In this paper, we present a dynamic epistemic logic suitable for resource-bounded agents. It is informed by empirical evidence on deductive reasoning performance and it therefore avoids the problem of logical omniscience. In particular, we introduce actions capturing how the agent learns, forgets, and applies inference rules. This is achieved due to our model, a variant of Kripke models extended with impossible worlds, and its updates, which modify its components (epistemic accessibility, rule availability, cognitive capacity) according to each action's effect. We further provide a sound and complete axiomatization, through a method connecting this semantic approach to logical omniscience with more syntactically-oriented ones. We finally use similar tools to model moderate introspective ability and thus avoid the unrealistic commitment to unbounded introspection.