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We propose 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 systems are considered where the agents do not possess the full reasoning capacities of ideal reasoners. 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 are lost. We shall show that axioms for epistemic logics must have the following form: if the agent knows all premisses 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 ‘dynamize’ epistemic logic, that is, to introduce a dynamic component into the language. We develop a logic based on this idea and show that it is suitable for formalizing the notion of actual, or explicit knowledge.

Reasoning about Rational, but not Logically Omniscient, Agents