CP-Nets, \pi -pref Nets, and Pareto Dominance
Abstract: 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.
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