In this paper we consider the notion of dialogic creative artificial intelligence (DCAI) systems, where co-creativity between a human user and a computational system is supported through dialogic interaction. By dialogue we mean both traditional language-based communication for explicit critique and persuasion (dialogue about creative artefacts) as well as a broader potentially non-linguistic notion of dialogue that emerges through the exchange of suggestions and changes (dialogue through

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... ve artefacts). To capture this, we define DCAI as occurring when both system and user are able to influence each others' creative objectives. The paper motivates our pursuit of dialogic interaction and provides some explanation of why we have defined it through its impacts rather than its mechanism of action. We provide two analyses to support our argument: an exploration of a commercial creativity support tool that has an extensive vocabulary for describing artefacts abstractly but does not meet our definition of dialogic interaction, and a case study of a creative interaction between two human professionals that exhibits dialogic interaction throughout. For the latter we consider how studies of human-human co-creation can offer non-obvious design concepts that might be applied to co-creative DCAI systems.