 A significant feature of modal logics in general (and this includes modal probabilistic logic) is the ability to support higher-order reasoning, that is, the reasoning about probabilities of probabilities. The importance of higher-order probabilities is clear from the role they play in, for example, Miller’s principle, which states that \(P_1(\phi\mid P_2(\phi) = b) = b\). Here, \(P_1\) and \(P_2\) are probability functions, which can have various interpretations, such as the probabilities of two agents, logical and statistical probability, or the probabilities of one agent at different moments in time (Miller 1966; Lewis 1980; van Fraassen 1984; Halpern 1991). Higher-order probability also occurs for instance in the Judy Benjamin Problem (van Fraassen 1981a) where one conditionalizes on probabilistic information. Whether one agrees with the principles proposed in the literature on higher-order probabilities or not, the ability to represent them forces one to investigate the principles governing them.