Conditional Preference-Nets, Possibilistic Logic, and the Transitivity of Priorities

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