Consequence operators for defeasible argumentation: characterization and logical properties

Abstract

Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a confluence point for many alternative logical frameworks. Different formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other con°icting arguments. In this context, defeasible consequence relationships for modeling argument and warrant as well as their logical properties have gained particular attention. This paper discusses two consequence operators for the LDSar framework for defeasible argumentation. The operators are intended for modeling argument construction and dialectical analysis (warrant), respectively. Their associated logical properties are studied and contrasted with SLD-based Horn logic. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks.