A Unified Algebraic Framework for Non-Monotonicity

Abstract

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 Log A G 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 Log A G theories, and prove that Log A G 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 Log A G captures the before-mentioned non-monotonic logical formalisms as well. Previous results show that Log A G subsumes possibilistic logic and any non-monotonic inference relation satisfying Makinson's rationality postulates. In this way, Log A G provides a powerful unified framework for non-monotonicity.