Automated reasoning using possibilistic logic: semantics, belief revision, and variable certainty weights

An approach to automated deduction under uncertainty, based on possibilistic logic, is described; for that purpose we deal with clauses weighted by a degree that is a lower bound of a necessity or a possibility measure, according to the nature of the uncertainty. Two resolution rules are used for coping with the different situations, and the classical refutation method can be generalized with these rules. Also, the lower bounds are allowed to be functions of variables involved in the clauses, which results in hypothetical reasoning capabilities. In cases where only lower bounds of necessity measures are involved, a semantics is proposed in which the completeness of the extended resolution principle is proved. The relation between our approach and the idea of minimizing abnormality is briefly discussed. Moreover, deduction from a partially inconsistent knowledge base can be managed in this approach and captures a form of nonmonotonicity