Conditional Preference-Nets, Possibilistic Logic, and the Transitivity of Priorities
Conditional Preference-nets (CP-nets for short) and possibilistic logic with symbolic weights are two different ways of expressing preferences, which leave room for incomparability in the underlying ordering between the different choices. Relations can be
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Abstract Conditional Preference-nets (CP-nets for short) and possibilistic logic with symbolic weights are two different ways of expressing preferences, which leave room for incomparability in the underlying ordering between the different choices. Relations can be expressed between the two settings. A CP-net can be mapped to a weighted set of formulas, one per node of the CP-net, and appropriate constraints between symbolic weights of formula are defined according to the observed priority of father nodes over children nodes in the CP-net. Thus, each potential choice can be associated with a vector of symbolic weights which acknowledges the satisfaction, or not, of each node formula. However, this local priority between father and children nodes in the CP-net does not seem to be transitive. It may happen that the same pair of vectors in the possibilistic representations of two CP-nets correspond to decisions that are comparable in one CP-net structure and incomparable in the other. This troublesome situation points out the discrepancies between the two representation settings, the difficulties of an exact translation of one representation into the other, and questions the faithfulness of the preference representation in CP-nets from a user’s point of view. This note provides a preliminary discussion of these issues, using examples
D. Dubois · H. Prade · F. Touazi (B) IRIT, University of Toulouse, 118 rte de Narbonne, Toulouse, France e-mail: [email protected] H. Prade e-mail: [email protected] F. Touazi e-mail: [email protected] M. Bramer and M. Petridis (eds.), Research and Development in Intelligent Systems XXX, 175 DOI: 10.1007/978-3-319-02621-3_12, © Springer International Publishing Switzerland 2013
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1 Introduction “CP-nets” [3] are a popular framework for expressing conditional preferences, based on a graphical representation. They are based on the idea that users’ preferences generally express that, in a given context, a partially described situation is strictly preferred to another antagonistic partially described situation, in a ceteris paribus way. It has been observed that preferences associated with a father node in a CP-net are then more important than the preferences associated with children nodes. This has motivated the idea of approximating CP-nets by means of a possibilistic logic representation of preferences. More precisely, each node of a CP-net is associated with preferences represented by one possibilistic logic formula, to which is attached a symbolic weight, the priority in favour of father node preferences being echoed by constraints between such symbolic weights [5, 9]. Thus, each interpretation is associated with a vector of symbolic weights which acknowledges the satisfaction, or not, of each node formula. This use of symbolic weights leaves room for a possible incomparability of interpretations, as in CP-nets. Recently, it has been suggested that depending on the order defined between the vectors of symbolic weights, one may approximate any CP-net from below and fro
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