Developments in computing, in multi-agent systems, and in artificial intelligence generally, are at the stage where an applied logic of argumentation would be extremely useful. The problem of finding a method for identifying, analyzing, and evaluating criticisms of irrelevance has not yet been solved. But the cases studied so far have already yielded many components o f such a method. In many o f these cases, fairly good reasons can be given forjudging an argument to be relevant or irrelevant. Yet some cases are open to dispute. In such cases, the proponent will claim that her argument is relevant even if the respondent has criticized it as irrelevant. What sort of evidence could be used to back up reasons for judging an argument to be relevant or irrelevant? What is needed is a comprehensive method that can collect, display, and process such evidence systematically. Such a method is put forward in chapter 6.