First-Order Queries over Temporal Databases Inexpressible in Temporal Logic

Queries over temporal databases involve references to time. We study diierences between two approaches of including such references into a rst-order query language (e.g., relational calculus): explicit (using typed variables and quantiiers) vs. implicit (using a nite set of modal connectives). We also show that though the latter approach|a rst-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 rst one in general. This result also settles a longstanding open problem about the expressive power of rst-order temporal logic. A consequence of this result is that there is no rst-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 rst-order deenable queries.