First-order queries over temporal databases inexpressible in temporal logic

Queries over temporal databases involve references to time. We study differences between two approaches of including such references into a first-order query language (e.g., relational calculus): explicit (using typed variables and quantifiers) vs. implicit (using a finite set of modal connectives). We also show that though the latter approach—a first-order query language with implicit references to time—is appealing by its simplicity and ease of use, it cannot express all queries expressible using the first one in general. This result also settles a longstanding open problem about the expressive power of first-order temporal logic. A consequence of this result is that there is no first-order complete query language subquery-closed with respect to a uniform database schema, and thus we cannot use temporal relational algebra over uniform relations to evaluate all first-order definable queries.