In this paper we ask whether approximation for abstract argumentation is useful in practice, and in particular whether reasoning with grounded semantics – which has polynomial runtime – is already an approximation approach sufficient for several practical purposes. While it is clear from theoretical results that reasoning with grounded semantics is different from, for example, skeptical reasoning with preferred semantics, we investigate how significant this difference is in actual argumentation frameworks. As it turns out, in many graphs models, reasoning with (...) grounded semantics actually approximates reasoning with other semantics almost perfectly. An algorithm for grounded reasoning is thus a conceptually simple approximation algorithm that not only does not need a learning phase – like recent approaches – but also approximates well – in practice – several decision problems associated to other semantics. (shrink)

The concept of strong admissibility plays an important role in dialectical proof procedures for grounded semantics allowing, as it does, concise proofs that an argument belongs to the grounded extension without having necessarily to construct this extension in full. One consequence of this property is that strong admissibility ceases to be a unique status semantics. In fact it is straightforward to construct examples for which the number of distinct strongly admissible sets is exponential in the number of arguments. We are (...) interested in characterizing properties of collections of strongly admissible sets in the sense that any system describing the strongly admissible sets of an argument framework must satisfy particular criteria. In terms of previous studies, our concern is the signature and with conditions ensuring realizability. The principal result is to demonstrate that a system of sets describes the strongly admissible sets of some framework if and only if that system has the property of being decomposable. (shrink)