Formal argumentation based dialogue models have attracted some research interests
recently. Within this line of research, we propose a formal model for
argumentation-based dialogues between agents, using assumption-based argumentation
(ABA). Thus, the dialogues amount to conducting an argumentation process
in ABA. The model is given in terms of ABA-specific utterances, debate trees
and forests implicitly built during and drawn from dialogues, legal-move functions
(amounting to protocols) and outcome functions. Moreover, we investigate
the strategic behaviour of agents in dialogues, using strategy-move functions. We
instantiate our dialogue model in a range of dialogue types studied in the literature,
including information-seeking, inquiry, persuasion, conflict resolution, and
discovery. Finally, we prove (1) a formal connection between dialogues and well-known
argumentation semantics, and (2) soundness and completeness results for
our dialogue models and dialogue strategies used in different dialogue types.