. This paper presents dialectical proof theories for Dung's preferred semantics of defeasible argumentation. The proof theories have the form of argument games for testing membership of some (credulous reasoning) or all preferred extensions (sceptical reasoning). The credulous proof theory is for the general case, while the sceptical version is for the case where preferred semantics coincides with stable semantics. The development of these argument games is especially motivated by applications of argumentation in automated negotiation, mediation of collective discussion and decision making, and intelligent tutoring. 1 Introduction An important approach to the study of nonmonotonic reasoning is that of logics for defeasible argumentation (for an overview see [25]). Within this approach, a unifying perspective is provided by the work of [9] and [4] (below called the `BDKT framework'). It takes as input a set of arguments ordered by a binary relation of `attack', and it produces...

. This paper proposes a formal framework for argumentative dialogue systems with the possibility of counterargument. The framework allows for claiming, challenging, retracting and conceding propositions. It also allows for exchanging arguments and counterarguments for propositions, by incorporating argument games for nonmonotonic logics. A key element of the framework is a precise denition of the notion of relevance of a move, which enables exible yet well-behaved protocols. 1 Introduction In recent years, dialogue systems for argumentation have received interest in several elds of articial intelligence, such as explanation [2], AI and law [4, 6], discourse generation [5], multi-agent systems [10, 1], and intelligent tutoring [9]. These developments justify a formal study of such dialogue systems; this paper contributes to this study by an attempt to integrate two relevant developments in the elds of argumentation theory and articial intelligence. In argumentation theory...