 To obtain a metric version of the Peircean system, a duration function has to be added. Let \(\dur(t_1,t_2,x)\) stand for the statement ‘\(t_1\) is \(x\) time units before \(t_2\)’, where \(t_1\) and \(t_2\) belong to the same chronicle, and where \(x\) is a positive  number[3].  Using this function (d) and (e) above are replaced by: