A Unified Algebraic Framework for Non-Monotonicity
This provides a foundational framework for comparing and integrating various non-monotonic approaches in AI and logic, addressing a long-standing theoretical gap.
The paper tackles the problem of unifying diverse non-monotonic reasoning formalisms by presenting LogAG, an algebraic graded logic that captures argument systems and thereby encompasses default logic, autoepistemic logic, negation as failure, circumscription, possibilistic logic, and inference relations satisfying Makinson's rationality postulates.
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.