Conditional labelling for abstract argumentation

Agents engage in dialogues having as goals to make some arguments acceptable or unacceptable. To do so they may put forward arguments, adding them to the argumentation framework. Argumentation semantics can relate a change in the framework to the resulting extensions but it is not clear, given an argumentation framework and a desired acceptance state for a given set of arguments, which further arguments should be added in order to achieve those justification statuses. Our methodology, called conditional labelling, is based on argument labelling and assigns to each argument three propositional formulae. These formulae describe which arguments should be attacked by the agent in order to get a particular argument in, out, or undecided, respectively. Given a conditional labelling, the agents have a full knowledge about the consequences of their attacks on the acceptability of each arguments, without having to recompute the overall labelling of the framework for each possible set of attacks they may raise.