In this paper, we study a query language about databases evolving in (infinite) time. The syntax of the query language is based on a predicate temporal logic. The semantics of the language is defined with infinite sequences of database states, which in this paper are determined either by pure Datalog programs or by negated Datalog programs with inﬂationary semantics. In general, other mechanisms for defining the semantics, such as production systems, can be used. We analyze the relative expressive power of such a query language and the standard Datalog queries for both pure and negated Datalog programs. We show that our query language has more expressive power than Datalog queries for both pure and negated Datalog programs in general. However, we also prove a surprising technical result that the existential fragment of temporal logic has the same expressive power as Datalog queries for negated Datalog programs with inﬂationary semantics. This result implies the collapse of the existential fragment of temporal logic for such programs: any temporal logic formula from that fragment can be reduced to an equivalent formula with a single possibility operator.