$c\in A$, if $c R a$ then for every coherent set $C\subseteq A$ containing $c$, $B R C$.

Using the notion of strong coherence and defense, the AFN semantics are built in a way corresponding to Dung semantics. It is easy to see that, through the notion of coherency, AFNs discard cyclic arguments both on the “inside” and the “outside”. This means we cannot accept them in an extension and they are not considered as valid attackers.

The last type of support we will consider here is the the *evidential support* [@inproc:eas]. It distinguishes between standard and *prima facie* arguments. The latter are the only ones that are valid without any support. Every other argument that we want to accept needs to be supported by at least one prima facie argument, be it directly or not.

An **evidential argumentation system** (EAS) is a tuple $(A, R, E)$ where $A$ is a set of **arguments**, $R \subseteq (2^A \setminus \emptyset) \times A$ is the **attack** relation, and $E \subseteq (2^A \setminus \emptyset) \times A$ is the **support** relation. We distinguish a special argument $\eta \in A$ s.t. $\nexists (x,y) \in R$ where $\eta \in x$; and $\nexists x$ where $(x, \eta) 