On the meta-logic of arguments

Abstract

Argumentation has received steadily increasing attention in the multi-agent systems community over the past decade, with particular interest in the use of argument models from the informal logic community. The formalisation of such argument systems is a necessary step if they are to be successfully deployed, and their properties rigorously understood. However, there is as yet no widely accepted approach to the formalisation of argument systems. In this paper, we take as our starting point the view that arguments and dialogues are inherently meta-logical, and that any proper formalisation of argument must embrace this aspect of their nature. For example, a statement that serves as a justification of an argument is is statement about an argument: the argument for which the justification serves must itself be referred to in the justification. From this starting position, we develop a formalisation of arguments using a hierarchical first-order meta-logic, in which statements in successively higher tiers of the argumentation hierarchy refer to statements further down the hierarchy. This enables us to give a clean formal separation between object-level statements, arguments made about these object level statements, and statements about arguments.