Correctly evaluating sentences containing 'now' under temporal operators requires keeping track of both the time of utterance and the time of evaluation separately

To evaluate (3)\('\) correctly so that it matches what we mean by (3), we must make sure that ‘now’ always refers back to the original time of utterance when ‘now’ lies in the scope of other temporal operators such as F. Therefore we need to keep track of which time is the time of utterance \((u)\) as well as which time is the time of evaluation \((t)\). So our indices take the form of a pair \(\langle u, e\rangle\), where \(u\) is the time of utterance, and \(e\) is the time of evaluation. Then