Possibilistic logic representation of preferences: relating prioritized goals and satisfaction levels expressions

The preferences of an agent can be expressed in various ways. The agent may indicate goals having different levels of priority for him, or provides classes of choices with their level of satisfaction for him. The first type of specification can be captured in possibilistic logic under the form of constraints on a necessity measure. It is shown in this paper that the second manner for expressing preferences can be encoded as constraints on a so-called ”guaranteed possibility” measure (a min-decomposable function with respect to disjunction). The paper shows how each representation is semantically associated with a possibility distribution (which plays the role of a value function), and how necessity-based possibilistic logic representations can be translated directly into a guaranteed possibilitybased representations and vice-versa. In logical terms, it corresponds to the transformation of a generalized CNF into a generalized DNF. Reasoning in guaranteed possibility-based logic is also discussed. Moreover, the two types of representations can also be shown to be equivalent to sets of conditional preference statements. Thus, different basic modes of preference expression can be captured in the same framework.