Conditional preference nets and possibilistic logic

Authors:
Didier Dubois;Henri Prade;Fayçal Touazi
Affiliations:
IRIT, University of Toulouse, Toulouse, France;IRIT, University of Toulouse, Toulouse, France;IRIT, University of Toulouse, Toulouse, France
Venue:
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2013

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Abstract

CP-nets (Conditional preference networks) are a well-known compact graphical representation of preferences in Artificial Intelligence, that can be viewed as a qualitative counterpart to Bayesian nets. In case of binary attributes it captures specific partial orderings over Boolean interpretations where strict preference statements are defined between interpretations which differ by a single flip of an attribute value. It respects preferential independence encoded by the ceteris paribus property. The popularity of this approach has motivated some comparison with other preference representation setting such as possibilistic logic. In this paper, we focus our discussion on the possibilistic representation of CP-nets, and the question whether it is possible to capture the CP-net partial order over interpretations by means of a possibilistic knowledge base and a suitable semantics. We show that several results in the literature on the alleged faithful representation of CP-nets by possibilistic bases are questionable. To this aim we discuss some canonical examples of CP-net topologies where the considered possibilistic approach fails to exactly capture the partial order induced by CP-nets, thus shedding light on the difficulties encountered when trying to reconcile the two frameworks.