The study of argumentation has recently received a lot of interest in the areas of Artificial Intelligence and Knowledge Representation with abstract argumentation frameworks due to Dung being its most successful formalization. Although such frameworks are of a relatively simple structure, reasoning in such frameworks is in general intractable. Thus tractable fragments have to be identified. One promising direction for this challenge is to apply methods from the area of parameterized complexity, in particular fixed-parameter tractability.
In this talk, we first give a brief motivation to the field and then present several of the semantics proposed for argumentation frameworks. We highlight some of the complexity results from the literature and then move over to fixed-parameter tractability results. To put such results to practice, dynamic algorithms have to be designed and we sketch their functioning when parameters such as tree-width or clique-width are employed.