We argue that to reflect participant interactivity in conversational dialogue, the Christiansen & Chater (C&C) perspective needs a formal grammar framework capturing word-by-word incrementality, as in Dynamic Syntax, in which syntax is the incremental building of semantic representations reflecting real-time parsing dynamics. We demonstrate that, with such formulation, syntactic, semantic, and morpho-syntactic dependencies are all analysable as grounded in their potential for interaction.