11 Temporal logic

Abstract

Temporal logic is one of the classic branches of modal logic. It is remarkably fruitful in the issues it has raised, the results it has given rise to, and as an applied tool. This chapter focuses on the key issues related to temporal logic and examines some topics in temporal logic that are considered both in computer science and in other fields. A basic round-up of the semantic options for handling time is describes and some logics (syntax and evaluation) that can be used are explained. The expressivity of classical and modal-style logics is compared. Kamp's famous 1968 expressive completeness theorem, the temporal reasoning, tableaux, resolution, filtration- and the finite model property, and other methods are discussed. Temporal logics come in many forms and that motivations from computing or linguistic applications and philosophical, theoretical or mathematical interests have driven temporal logic research in many disparate directions. The structures supporting varying granularity of focus and the options when propositions depend on several time points are considered.