Although reasoning about what is the case has been the historic focus of logic, reasoning about what should be done is an equally important capacity for an intelligent agent. Reasoning about what to do in a given situation- termed practical reasoning in the philosophical literature- has important differences from reasoning about what is the case. The acceptability of an argument for an action turns not only on what is true in the situation, but also on the values and aspirations of the agent to whom the argument is directed. There are three distinctive features of practical reasoning: first, that practical reasoning is situated in a context, directed towards a particular agent at a particular time; second, that since agents differ in their aspirations there is no right answer for all agents, and rational disagreement is always possible; third, that since no agent can specify the relative priority of its aspirations outside of a particular context, such prioritisation must be a product of practical reasoning and cannot be used as an input to it. In this paper we present a framework for practical reasoning which accommodates these three distinctive features.

One difficulty that arises in abstract argument systems is that many natural questions regarding argument acceptability are, in general, computationally intractable having been classified as complete for classes such as NP, co-NP, and  ¢¡ £. In consequence, a number of researchers have considered methods for specialising the structure of such systems so as to identify classes for which efficient decision processes exist. In this paper the effect of a number of graph-theoretic restrictions is considered: ¤-partite systems (¤¦¥¨ § ) in which the set of arguments may be partitioned into ¤ sets each of which is conflict-free; systems in which the numbers of attacks originating from and made upon any argument are bounded; planar systems; and, finally, those of ¤-bounded treewidth. For the class of bipartite graphs, it is shown that determining the acceptability status of a specific argument can be accomplished in polynomial-time under both credulous and sceptical semantics. In addition we establish the existence of polynomial time methods for systems having bounded treewidth when deciding the following: whether a given (set of) arguments is credulously accepted; if the system has a non-empty preferred extension; has a stable extension; is coherent;

Two--Party Immediate Response Disputes (TPI-disputes) are a dialogue game formalism providing a sound and complete proof scheme for credulous reasoning in argument systems.