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					          Representing Time

               Prof. Richard Fikes
                       CS222

                      Fall 1998

             Computer Science Department
                 Stanford University



12/2/98
                Senses of Time - 1
A      physical dimension (the Time-Dimension)
Time       plenum
    Large temporal space in which all events are
     located
    E.g., “time line”
          “temporally possible worlds”
Time       intervals
    Pieces of time
    E.g., “during the 1994 Winter Olympics”
          “the 16th century”
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                                           30, 1993”
          “10:50 to 11:00 a.m. on MaySystems Laboratory, Stanford University
                                 Knowledge
             Senses of Time - 2
     Durations
      E.g., “a century”
           “25 minutes”
           “as long as it takes for the kettle to boil”

     Time   points
      A time interval of 0 duration

     Position   on a temporal coordinate system
      E.g., “March 14, 1994”
           “3:45 p.m.”
3                              Knowledge Systems Laboratory, Stanford University
    Views of Intervals and Points
 View      1: Points are intervals
       Time is discrete
       Points are single clock ticks
       Points are called “moments”
       Points have no subintervals
         › No internal separable time points
       Points do not overlap or contain one another



4                                 Knowledge Systems Laboratory, Stanford University
    Views of Intervals and Points
 View        2 - Point continuum
       Point is a primitive object
       An interval is a set of points
       Intervals are either open or closed
       A closed interval can consists of a single
        point
 View        3 - Glass continuum
       Interval is a primitive object
       The point where intervals meet is not
        contained in either interval
       No distinction between open and closed
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        intervals
                                 Knowledge Systems Laboratory, Stanford University
       An interval cannot consist of a single point
                     Representations
 Timeless         Quantification
       Functions and relations have a time argument
         E.g., (Married Joe Anne 1993)
         › Situation calculus
       Objects have time intervals associated with them
         E.g., (contains (time-of (Marriage Joe Anne)) 1993)

 Sentences          “hold true” at times
    E.g., (holds (Married Joe Anne) 1993)

 Tense       logics
    E.g., (F (Married Joe Anne))
          (F (and (not (Married Joe Anne)) (P (Married Joe
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        Anne)                      Knowledge Systems Laboratory, Stanford University
    Relations on Time Intervals




7                 Knowledge Systems Laboratory, Stanford University
     Using the Interval Relations

 “The      reign of Elizabeth II followed that of George
     VI.”
        (After (ReignOf ElizabethII) (ReignOf GeorgeVI))

 “The      reign of Elvis overlapped with the 1950’s.”
        (Overlaps Fifties (ReignOf Elvis))
        (= (Start Fifties) (Start AD1950))
        (= (End Fifties) (End AD1959))


 8                                     Knowledge Systems Laboratory, Stanford University
             Time Abstractions
 Time      points can be abstracted
    Time-Point
      *Year-Of:
      *Month-Of:
      *Day-Of:
      ...

 Intervals    can have abstract start and end
    times
    E.g., [1984 May-1993]
9                            Knowledge Systems Laboratory, Stanford University
Example Axiom For Abstract Points




10               Knowledge Systems Laboratory, Stanford University

				
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