# Time

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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
5
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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