the presence of $c$ also “forces” a cycle between $a$ and $b$. The acceptance conditions of all arguments are satisfied, thus this simple check is not good enough to verify if a cycle occurs. Only looking at the whole evaluations shows us that $a$ and $b$ are both blocked by $c$. Although $a$ and $b$ are pd–acyclic in $E$, we see that their evaluations are in fact blocked and this second level of conflict needs to be taken into account by the semantics.

\[-&gt;,&gt;=stealth,shorten &gt;=1pt,auto,node distance=1.5cm, thick,main node/.style=[circle,fill=none,draw,minimum size = 0.7cm,font=****]{}, condition/.style=[circle,fill=none,draw=none,minimum size = 0.3cm,font=****]{}\]

\(a) [$a$]{}; (b) \[left of=a\] [$b$]{}; (c) \[right of=a\] [$c$]{};

(ca) \[above of= a, yshift=-0.8cm\] [$\neg c \lor b$]{}; (cb) \[above of= b, yshift=-0.8cm\] [$a$]{}; (cc) \[above of= c, yshift=-0.8cm\] [$c$]{};

\(a) edge \[bend left\] node (b) (b) edge \[bend left\] node (a) (c) edge node (a) (c) edge \[loop right\] node (c);

\[ex:cf\]

As a final remark, please note that it can be the case that an evaluation is self–blocking. We can now proceed to recall existing and introduce new semantics of the abstract dialectical frameworks.

Extension–Based Semantics of ADFs {#sec:sem}
=================================

Although various semantics for ADFs have already been defined in the original 