Complete Semantics

A set E⊆AE \subseteq A is a complete extension iff EE is admissible and for every argument a∈Aa \in A defended by EE, we have a∈Ea \in E.

Signature

An exact characterisation of sig(co)\mathsf{sig}(\mathsf{co}) is open. Every S∈sig(co)\mathbb{S} \in \mathsf{sig}(\mathsf{co}) has S≠∅\mathbb{S} \neq \emptyset, is com-closed and contains ⋂S∈SS\bigcap_{S \in \mathbb{S}} S, but not every such S\mathbb{S} is in sig(co)\mathsf{sig}(\mathsf{co}) (Dunne et al., 2015).

Reference

Dung, P.M. (1995). On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games. Artificial Intelligence, 77(2), pp. 321–357.

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