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Representing Time

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”

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Representing Time

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  1. Representing Time Prof. Richard Fikes CS222 Fall 1998 Computer Science Department Stanford University 12/2/98

  2. 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” “10:50 to 11:00 a.m. on May 30, 1993”

  3. 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.”

  4. 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

  5. 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 intervals • An interval cannot consist of a single point

  6. Styles of Temporal 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 Anne)

  7. Relations on Time Intervals

  8. 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))

  9. 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]

  10. Example Axiom For Abstract Points

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