\[above of= b, yshift=-0.8cm\] [$a \land c$]{}; (cc) \[above of= c, yshift=-0.8cm\] [$\bot$]{}; (cd) \[above of= d, yshift=-0.8cm\] [$d$]{};

(a.east)–(b.west); (c.west)–(b.east); (d.east)–(a.west); (d) edge \[loop left\] node (d);

Let $(\{a,b,c,d\}, \{ \varphi_a: b\rightarrow d, \varphi_b:  a\land c, \varphi_c: \bot, \varphi_d:d\})$ be an ADF depicted in Figure \[fig:dec\]. Example of a decisively in interpretation for $a$ is $v=\{b: {\mathbf{f}}\}$. It simply means that knowing that $b$ is false, not matter the value of $d$, the implication is always true and thus the acceptance condition satisfied. From the more technical side, it is the same as checking that both completions to $\{b,d\}$, namely $\{b:{\mathbf{f}}, d:{\mathbf{t}}\}$ and $\{b:{\mathbf{f}}, d:{\mathbf{f}}\}$ satisfy the condition. Example of a decisively out interpretation for $b$ is $v'=\{c: {\mathbf{f}}\}$. Again, it suffices to falsify one element of a conjunction to know that the whole formula will evaluate to false.

Acyclicity
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Let us now focus on the issue of positive dependency cycles. Please note we refrain from calling them support cycles in the ADF setting in order not to confuse them with specific definitions of support available in the literature [@article:newbaf].

Informally speaking, an argument takes part in a cycle if its acceptance depends on itself. An intuitive way 