an interpretation $v'$ defined on $Z$ in a way that $\forall a \in A \; v(a) = v'(a)$. By a ${\mathbf{t}}/{\mathbf{f}}$ completion we will understand $v'$ that maps all arguments in $Z\setminus A$ respectively to ${\mathbf{t}}/{\mathbf{f}}$.

The similarity between the concepts of completion and extending interpretation should not be overlooked. Basically, given a three–valued interpretation $v$ defined over $S$, the set $\lbrack v \rbrack_2$ precisely corresponds to the set of completions to $S$ of the two–valued part of $v$. However, the extension notion from the three–valued setting can be very misleading when used in the extension–based semantics. Therefore, we would like to keep the notion of completion.

We say that a two–valued interpretation $v$ is **decisive** for an argument $s \in S$ iff for any two completions $v_{par(s)}$ and $v'_{par(s)}$ of $v$ to $A \cup par(s)$, it holds that $v_{par(s)}(C_s) =v'_{par(s)}(C_s)$. We say that $s$ is **decisively out/in** wrt $v$ if $v$ is decisive and all of its completions evaluate $C_s$ to respectively $out,in$.

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