 It is often informative to see how qualitative update dynamics emerge from the finer structure of degrees of belief. We will see in this section several versions of the following kind of “representation” result: every agent satisfying a certain set of qualitative dynamical update principles can be thought of as an agent updating graded beliefs of a certain structure and, conversely, every agent with graded beliefs of that structure will satisfy the same set of qualitative dynamical principles. These results suggest bridge principles connecting full and partial representations of belief.