A study of accrual of arguments, with applications to evidential reasoning

ABSTRACT

This paper presents a logical formalisation of accrual of arguments as a form of inference. The formalisation is given within the logical framework of Dung as instantiated by Pollock, and is shown to satisfy three principles that any treatment of accrual should satisfy. The formalisation of accrual as inference is contrasted to knowledge-representation treatments of accrual. Also, the formalisation is applied to some concepts from the theory of evidential legal reasoning.

REFERENCES

• 1: T. Anderson and W. Twining. Analysis of Evidence. How to Do Things with Facts Based on Wigmore's Science of Judicial Proof. Little, Brown and Company, Boston, MA, 1991.
• 2: Trevor J. M. Bench-Capon, Try to see it my way: modelling persuasion in legal discourse, Artificial Intelligence and Law, v.11 n.4, p.271-287, January 2003 [doi>10.1023/B:ARTI.0000045997.45038.8f]
• 3: Floris Bex , Henry Prakken , Chris Reed , Douglas Walton, Towards a formal account of reasoning about evidence: argumentation schemes and generalisations, Artificial Intelligence and Law, v.11 n.2-3, p.125-165, January 2003 [doi>10.1023/B:ARTI.0000046007.11806.9a]
• 4: Phan Minh Dung, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games, Artificial Intelligence, v.77 n.2, p.321-357, Sept. 1995 [doi>10.1016/0004-3702(94)00041-X]
• 5: J. Hage. A theory of legal reasoning and a logic to match. Artificial Intelligence and Law, 4:199--273, 1996.
• 6: J. Hage. Reasoning With Rules. An Essay on Legal Reasoning and Its Underlying Logic. Law and Philosophy Library. Kluwer Academic Publishers, Dordrecht/Boston/London, 1997.
• 7: P. Krause, S. Ambler, M. Elvang-Gøransson, and J. Fox. A logic of argumentation for reasoning under uncertainty. Computational Intelligence, 11(1):113--131, 1995.
• 8: John L. Pollock, How to reason defeasibly, Artificial Intelligence, v.57 n.1, p.1-42, Sept. 1992 [doi>10.1016/0004-3702(92)90103-5]
• 9: John L. Pollock, Justification and defeat, Artificial Intelligence, v.67 n.2, p.377-407, June 1994 [doi>10.1016/0004-3702(94)90057-4]
• 10: John L. Pollock, Cognitive Carpentry: A Blueprint for how to Build a Person, MIT Press, Cambridge, MA, 1995
• 11: J. Pollock. Perceiving and reasoning about a changing world. Computational Intelligence, 14:498--562, 1998.
• 12: H. Prakken and G. Sartor. A dialectical model of assessing conflicting arguments in legal reasoning. Artificial Intelligence and Law, 4:331--368, 1996.
• 13: H. Prakken and G. Sartor. Modelling reasoning with precedents in a formal dialogue game. Artificial Intelligence and Law, 6:231--287, 1998.
• 14: H. Prakken and G. Vreeswijk. Logics for defeasible argumentation. In D. Gabbay and F. Günthner, editors, Handbook of Philosophical Logic, volume 4, pages 219--318. Kluwer Academic Publishers, Dordrecht/Boston/London, second edition, 2002.
• 15: B. Verheij. Accrual of arguments in defeasible argumentation. In Proceedings of the Second Dutch/German Workshop on Nonmonotonic Reasoning, pages 217--224, Utrecht, 1995.
• 16: B. Verheij. Rules, reasons, arguments: formal studies of argumentation and defeat. Doctoral dissertation University of Maastricht, 1996.
• 17: B. Verheij, J. Hage, and H. van der Herik. An integrated view on rules and principles. Artificial Intelligence and Law, 6:3--26, 1998.
• 18: G. Vreeswijk. Argumentation in Bayesian belief networks. In I. Rahwan, P. Moraitis, and C. Reed, editors, Argumentation in Multi-Agent Systems, number 3366 in Springer Lecture Notes in AI, pages 111--129. Springer Verlag, Berlin, 2005.