On Epistemic Logic and Logical Omniscience

We consider the logical omniscience problem of epistemic logic. We argue that the problem is due to the way in which knowledge and belief are captured in Hintikka's possible worlds semantics. We describe an alternative approach in which propositions are sets of worlds, and knowledge and belief are simply a list of propositions for each agent. The problem of the circularity in the definition is solved by giving a constructive definition of belief and knowledge worlds. We show how to incorporate notions such as reasoning and context of use in our model. We also demonstrate the power of our approach by showing how we can emulate in it other epistemic models.