CP-Nets, \(\pi \)-pref Nets, and Pareto Dominance

  • Nic WilsonEmail author
  • Didier Dubois
  • Henri Prade
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11940)


Two approaches have been proposed for the graphical handling of qualitative conditional preferences between solutions described in terms of a finite set of features: Conditional Preference networks (CP-nets for short) and more recently, Possibilistic Preference networks (\(\pi \)-pref nets for short). The latter agree with Pareto dominance, in the sense that if a solution violates a subset of preferences violated by another one, the former solution is preferred to the latter one. Although such an agreement might be considered as a basic requirement, it was only conjectured to hold as well for CP-nets. This non-trivial result is established in the paper. Moreover it has important consequences for showing that \(\pi \)-pref nets can at least approximately mimic CP-nets by adding explicit constraints between symbolic weights encoding the ceteris paribus preferences, in case of Boolean features. We further show that dominance with respect to the extended \(\pi \)-pref nets is polynomial.



This material is based upon works supported by the Science Foundation Ireland under Grants No. 12/RC/2289 and No. 12/RC/2289-P2 which are co-funded under the European Regional Development Fund.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Insight Centre for Data Analytics, School of Computer Science and ITUniversity College CorkCorkIreland
  2. 2.IRIT-CNRS Université Paul SabatierToulouseFrance

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