Relating Carneades with abstract argumentation via the ASPIC⁺framework for structured argumentation

Abstract

Carneades is a recently proposed formalism for structured argumentation with varying proof standards, inspired by legal reasoning, but more generally applicable. Its distinctive feature is that each statement can be given its own proof standard, which is claimed to allow a more natural account of reasoning under burden of proof than existing formalisms for structured argumentation, in which proof standards are defined globally. In this article, the two formalisms are formally related by translating Carneades into the ASPIC + framework for structured argumentation. Since ASPIC + is defined to generate Dung-style abstract argumentation frameworks, this in effect translates Carneades graphs into abstract argumentation frameworks. For this translation, we prove a formal correspondence and show that certain rationality postulates hold. It is furthermore proved that Carneades always induces a unique Dung extension, which is the same in all of Dung's semantics, allowing us to generalise Carneades to cycle-containing structures.

Towards Formal Representation and Evaluation of Arguments

“…For example, Dung's abstract frameworks have been developed and furnished with a numerical semantics (Brewka and Woltran 2010;Gabbay 2012), and the numerical formalism of Carneades has been translated into the formalism of ASPIC? (van Gijzel and Prakken 2012).…”

Revisiting Abstract Argumentation Frameworks

“…This would involve broadening the range of networks considered in this paper, to include (for example) networks in which arguments or statements are asserted as being for, or against a claim. That the latter reconstructions are possible is attested to by a recent translation of the Carneades model of argumentation to ASPIC + [16] (Carneades models arguments for and against claims). In this paper I have also suggested how recursive attacks on attacks, and indeed attacks on supports, can intuitively be motivated in the context of everyday reasoning and debate.…”

Haskell Gets Argumentative

“…To take this even further, there has been much work recently on the formalisation of translations between conceptually very different argumentation models [10,19,1,14]. Such a translation can be very difficult to establish and verify.…”

“…Since Dung's seminal work, a range of other computational argumentation frameworks have been proposed, and the study of their relative merits and exact, mathematical relationships is now an active sub-field in its own right [2,1,10,14,19]. However, a problem here is the lack of concrete realisations of many of these frameworks.…”