  Tremendous research effort 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 different
approaches is much called for. In this paper, we present an algebraic graded
logic we refer to as LogAG capable of encompassing a wide variety of
non-monotonic formalisms. We build on Lin and Shoham's argument systems first
developed to formalize non-monotonic commonsense reasoning. We show how to
encode argument systems as LogAG theories, and prove that LogAG captures the
notion of belief spaces in argument systems. Since argument systems capture
default logic, autoepistemic logic, the principle of negation as failure, and
circumscription, our results show that LogAG captures the before-mentioned
non-monotonic logical formalisms as well. Previous results show that LogAG
subsumes possibilistic logic and any non-monotonic inference relation
satisfying Makinson's rationality postulates. In this way, LogAG provides a
powerful unified framework for non-monotonicity.
