Splitting

A semantics $\sigma$ satisfies Splitting iff for every splitting $(F_1, F_2, R_3)$ of $F$ (no attacks from $F_2$ into $F_1$ ), the extensions of $F$ are exactly the sets $E_1 \cup E_2$ with $E_1 \in \sigma(F_1)$ and $E_2$ an extension of $F_2$ after removing what $E_1$ attacks.

Reference

Dvořák, W., Ulbricht, M. & Woltran, S. (2022). Recursion in Abstract Argumentation is Hard — On the Complexity of Semantics Based on Weak Admissibility. Journal of Artificial Intelligence Research, 74, pp. 1403–1447.