Helplessness, a belief that the world is not subject to behavioral control, has long been central to our understanding of depression, and has influenced cognitive theories, animal models and behavioral treatments. However, despite its importance, there is no fully accepted definition of helplessness or behavioral control in psychology or psychiatry, and the formal treatments in engineering appear to capture only limited aspects of the intuitive concepts. Here, we formalize controllability in terms of characteristics of prior distributions over affectively charged environments. We explore the relevance of this notion of control to reinforcement learning methods of optimising behavior in such environments and consider how apparently maladaptive beliefs can result from normative inference processes. These results are discussed with reference to depression and animal models thereof. (Contains 8 figures.)