This paper extends the Argument Interchange Format to enable it to represent dialogic argumentation. One of the challenges is to tie together the rules expressed in dialogue protocols with the inferential relations between premises and conclusions. The extensions are founded upon two important analogies which minimise the extra ontological machinery required. First, locutions in a dialogue are analogous to AIF I-nodes which capture propositional data. Second, steps between locutions are analogous to AIF S-nodes which capture inferential movement. This paper shows how these two analogies combine to allow both dialogue protocols and dialogue histories to be represented alongside monologic arguments in a single coherent system.