This paper builds upon the proposed dialogical extensions to the AIF, termed AIF+, by making explicit the representation of the role of illocutionary force in the connection between argument structures and dialogical structures. Illocutionary force is realised in the form of Illocutionary Application (YA-) nodes that provide an explicit linkage between the locutions uttered during a dialogue and the underlying arguments expressed by the content of those locutions. This linkage is explored in the context of two contrasting dialogue games from the literature, demonstrating how the approach can support the development of computational models in which the speech-act function of communicative moves can be accounted for.