Modelling Inference in Argumentation through Labelled Deduction: Formalization and Logical Properties

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 conflicting arguments. In this context, defeasible consequence relationships for modelling argument and warrant as well as their logical properties have gained particular attention. This article analyzes two non-monotonic inference operators C_arg and C_war intended for modelling argument construction and dialectical analysis (warrant), respectively. As a basis for such analysis we will use the LDS_ar framework, a unifying approach to computational models of argument using Labelled Deductive Systems (LDS). In the context of this logical framework, we show how labels can be used to represent arguments as well as argument trees, facilitating the definition and study of non-monotonic inference operators, whose associated logical properties are studied and contrasted. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. Mathematics Subject Classification (2000): Primary 03B22; Secondary 03B42.