(i.e. $a S...S c$) and $c R b$. We say that $a$ **secondary attacks** $b$ if there is some argument $c$ s.t. $c S...S b$ and $a R c$. We say that $B\subseteq A$ is:

-   **+conflict–free** iff $\nexists a, b \in B$ s.t. $a$ (directly or indirectly) attacks $b$.

-   **safe** iff $\nexists b\in A$ s.t. $b$ is at the same time (directly or indirectly) attacked by $B$ and either there is a sequence of supports from an element of $B$ to $b$, or $b \in B$.

-   **closed under $S$** iff $\forall b\in B, a \in A$, if $bSa$ then $a\in B$.

The definition of defense remains the same and any Dung semantics is specialized by choosing an given notion of conflict–freeness or safety. Apart from the stable semantics, no assumptions as to cycles occurring in the support relation are made. The later developed deductive support [@inproc:support] remains in the BAF setting and is also modeled by new indirect attacks [@article:newbaf]. Consequently, acyclicity is not required. The most recent formulation of the framework with necessary support is as follows [@incoll:newafn]:

An **argumentation framework with necessities** is a tuple $(A, R, N)$, where $A$ is the set of **arguments**, 