Logical Omniscience vs. Logical Ignorance

We propose in the paper a new solution to the so-called Logical Omniscience Problem of epistemic logic. Almost all attempts in the literature to solve this problem consist in weakening the standard epistemic systems: weaker sytems are considered where the agents do not possess the full reasoning capacities of an ideal reasoner. We shall argue that this solution is not satisfactory: in this way omniscience can be avoided, but many intuitions about the concepts of knowledge and belief get lost. We shall show that axioms for epistemic logics must have the following form: if the agent knows all premises of a valid inference rule, and if she thinks hard enough, then she will know the conclusion. To formalize such an idea, we propose to "temporalize" epistemic logic, that is, to introduce a temporal component into the language. We develop a logic based on this idea and show that it is suitable for formalizing the notion of explicit belief