David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Argument and Computation 1 (2):93-124 (2011)
An abstract framework for structured arguments is presented, which instantiates Dung's ('On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n- Person Games', Artificial Intelligence , 77, 321-357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog
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Floris J. Bex, Peter J. van Koppen, Henry Prakken & Bart Verheij (2010). A Hybrid Formal Theory of Arguments, Stories and Criminal Evidence. Artificial Intelligence and Law 18 (2):123-152.
Yining Wu, Martin Caminada & Dov M. Gabbay (2009). Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming. Studia Logica 93 (2/3):383 - 403.
Floris Bex & Bart Verheij (2013). Legal Stories and the Process of Proof. Artificial Intelligence and Law 21 (3):253-278.
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Henry Prakken (2012). Reconstructing Popov V. Hayashi in a Framework for Argumentation with Structured Arguments and Dungean Semantics. Artificial Intelligence and Law 20 (1):57-82.
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