Bipolar ADF (BADF)

An ADF is bipolar iff each of its links is supporting or attacking. A link $(b, a) \in L$ is supporting iff for all $R \subseteq$ $par(a)$, $C_a$$(R) = \mathsf{t}$ implies $C_a(R \cup \{b\}) = \mathsf{t}$, and attacking iff for all $R \subseteq par(a)$, $C_a(R \cup \{b\}) = \mathsf{t}$ implies $C_a(R) = \mathsf{t}$.

Link types

A link that is both supporting and attacking (called redundant) has no influence on its target and can be deleted (Brewka & Woltran, 2010).

Complexity results for bipolar ADFs assume that the supporting links $L^+$ and the attacking links $L^-$ are given with the ADF, i.e. the link types are known (Strass & Wallner, 2015). Recognising bipolarity is itself coNP-hard, and deciding the type of a single link is intractable as well (Brewka & Woltran, 2010).