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9 A.I. & L. 1 (2001)

handle is hein.journals/artinl9 and id is 1 raw text is: Artificial Intelligence and Law 9: 1-28, 2001. # © 2001 Kluwer Academic Publishers. Printed in the Netherlands. Argument construction and reinstatement in logics for defeasible reasoning JOHN F. HORTY Philosophy Department and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, U.S.A. E-mail: horty@umiacs.umd.edu, www.umiacs.umd.edu/users/horty Abstract. This paper points out some problems with two recent logical systems - one due to Prakken and Sartor, the other due to Kowalski and Toni - designed for the representation of defeasible arguments in general, but with a special emphasis on legal reasoning. 1. Introduction In recent years, researchers in nonmonotonic logic have turned increasing atten- tion to formal systems in which nonmonotonic reasoning is analyzed through the study of interactions among competing defeasible arguments; a survey appears in Prakken and Vreewsijk (forthcoming). These argument systems are promising for several reasons. First, they often allow a more natural treatment of priorities among conflicting defeasible rules than the standard fixed-point or model-preference ap- proaches, such as default logic or circumscription. Second, the explicit emphasis on the manipulation and comparison of arguments - finite syntactic entities - sug- gests immediate implementational possibilities; these systems are often developed within the logic programming paradigm. Finally, the formal study of relations among conflicting arguments is particularly important for the application of tech- niques from artificial intelligence to fields in which adversarial reasoning figures prominently, such as negotiation or, of course, the law. I focus in this paper on two recent argument systems, both of which are heavily indebted to the work of Dung (1995) and Bondarenko et al. (1997). The first of these systems is due to Prakken and Sartor, with an initial proposal appearing in Prakken and Sartor (1996) and more elaborate developments in Prakken and Sartor (1996, 1997). This system, which will be referred to as the PS logic, extends the standard language of logic programming with strong negation and a connective representing defeasible implication; it allows for reasoning with prioritized defeas- ible rules and also for reasoning about the priorities themselves that govern these rules. The system has been provided with a fixed-point semantics, as well as a proof theory in the form of a dialogue game, intended to model the structure

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