Metric temporal reasoning with less than two clocks

We introduce a new way of defining metric temporal logic on a real-numbers flow of time. The idea is based on having semantics which allow us to refer to a single universal clock of arbitrary precision in order to impose metric constraints. This gives us a new metric temporal logic which is very expressive, is natural to use, can be applied in very general situations, affords a wide range of useful abbreviations and operators, has a PSPACE decision procedure, and has the promise of being amenable to standard reasoning techniques. Thus it has it many advantages over the existing metric temporal logics. We provide a decision procedure via conversion to a non-metric temporal logic, hence doing metric reasoning with no clocks.