A Hierarchy of Temporal Logics with Past (Extended Abstract)

We extend the classical hierarchy of branching-time temporal logics between UB and CTL by studying which additional expressive power (if any) stems from the incorporation of past-time modalities. In addition, we propose a new temporal combinator, N for \Now", that brings new and interesting expressive power. In several situations, non-trivial translation algorithms exist from a temporal logic with past to a pure-future fragment. These algorithms have important practical applications e.g. in the eld of model-checking.