Application of personality type to chat bot interface

One of the growing trends in UX design is the emergence of conversational UI (there's probably too many articles to provide a comprehensive list here, but please feel free to provide as a comment your favourite), and there is no question about the importance of UX design when it comes to crafting the right experience (not just about the technical implementation details like the AI).

Given that there is so much emphasis on different personality types (e.g. Myers Brigg Test, introvert vs. extrovert, etc.) in general conversation and how we communicate with each other, I am interested to know whether there are research on how to incorporate insights from personality research to chat bot interfaces and conversational UI design in general.

UPDATE: Since this question was last asked, a lot more chat bots have surfaced online. I would be interested in examples of documented chat bot interface designs by the companies included in design systems or style guides.