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

[16]  Ulrich Endriss,et al.  Conditional Importance Networks: A Graphical Language for Representing Ordinal, Monotonic Preferences over Sets of Goods , 2009, IJCAI.

[17]  Eyke Hüllermeier,et al.  Learning Conditional Lexicographic Preference Trees , 2014 .

[18]  Lirong Xia,et al.  Voting on multi-issue domains with conditionally lexicographic preferences , 2018, Artif. Intell..

[19]  Adnan Darwiche.  Compiling Knowledge into Decomposable Negation Normal Form , 1999, IJCAI.

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

[21]  G Gigerenzer,et al.  Reasoning the fast and frugal way: models of bounded rationality. , 1996, Psychological review.

[22]  Peter C. Fishburn,et al.  LEXICOGRAPHIC ORDERS, UTILITIES AND DECISION RULES: A SURVEY , 1974 .

[23]  Thomas Lukasiewicz,et al.  Complexity Results for Preference Aggregation over (m)CP-nets: Pareto and Majority Voting , 2018, Artif. Intell..

[24]  Hélène Fargier,et al.  Learning Lexicographic Preference Trees From Positive Examples , 2018, AAAI.

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

[26]  Yann Chevaleyre,et al.  Learning conditionally lexicographic preference relations , 2010, ECAI.

[27]  Craig Boutilier,et al.  Local Utility Elicitation in GAI Models , 2005, UAI.

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

[29]  Pierre Marquis,et al.  A Knowledge Compilation Map for Ordered Real-Valued Decision Diagrams , 2014, AAAI.

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

[31]  Nic Wilson,et al.  Computational techniques for a simple theory of conditional preferences , 2011, Artif. Intell..