Possibilistic Conditional Preference Networks

The paper discusses the use of product-based possibilistic networks for representing conditional preference statements on discrete variables. The approach uses non-instantiated possibility weights to define conditional preference tables. Moreover, additional information about the relative strengths of symbolic weights can be taken into account. It yields a partial preference order among possible choices corresponding to a symmetric form of Pareto ordering. In the case of Boolean variables, this partial ordering coincides with the inclusion between the sets of preference statements that are violated. Furthermore, this graphical model has two logical counterparts in terms of possibilistic logic and penalty logic. The flexibility and the representational power of the approach are stressed. Besides, algorithms for handling optimization and dominance queries are provided.