12/2/98

Prof. Richard Fikes

Representing Representing TimeTime

Computer Science DepartmentStanford University

CS222

Fall 1998

2 Knowledge Systems Laboratory, Stanford University

Senses of Senses of Time - 1Time - 1 A physical dimension (the Time-

Dimension)

Time plenumLarge temporal space in which all events are located

E.g., “time line”“temporally possible worlds”

Time intervalsPieces of timeE.g., “during the 1994 Winter Olympics”

“the 16th century”“10:50 to 11:00 a.m. on May 30,

1993”

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Senses of Time - 2Senses of Time - 2Senses of Time - 2Senses of Time - 2 Durations

E.g., “a century”

“25 minutes”

“as long as it takes for the kettle to boil”

Time pointsA time interval of 0 duration

Position on a temporal coordinate systemE.g., “March 14, 1994”

“3:45 p.m.”

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Views of Intervals and Views of Intervals and PointsPoints

Views of Intervals and Views of Intervals and PointsPoints

View 1: Points areare 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

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Views of Intervals and Views of Intervals and PointsPoints

Views of Intervals and Views of Intervals and PointsPoints

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

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Styles of Temporal Styles of Temporal RepresentationsRepresentations

Styles of Temporal Styles of Temporal RepresentationsRepresentations

Timeless Quantification Functions and relations have a time argument

E.g., (Married Joe Anne 1993)› Situation calculus

Objects have time intervals associated with themE.g., (contains (time-of (Marriage Joe Anne)) 1993)

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

Tense logicsE.g., (F (Married Joe Anne))

(F (and (not (Married Joe Anne)) (P (Married Joe Anne)

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Relations on Time Relations on Time IntervalsIntervals

Relations on Time Relations on Time IntervalsIntervals

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Using the Interval Using the Interval RelationsRelations

Using the Interval Using the Interval RelationsRelations

“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))

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Time AbstractionsTime AbstractionsTime AbstractionsTime Abstractions Time points can be abstracted

Time-Point*Year-Of:*Month-Of:*Day-Of:...

Intervals can have abstract start and end timesE.g., [1984 May-1993]

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Example Axiom For Abstract Example Axiom For Abstract PointsPoints

Example Axiom For Abstract Example Axiom For Abstract PointsPoints