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Evaluating Abstract Dialectical Frameworks with ASP

A widespread modeling language for abstract argumentation is the argumentation framework due to Dung [1]. However relating arguments in this framework is solely based on the notion of direct binary attacks. More sophisticated relations require auxiliary structures tailored to the chosen semantics. We present a system called ADFsys based on the more general abstract dialectical frameworks (ADFs) [2] to overcome this technical necessity. The idea of ADFs is to apply the expressiveness of propositional logic to represent relations between arguments and hence generalize argumentation frameworks. Each argument comes with an acceptance condition, which states when it can be accepted. This condition refers to the status of the other arguments. Figure 1 shows an example ADF, where the argument a can only be accepted if not both b and d are accepted. The arrows represent dependencies between the arguments.