A cornucopia of applications

Modal logic has been used by logicians, philosophers, the “artificial intelligentsia” and computer scientists for many purposes. There is a cornucopia of applications of modal logic to problems and concepts in each of these discipline areas. We shall be looking at a very small number of those applications.

Logicians have used modal logic to try to produce logics that capture the notions of possibility, logical necessity and proof. These applications consider modal logic from an alethic point of view: from the point of view of issues related to truth. We turn to these in Chapter 9.

Philosophers, quantum physicists, and artificial intelligence researchers who work in the area of planning all have a deep interest in questions about time. Applications of modal logic to questions of time used to be known as “tense” (from past, present and future tense) applications. But in these days of disdain for grammar, such applications are called temporal. In Chapter 10 we introduce temporal applications for modal logic. Dynamic logic is an application of modal logic that is closely related to temporal logic.

Dynamic logic was first generated by computer scientists who applied modal logic to the study of processes in machines. It was first seen as a logic for state changes. Philosophers have begun to use dynamic logic in the study of action, and of belief change. In Chapter 11 we consider some elementary dynamic logic.