  In this paper an approach to automated deduction under uncertainty,based on
possibilistic logic, is proposed ; for that purpose we deal with clauses
weighted by a degree which 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 refutation method can be
generalized. Besides the lower bounds are allowed to be functions of variables
involved in the clause, which gives hypothetical reasoning capabilities. The
relation between our approach and the idea of minimizing abnormality is briefly
discussed. In case where only lower bounds of necessity measures are involved,
a semantics is proposed, in which the completeness of the extended resolution
principle is proved. Moreover deduction from a partially inconsistent knowledge
base can be managed in this approach and displays some form of
non-monotonicity.
