Tremendous research e↵ort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the di↵erent approaches is much called for. In this paper, we present an algebraic graded logic we refer to as LogAG capable of encompassing various non-monotonic logics. One of the most widely studied logics of uncertainty is possibilistic logic tailored for non-monotonic reasoning under

more »

... omplete and partially inconsistent knowledge. We show how to encode possibilistic theories as LogAG theories, and prove that the LogAG logical consequence relation subsumes its possibilistic counterpart. Since possibilistic logic subsumes any non-monotonic inference relation satisfying Makinson's rationality postulates, our results prove that LogAG subsumes such inference relations as well while remaining immune to the drowning problem.