Time
Time is important to any agent that takes action, and there has been much work on the representation of time intervals.
Two kinds of intervals exist namely,
- Moments interval.
- Extended intervals.
The distinction is that only moments have zero duration,
Partition ({Moments, ExtendedIntervals}, Intervals)
i ∈ Moments ⇔ Duration(i) = Seconds(0).
Next a time scale is invented and associate points on the scale with moments,. giving absolute times. The time scale is arbitrary, it is measured n seconds and say that the moment at midnight (GMT) on January 1, 1900, has time 0.
Functions Used: The following are the functions used.
- The functions Start and End pick out the earliest and latest moments in an interval,
- The function Time delivers the point on the time scale for a moment.
- The function Duration gives the difference between the end time and the start, time.
Interval(i) ⇒ Duration(i) = (Time(End(i)) - Time(Start(i)))
Time(Star(AD1900)) = Seconds(0)
Time(Start(AD2001)) = Seconds(3187324800)
Time(End(AD2001)) = Seconds(3218860800).
Duration(AD2001) = Seconds(31536000).
- A function Date is introduced to make these numbers easier to read. It takes six arguments (hours, minutes, seconds, day, month, and year) and returns a time point,
Time(Start(AD2001) = Date(0, 0, 0, 1, Jan, 2001).
Date(0, 20, 21, 24, 1, 1995) = Seconds(3000000000).
Two intervals Meet if the end time of the first equals the start time of the second. It is possible to define predicates such as Before, After, During, and Overlap solely in terms of Meet, but it is more sensitive to define them in terms of points on the time scale.
Meet(i, j) ⇔ Time(End(i)) – Time(Start(j)).
Before(i, j) ⇔ Time(End(i)) < Time(Start(j)).
After(j, i) ⇔ Before(i, j).
During(i, j) ⇔ Time(Start(j)) ≤ Time(Star(i)) ∧ Time(End(i)) : S Time(End(j)).
Overlap(i, j) ⇔ ∃During(k, I) â´· During(k, j)
