Necessary Support

Under the necessary support interpretation of a BAF $B = (A, R, S)$, an argument $a$ supports an argument $b$ if the acceptance of $a$ is a necessary condition for the acceptance of $b$.

Remarks

Given a semantics $\sigma$, the necessary $\sigma$-extensions ($\mathsf{b}\text{-}\mathsf{nec}\text{-}\sigma$) of $B$ are the deductive $\sigma$-extensions of $(A, R, S^{-1})$, i.e. with all supports reversed.