We consider an alternative interpretation of classical Dung argumentation framework (af) semantics by introducing the concept of “forbidden sets”. In informal terms, such sets are well-defined with respect to any extension-based semantics and reflect those subsets of argument that collectively can never form part of an acceptable solution. The forbidden set paradigm thus provides a parametric treatment of extension-based semantics. We present some general properties of forbidden set structures and describe the interaction between forbidden sets for a number of classical semantics. Finally we establish some initial complexity results in the arena of forbidden set decision problems.