Approximating Defeasible Logics to Improve Scalability

TL;DR

This paper explores how a more scalable defeasible logic, DL(∂∥), can be used to efficiently approximate conclusions of the less scalable DL(∂) logic, enhancing computational performance in legal and explainable AI applications.

Contribution

It identifies conditions for substituting DL(∂∥) for DL(∂) without changing conclusions and for partial approximation, improving scalability in defeasible reasoning.

Findings

DL(∂∥) can replace DL(∂) without altering conclusions under certain conditions.

DL(∂∥) can draw some valid conclusions, reducing computational load.

The approach enhances scalability of defeasible logic reasoning.

Abstract

Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The defeasible logic $DL(\partial_{||})$ was introduced as a more scalable alternative to $DL(\partial)$, which is better known. In this paper we consider the use of (implementations of) $DL(\partial_{||})$ as a computational aid to computing conclusions in $DL(\partial)$ and other defeasible logics, rather than as an alternative to $DL(\partial)$. We identify conditions under which $DL(\partial_{||})$ can be substituted for $DL(\partial)$ with no change to the conclusions drawn, and conditions under which $DL(\partial_{||})$ can be used to draw some valid conclusions, leaving the remainder to be drawn by $DL(\partial)$.