Representing the semantics of abstract dialectical frameworks based on arguments and attacks

Abstract dialectical frameworks have been proposed as a generalization of the abstract argumentation frameworks. The semantics of abstract dialectical frameworks is defined by identifying different classes of models. In this paper, we show that the semantics of abstract dialectical frameworks could naturally be defined based on simple notions of arguments and attacks like in abstract argumentation. This insight allows us to adapt directly the semantical concepts in abstract argumentation to abstract dialectical frameworks that not only capture the standard semantics of abstract dialectical frameworks, but also suggest other new semantics based on the idea of “rejection as assumption” (raa) (similar to the concept of “negation as assumption” in assumption-based argumentation and logic programming) like the well-founded semantics or the raa-preferential semantics.

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