Metric temporal logic revisited

Abstract

We introduce a new way of defining metric temporal logic over the continuous real model of time. The semantics refer to a single universal clock in order to impose metric constraints to any desired precision. Furthermore, the expression of any non-metric aspects can correctly utilise the full power of continuous time temporal logic. Syntactic constructs afford the convenient succinct expression of many useful and typical constraints including some interesting requirements for regular occurrences. A decision procedure is provided via a simple translation into an existing non-metric temporal logic and this gives a workable complexity and the possibility of automated reasoning. There are advantages in expressiveness, naturalness, generality and amenability to reasoning techniques over the existing metric temporal logics. Combining purely continuous with adequate metric aspects in one language makes the logic very suitable for dealing with hybrid systems.