Temporal Connectives versus Explicit Timestamps in Temporal Query Languages

Some temporal query languages work directly on a timestamp representation of the temporal database, while others provide a more implicit access to the flow of time by means of temporal connectives. We study the differences in expressive power between these two approaches. We first consider first-order logic (i. e., the relational calculus). We show that first-order future temporal logic is strictly less powerful than the relational calculus with explicit timestamps. We also consider extensions of the relational calculus with iteration constructs such as least fixpoints or while-loops. We again compare augmentations of these languages with temporal left and right moves on the one hand, and with explicit timestamps on the other hand. For example, we show that a version of fixpoint logic with left and right moves lies between the explicit timestamp versions of first-order and fixpoint logic, respectively