Skeptical Acceptance

Given a semantics $\sigma$, an argument $a \in A$ is skeptically accepted iff $a \in E$ for every $\sigma$-extension $E \in \sigma(F)$, i.e. $a \in \mathsf{skep}_\sigma(F) = \bigcap \sigma(F)$.

Remarks

If $\sigma(F) = \emptyset$, every argument is skeptically accepted (Dvořák & Dunne, 2018).

The associated decision problem is $\textsc{Skept}_\sigma$.