Dialogical generalisations of formal logic-based argumentation are typically restricted to a limited set of locutions e.g., assert, why, claim or prefer. However, the use of enthymemes (i.e., arguments with incomplete logical structure) warrant extending this set of locutions. This paper formalises the use of additional novel locutions that account for the use of enthymemes and are typical of real world dialogues. We thus close the gap between formal logic-based models of dialogue and the kinds of dialogue studied by the informal logic community, which focus on more human-oriented models of dialogue. This is important if formal models of dialogues are to provide normative support for human-human debate, as well as for enabling computational and human agents to jointly reason via dialogue.