Abstract : 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. This paper is the extended version of the paper presented at the 11th International Conference on Computational Models of Natural Argument (CMNA 2013), 14 June 2013, Rome, Italy. It reports on the initial steps of a project on argument mining from dialogue. Note that since then the corpus size and the annotation scheme have evolved, however, the method presented here is still valid and the project has developed accordingly.