Neurons in prefrontal cortex (PFC) encode rules, goals, and other abstract information thought to underlie cognitive, emotional, and behavioral flexibility. Here we show that the amygdala, a brain area traditionally thought to mediate emotions, also encodes abstract information that could underlie this flexibility. Monkeys performed a task in which stimulus-reinforcement contingencies varied between two sets of associations, each defining a context. Reinforcement prediction required identifying a stimulus and knowing the current context. Behavioral evidence indicated that monkeys utilized this information to perform inference and adjust their behavior. Neural representations in both amygdala and PFC reflected the linked sets of associations implicitly defining each context, a process requiring a level of abstraction characteristic of cognitive operations. Surprisingly, when errors were made, the context signal weakened substantially in the amygdala. These data emphasize the importance of maintaining abstract cognitive information in the amygdala to support flexible behavior. Saez et al. study mechanisms in the amygdala and pre-frontal cortex relevant to the cognitive regulation of emotion. Surprisingly, they report that the encoding of abstract cognitive information by the amygdala, more than pre-frontal cortex, correlates with accurate reinforcement prediction.