 Anyone who allows for the existence of both full and partial belief inherits a thorny problem: how are full beliefs related to partial beliefs? That seemingly innocent question leads to a treacherous search for  bridge principles connecting a rational agent’s partial beliefs with her full beliefs. Theorists engaged in the search for bridge principles usually take for granted some set of rationality principles governing full belief and its revision, e.g. AGM theory, or a rival system of non-monotonic reasoning. Theorists usually also take for granted that partial belief ought to be representable by probability functions obeying some flavor of Bayesian rationality. The challenge is to propose additional rationality postulates governing how a rational agent’s partial beliefs cohere with her full beliefs. In this section, we will for the most part accept received wisdom and assume that orthodox Bayesianism is the correct model of partial belief and its updating. We will be more open-minded about the modeling of full belief and its rational revision. 