Rethinking Epistemic Logic Mark Jago 1 Introduction Hintikka’s logic of knowledge and belief [8] has become a standard logical tool for dealing with intentional notions in artificial intelligence and computer science. One reason for this success is the adoption by many computer scientists of modal logics in general, as tools for reasoning about relational structures. Many areas of interest to computer scientists, from databases to the automata which underlie many programs, can be thought of as relational structures; such structures can be reasoned about using modal logics. Hintikka’s work can be seen as the start of what is known to philosophers, logicians and computer scientists as formal epistemology : that branch of epistemology which seeks to uncover the formal properties of knowledge and belief. In Reasoning About Knowledge [6], Fagin, Halpern, Moses and Vardi showed how logics based on Hintikka’s ideas can be used to solve many real-world prob- lems; these were problems about other agent’s knowledge, as well as problems in which agents reason about the world. Solutions to such problems have ap- plications in distributed computing, artificial intelligence and game theory, to name a but a few key areas. With the appearance of Reasoning About Knowl- edge, Hintikka’s approach was firmly cemented as the orthodox logical account of belief for philosophers and computer scientists alike. It is rare for an orthodox account of such popularity to receive no criticism and Hintikka’s framework is no exception. One major source of objections is the so-called problem of logical omniscience whereby, as a result of the modal semantics applied to ‘knows’ (and ‘believes’), agents automatically know every tautology as well as every logical consequence of their knowledge. Just how such a consequence should be viewed is a moot point; perhaps this notion of knowl- edge applies to ideal agents, or perhaps it is an idealised notion, saying what a non-ideal agent should believe (given what it already does believe). Although neither account is entirely satisfactory, defenders of the approach claim that, in many cases, the assumptions are harmless, and that the applications which such logics have found speak for themselves. [11] surveys logics for which logical omniscience is a problem and concludes that an alternative logic of knowledge and belief is required, if real-world agents are to be modelled with any kind of fidelity. However, my aim here is not to criticise Hintikka’s approach on the ground of logical omniscience. Instead, I show that the assumptions required by Hintikka’s approach cannot be justified by an acceptable account of belief. I concentrate throughout on the notion of belief, rather than that of knowledge, as the former is (usually) regarded as the more primitive notion; an account of knowledge will usually proceed from an account of belief. Hintikka’s logic is not in itself such 1