Bipolarity in possibilistic logic and fuzzy rules

Extended Abstract. The ideas and results presented in this extended abstract are the fruit of jointworks with Salem Benferhat, Souhila Kaci and Laurent UghettoInternational audiencePossibility theory has been developed in the last twenty years, mainly as a framework for modelling states of partial ignorance on the basis of possibility distributions encoding complete pre-orders. Possibility measures of events, defined as the maximum of the distribution over the set of models of the considered events, together with the dual measures of necessity, are then used for assessing uncertainty. As such, possibility theory relies on a minimal specificity principle which states that the possibility level associated to a possible world should be the largest one which is compatible with the constraints representing the available information. It agrees in particular with the classical view of logical modelling according to which each piece of information declares some worlds impossible (the other worlds forming a subset of tentatively possible ones). When pieces of information are conjunctively combined, the resulting set of the possible worlds is indeed the largest set compatible with all pieces of information. Possibility theory extends this view by allowing intermediary levels between what is fully possible and what is completely impossible