Two party immediate response disputes: Properties and efficiency

Two Party Immediate Response Disputes (TPI-disputes) are one class of dialogue or argument game in which the protagonists take turns producing counter arguments to the ‘most recent’ argument advanced by their opponent. Argument games have been found useful as a means of modelling dialectical discourse and in providing semantic bases for proof theoretic aspects of reasoning. In this article we consider a formalisation of TPI-disputes in the context of finite Argument Systems. Our principal concern may, informally, be phrased as follows: given a specific argument system, H and argument, x withinH, what can be stated concerning the number of rounds a dispute might take for one of its protagonists to accept that x has some defence respectively cannot be defended?