Reduction-Based Approaches to Implement Modgil’s Extended Argumentation Frameworks

This paper reconsiders Modgil’s Extended Argumentation Frameworks (EAFs) that extend Dung’s abstract argumentation frameworks by attacks on attacks. This allows to encode preferences directly in the framework and thus also to reason about the preferences themselves. As a first step to reduction-based approaches to implement EAFs, we give an alternative (but equivalent) characterization of acceptance in EAFs. Then we use this characterization to provide EAF encodings for answer set programming and propositional logic. Moreover, we address an open complexity question and the expressiveness of EAFs.