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.

Meta-Argumentation Modelling I: Methodology and Techniques

“…An approach to meta-argumentation is provided also by Wooldridge et al [53]. The starting point of this work is the same of our one and consists in the view that arguments and dialogues are inherently meta-logical processes.…”

“…Wooldridge et al [53] argue that one cannot think of argumentation without thinking of meta-argumentation too. They claim that…”

“…What are the techniques of meta-argumentation, and how do they build on existing new ideas in argumentation? We focus here on flattening algorithms for fibring argumentation frameworks [30,29], representation techniques for extended argumentation [35,36], and specification formalisms and logics of argumentation [15,31,14,53]. Figure 3 provides an abstract example of argument instantiation.…”

Arguments, Meta-arguments, and Metadialogues: A Reconstruction of Krabbe, Govier, and Woods

“…This is apparent from the work of such authors as Perlis (1988), Costantini (2002), and Wooldridge et al (2005). In particular, the last three co-authors have developed a formalization of meta-arguments which takes as its ''starting point the view that arguments and dialogues are inherently meta-logical processes.…”

“…In particular, the last three co-authors have developed a formalization of meta-arguments which takes as its ''starting point the view that arguments and dialogues are inherently meta-logical processes. By this we mean that the arguments made by protagonists in a debate must refer to each other'' (Wooldridge et al, 2005, section 1). And they give the example of the following hierarchy of argumentation in a legal context: arguments by prosecuting and by defense attorneys in a lower court; arguments about these arguments by the judge presiding this court; attorneys' arguments at a court of appeals; judges' arguments in the appeals court; and so on for attorneys' and judges' arguments in the supreme court.…”