Epistemic Logic for AI and Computer Science, Cambridge Tracts in Computer Science No. 41
Meyer, J.J.C. Hoek, W.V.D.
Epistemic logic has grown from its philosophical beginnings to find diverse applications in computer science as a means of reasoning about the knowledge and belief of agents. This book, based on courses taught at universities and summer schools, provides a broad introduction to the subject; many exercises are included together with their solutions. The authors begin by presenting the necessary apparatus from mathematics and logic, including Kripke semantics and the well-known modal logics K, T, S4 and S5. Then they turn to applications in the contexts of distributed systems and artificial intelligence: topics that are addressed include the notions of common knowledge, distributed knowledge, explicit and implicit belief, the interplays between knowledge and time, and knowledge and action, as well as a graded (or numerical) variant of the epistemic operators. The problem of logical omniscience is also discussed extensively. Halpern and Moses theory of honest formulae is covered, and a digression is made into the realm of non-monotonic reasoning and preferential entailment. Moores autoepistemic logic is discussed, together with Levesques related logic of all I know.