Illocutionary structure in real language use is intricate and complex, and nowhere more so than in argument and debate. Identifying this structure without any theoretical scaffolding is extremely challenging even for humans. New work in Inference Anchoring Theory has provided significant advances in such scaffolding which are helping to allow the analytical challenges of argumentation structure to be tackled. This paper demonstrates how these advances can also pave the way to automated and semi-automated research in understanding the structure of natural debate.