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In this paper we propose two languages, called Future Temporal Logic (FTL) and Past Temporal Logic (PTL), for specifying temporal triggers. Some examples of trigger conditions that can be specified in our language are the following: 驴The value of a certain attribute increases by more than 10% in 10 minutes,驴驴A tuple that satisfies a certain predicate is added to the database at least 10 minutes before another tuple, satisfying a different condition, is added to the database.驴 Such triggers are important for monitor and control applications.In addition to the languages, we present algorithms for processing the trigger conditions specified in these languages, namely, procedures for determining when the trigger conditions are satisfied. These methods can be added as a 驴temporal驴 component to an existing database management systems. A preliminary prototype of the temporal component that uses the FTL language has been built on top of Sybase running on SUN workstations.