Approximating Defeasible Logics to Improve Scalability

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 $DL(\partial)$.