Epistemic Logic for AI and Computer Science

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. Moore''s autoepistemic logic is discussed together with Levesque''s related logic of ''all I know''. Furthermore it is shown how one can base default and counterfactual reasoning on epistemic logic.