Learning rules with exceptions may be of interest, especially if the exceptions are not important in some sense. Standard Inductive Logic Programming (ILP) algorithms and classical first order logic are not well-suited for managing rules with exceptions. Indeed, a hypothesis that is induced accumulates all the exceptions of the rules contained in it. Moreover, with multiple-class problems, classifying an example in two different classes (even if one is the right one) is not correct, so a rule that contains some exceptions may prevent another rule which has no exception from being useful. This paper proposes a new possibilistic logic framework for weighted ILP. It induces rules which are progressively more and more accurate, and allows us to manage exceptions by controlling their accumulation. In this setting, we first propose an algorithm for learning rules when the background knowledge and the examples are stratified into layers having different levels of priority or certainty. This allows the induction of general but uncertain rules together with more specific and less uncertain rules. A second algorithm is presented, which does not require an initial weighted database, but still learn a default set of rules in the possibilistic setting.