Whereas formal mathematical theories are well studied, computers cannot yet adequately represent and reason about mathematical dialogues and other informal texts. To address this gap, we have developed a representation and reasoning strategy that draws on contemporary argumentation theory and classic AI techniques for representing and querying narratives and dialogues. In order to make the structures that these modelling tools produce accessible to computational reasoning, we encode representations in a higher-order nested semantic network. This system, for which we have developed a preliminary prototype in LISP, can represent both the content of what people say, and the dynamic reasoning steps that move from one step to the next.