Is There a Logic of Provability for Nonmonotonic Reasoning?

Nonmonotonic logic is a well developed research area gathering the logical formalisms that handle commonsense reasoning. One of the central issue in the area is to establish a notion of nonmonotonic provability, which is usually characterized via some modal logic. In MST93] a clear paradigm has been proposed that classiies modal monotonic logics , augmented with the \negation by fail-ure" to prove rule. It turns out that it is not the only one. In this paper we propose different paradigms for formalizing the notion of nonmonotonic provability. We present a xed point construction allowing the interpretation of the necessity modal operator as a nonmonotonic provability operator analogously to that used in the modal logic of prov-ability for Peano Arithmetic. We show that it faithfully interprets both default and au-toepistemic logics and we highlight its connections with the standard xed point construction a la McDermott and Doyle. This new paradigm provides a diierent perspective in the classiication of modal nonmono-tonic logics.