In this talk we describe a mixed Bayesian-frequentist framework for learning and knowledge acquisition about a proposition that is either true or false. We define learning as having true belief about the proposition, whereas knowledge additionally requires that this belief is justified. The set of possible states of reality are modelled as the parameter space of a statistical model. A Bayesian approach is used in order to quantify degrees of beliefs, whereas a frequentist approach is needed to tell if these beliefs are true and justified. When data is collected sequentially, this gives rise to learning and knowledge acquisition processes, and under certain conditions asymptotic results are available for these processes. The framework is illustrated with several examples; online math tests, game theory, dating of historical events and whether chat robots can acquire knowledge about moral values.