Mastering the Processing of Preferences by Using Symbolic Priorities in Possibilistic Logic

The paper proposes a new approach to the handling of preferences expressed in a compact way under the form of conditional statements. These conditional statements are translated into classical logic formulas associated with symbolic levels. Ranking two alternatives then leads to compare their respective amount of violation with respect to the set of formulas expressing the preferences. These symbolic violation amounts, which can be computed in a possibilistic logic manner, can be partially ordered lexicographically once put in a vector form. This approach is compared to the ceteris paribus-based CP-net approach, which is the main existing artificial intelligence approach to the compact processing of preferences. It is shown that the partial order obtained with the CP-net approach fully agrees with the one obtained with the proposed approach, but generally includes further strict preferences between alternatives (considered as being not comparable by the symbolic level logic-based approach). These additional strict preferences are in fact debatable, since they are not the reflection of explicit user's preferences but the result of the application of the ceteris paribus principle that implicitly, and quite arbitrarily, favors father node preferences in the graphical structure associated with conditional preferences. Adding constraints between symbolic levels for expressing that the violation of father nodes is less allowed than the one of children nodes, it is shown that it is possible to recover the CP-net-induced partial order. Due to existing results in possibilistic logic with symbolic levels, the proposed approach is computationally tractable.