a set $T\subseteq A$ against $a$, it is the case that $S$ carries out an e–supported attack against a member of $T$.

The notion of conflict–freeness is easily adapted to take set, not just binary conflict into account. With this and the notion of acceptability, the EASs semantics are built just like AF semantics. From the fact that every valid argument needs to be grounded in the environment it clearly results that EAS semantics are acyclic both on the inside and outside.

Abstract Dialectical Frameworks {#sec:adf}
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Abstract dialectical frameworks have been defined in [@inproc:adf] and further studied in [@tofix:newadf; @inproc:adm; @report:strass; @strass13instantiating; @strass-wallner14complexity]. The main goal of ADFs is to be able to express arbitrary relations and avoid the need of extending AFs by new relation sets each time they are needed. This is achieved by the means of the acceptance conditions, which define what arguments should be present in order to accept or reject a given argument.

An **abstract dialectical framework** (ADF) as a tuple $(S, L, C)$, where $S$ is a set of abstract **arguments** (nodes, statements), $L \subseteq S \times S$ is a set of **links** (edges) and $C = \{C_ s \}_{s\in S}$ is a 