Extension semantics are formal methods that evaluate acceptability status of arguments in argumentation graphs where arguments may attack each other. Understanding and explaining their outcomes is of utmost importance in applications like decision making. Consequently, a plethora of works has been devoted to answer questions of the form "why an argument A is (not) accepted under semantics δ". Existing approaches explain the inner working and decision logic of δ. Their explanations refer thus to the semantics's building blocks like attack, defence and admissibility.

This paper complements the existing landscape with a post-hoc approach that discloses relationships between argumentation graphs and outputs of a semantics, regardless of its internals. The new approach offers several advantages, namely it explains more acceptability statuses than just the two (accepted, not accepted) considered in the literature, treats all statuses in a similar way, applies to any extension semantics that satisfies two key properties (monotonicity and maximality), and provides subsets of attackers, thus the size of its explanations is bounded by the number of attackers of an argument. We characterize the types of attacks that may target an argument. We show that some have no impact on their target's status while others are influential. Then, we introduce three explanation functions that harness influential attacks. One of them provides sufficient reasons that guarantee an argument's status while the others identify changes in the graph that guarantee a change of status to any value (counterfactuals) or to a specified one (contrastive). We show that sufficient reasons are minimal hitting sets of the counterfactuals and vice-versa.