# A Unified Algebraic Framework for Non-Monotonicity

## TL;DR

This paper introduces LogAG, an algebraic graded logic framework that unifies various non-monotonic reasoning formalisms, enabling comparison and formal analysis of their underlying principles.

## Contribution

The paper presents LogAG, a novel algebraic framework that captures multiple non-monotonic logics and argument systems, unifying them under a single formalism.

## Key findings

- LogAG encodes argument systems and captures belief spaces.
- LogAG encompasses default logic, autoepistemic logic, and circumscription.
- LogAG subsumes possibilistic logic and rational inference relations.

## 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 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.