an analysis of similarities and differences between the extension and labeling–based semantics in the context of produced extensions.

The paper is structured as follows. In Sections \[sec:dungintro\] to \[sec:adf\] we provide a background on argumentation frameworks. Then we introduce the new extension–based semantics and analyze their behavior in Section \[sec:sem\]. We close the paper with a comparison between the new concepts and the existing labeling–based approach.

Dung’s Argumentation Frameworks {#sec:dungintro}
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Let us recall the abstract argumentation framework by Dung [@article:dung] and its semantics. For more details we refer the reader to [@article:semintro].

A **Dung’s abstract argumentation framework** (AF for short) is a pair $(A, R)$, where $A$ is a set of arguments and $R \subseteq A \times A$ represents an attack relation.

Let $AF = (A, R)$ be a Dung’s framework. We say that an argument $a \in A$ is **defended**[^2] by a set $E$ in $AF$, if for each $b \in A$ s.t. $(b, a)\in R$, there exists $c \in E$ s.t. $(c, b)\in R$. A set $E \subseteq A$ is:

-   **conflict–free** in $AF$ iff for each $a, b \in E,\, (a,b) \notin R$.

-   **admissible** iff conflict–free and defends all of its members.

-   **preferred** iff 