We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a formal reasoning framework capable of handling diverse discussion and argumentation models. Second, we generalise Dung’s notion of extensions to cases where two or more graph nodes in an argumentation framework are equivalent. Third, we connect these two contributions by showing that the generalised extensions are first-order characterisable within the proposed discussion-graph semantics. Propositional characterisability of all Dung’s extensions is an immediate consequence.