| This dissertation adds to dynamic epistemic logic temporal operators that help us reason about time. Dynamic epistemic logic allows us to express changes in knowledge and beliefs as a result of actions such as public and private announcements. Its foundation is epistemic logic, which is a useful tool in reasoning about knowledge and beliefs of agents and has applications in artificial intelligence, computer security, philosophy, and game theory. But epistemic logic alone will only take a snapshot of the knowledge and beliefs of agents in a situation that is constantly changing. Logics that combine time and change with epistemic logic can greatly improve our ability to reason about the types of situations that epistemic logic has been used for. Dynamic epistemic logic (DEL) combines epistemic logic with statements that express new knowledge and beliefs as a result of actions. But another approach is temporal epistemic logic (TEL), which combines temporal logic with epistemic logic, allowing both past and future knowledge and beliefs to be expressed. The logics introduced in this dissertation, called temporal dynamic epistemic logics (TDEL), capture both DEL's ability to express consequences of actions and TEL's ability to express features of the past and future irrespective of their causes. Such languages help in reasoning about a number of philosophical puzzles, such as the Sum and Product problem, and paradoxes such as Moore's paradox. A sound and complete proof system is provided for a language that adds to DEL the ability to express features of the past. Decidability of the language follows from the proof of its completeness. The completeness and decidability of some related languages are discussed. |
