such interpretation can be found.

An **acyclic positive dependency evaluation** $ace^a$ for $a \in A$ based on a given pd–function $pd$ is a pair $((a_0,...,a_n), B)$, [^5] where $B = \bigcup_{i=0}^n \, pd(a_i)^{{\mathbf{f}}}$ and $(a_0,...,a_n)$ is a sequence of distinct elements of $A$ s.t.:

$\forall_{i=0}^n \, pd(a_i) \neq \mathcal{N}$,

$a_n = a$,

$pd(a_0)^{\mathbf{t}}= \emptyset$, and

$\forall_{i=1}^n, \, pd(a_i)^{{\mathbf{t}}} \subseteq \{a_0,...,a_{i-1}\}$.

We will refer to the sequence part of the evaluation as **pd–sequence** and to the $B$ as the **blocking set**. We will say that an argument $a$ is **pd–acyclic** in $A$ iff there exist a pd–function on $A$ and a corresponding acyclic pd–evaluation for $a$.

We will write that an argument has an acyclic pd–evaluation on $A$ if there is some pd–function on $A$ from which we can produce the evaluation. There are two ways we can “attack” an acyclic evaluation. We can either discard an argument required by the evaluation or accept one that is capable of preventing it. This corresponds to rejecting a member of a pd–sequence or accepting an argument from the blocking set. We can now formulate this “conflict” by the means of an interpretation:

Let $A\subseteq S$ be a set of arguments and $a \in 