Chapter 4 Modal varieties of temporal logic

This chapter provides a rudimentary introduction to a number of different systems of temporal logic that have been developed from a modal logic basis. We assume that the reader has some familiarity with propositional and first order logic but assume no background in modal logic, although some reference to modal logic does occasionally occur. Our purpose is to take a tour through a few key "modal" forms of temporal logic, from linear to branching and from points to intervals, present their salient properties and features, for example, syntactic and semantic expressiveness, inference systems, satisfiability and decidability results, and provide sufficient insight into these families of logics to support the interested reader in undertaking further study or to use such logics in practice. The field is vast and there are many other important systems of temporal logic we could have developed; space is limited however and we have therefore focussed primarily on the development on the modal forms of linear time temporal logics.