Optimisation and Approximation in Abstract Argumentation: The Case of Admissibility

We propose two soft notions of the notion of admissibility in abstract argumentation. The first one weakens the defence notion by allowing, to a certain degree, undefended attacks, and the second one allows, to a certain degree, conflicts within sets of arguments. We analyse these new semantical notions based on the computational complexity of optimisation and approximation. Finally, we discuss and analyse soft notions for preferred semantics.