Knowledge Systems Laboratory, Stanford University
10
Functions on Time-Interval
uStarting-Point and Ending-Point
„Defining axiom for Starting-Point:
> (=>  (and  (Time-Point ?s)  (Time-Interval ?i))
>        (<=>  (Starting-Point ?i ?s)
>                 (and     (not    (exists   ?j   (and  (Time-Point ?j)
>                                                                   (Before ?j ?s)
>                                                           (Point-In-Interval ?j ?i))))
>                             (forall   ?p   (=>  (Time-Point ?p)
>                                                         (not    (exists   ?k   (and  (Time-Point ?k)
•                                                                                   (Before ?k ?p)
>                                                                                                   (Point-In-Interval ?k ?i))))
>                                                         (or  (Equal-Point ?p ?s)  (Before ?p ?s)))))))
uDuration
„Convex time interval
>Time quantity whose magnitude is the difference between the location of the interval’s
> ending point and starting point
„Non-convex time interval
>Sum of durations of all convex time intervals contained in it