E$. If a semantics $\sigma$ returns more than one extension, the choice function $g^{\cup} \circ \sigma (AF) = \bigcup_{E \in \sigma(AF)} E$ returns the union of the set of extensions returned by $\sigma$. We call such a function a *lenient* choice function.

2.  $g^{\cap} \circ \sigma(AF) = \bigcap_{E \in \sigma(AF) E}$. If a semantics $\sigma$ returns more than one extension the choice function $g^{\cap} \circ \sigma (AF) = \bigcap_{E \in \sigma(AF)} E$ returns the intersection of the set of extensions returned by $\sigma$. We call such a function a *skeptical* choice function.

However, for the purpose of evaluating argumentation semantics, it makes sense to define the aggregation of extensions as part of the semantics itself, for example as follows:

1.  $g^{i} \circ \sigma^{\cup}_{stage}(AF)$ returns the lenient stage extension of $AF$.

2.  $g^{i} \circ \sigma^{\cap}_{stage}(AF)$ returns the skeptical stage extension of $AF$.

3.  $g^{i} \circ \sigma^{\cap}{grounded}(AF)$ and $g^{i} \circ \sigma^{\cup}{grounded}(AF)$ return the grounded extension of $AF$. There is always exactly one grounded extension, from which it follows that $g^{i} \circ \sigma^{\cap}{grounded}(AF) = g^{i} \circ \sigma^{\cup}{grounded}(AF)$. The same applies to ideal and eager semantics.

For this, we characterize $g^{i}$ as the identity function: $$\begin{aligned}
    g^{i} \circ \sigma(AF) = \sigma(AF)\end{aligned}$$

It is important 