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Temporal Constraints Between Cyclic Geographic Events
Jorge Campos1,2 and Kathlenn Hornsby2
{jorge,khornsby}@spatial.maine.edu
1 Núcleo de Pesquisa em Rede de Computadores Universidade Salvador (Unifacs)2 National Center for Geographic Information and Analysis and Department of Spatial Information Science and Engineering University of Maine
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Outline
•Temporal Characteristics of Events
•Temporal Constraints Between Intervals
•A Temporal Model for Cyclic Events
•Cyclic Temporal Constraints
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Events
Events are abstractions that represent phenomena, activities, and processes of the real world.
Temporal Characteristics of Events:
Evi=(Si,Ei)
Convex intervals as the temporal construct representingthe time when event is true or is happening
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Temporal Constraints
Temporal Constraints specify values (or range of values) to the intervals’ endpoints
Unary Temporal Constraints:
Binary Temporal Constraints:
Evi=(Si=3 , Ei=5)
Evi=(Si=2 Si=3 , Ei>5 Ei<7)
(Evi, Evj, )
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Examples of Binary Temporal Constraints
Triples of Temporal
Constraints
Endpoints Relation
(Evi, Evj, before) Si<Sj Ei<Ej
(Evi, Evj, meets) Si<Sj Ei=Ej
(Evi, Evj,startTogether) Si=Sj
(Evi, Evj, centered) (Si+ Ei)/2=(Sj+ Ej)/2
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Events of an Aircraft’s Operation
refuel
tires pressure taxiing
take-off
t
centered
before
meets
(tires pressure, refuel, centered)(refuel, taxiing, before)(taxiing, take-off, meets)
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Temporal Representation of Cyclic Events
CycEvi=(Si,Ei,D)
CycEvi=({...,Sin-1, Si
n, Sin+1...},{...,Ei
n-1, Ein, Ei
n+1...})
t
CycEvinCycEvi
n-1CycEvin-2 CycEvi
n+1 CycEvin+2
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Temporal Constraints Between Cyclic Events
University policy: “whenever possible there is at least one bus running on the campus”
t
centered
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Temporal Constraints Between Cyclic Events
University policy: “whenever possible there is at least one bus running on the campus”
New fact: “A new construction site will close off some streets in the route of the blue bus”
t
centered
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Temporal Constraints Between Cyclic Events
t“maximize the occurrence of periods of non-concurrent activities”
centered
University policy: “whenever possible there is at least one bus running on the campus”
New fact: “A new construction site will close off some streets in the route of the blue bus”
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t
period of equivalence
A Model of Temporal Relations for Cyclic Events
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A Model of Temporal Relations for Cyclic Events
t
overlappedBy
overlaps
meets
contains
metBy
t
period of equivalence
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All Possible Characteristic Sets of Correlations
{contains, meets, overlappedBy, overlaps, metBy}
{startedBy, overlaps, overlappedBy, overlaps}
{contains, overlaps, overlappedBy, overlaps}
{finishedBy, overlappedBy, overlaps, overlappedBy}
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Instances of Cyclic Temporal Constraints
MaximizeRelation
MinimizeRelationwhere Relation is
DisconnectedMeetsOverlappsFinishedByStartsContainsContainedByEqualsFinishesStartedByOverlappedByMetBy
Cyclic Constraint - Select one possible configuration amongall possible representative sets of temporal relations
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An Instance of Cyclic Constraint
University policy: “whenever possible there is at least one bus running on the campus”
maximize the occurrence of periods of non-concurrent activities
MaximizeDisconnected
startedBy overlaps overlappedBy overlaps
contains overlaps overlappedBy overlaps
contains meetsoverlappedByoverlapsmetBy
finishedByoverlappedBy overlapsoverlappedBy
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Selecting the “Closest” Configuration
startedBy overlaps overlappedBy overlaps
contains overlaps overlappedBy overlaps
contains meetsoverlappedByoverlapsmetBy
finishedByoverlappedBy overlapsoverlappedBy
maximizeDisconnected
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Selecting the “Closest” Configuration
startedBy overlaps overlappedBy overlaps
contains overlaps overlappedBy overlaps
contains meetsoverlappedByoverlapsmetBy
finishedByoverlappedBy overlapsoverlappedBy
maximizeDisconnected
D M O
Fb
C
Sb
E Ob D
S
Cb
F
M
b
D DM M
b
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A New Temporal Configuration of the Bus
t
{overlappedBy, contains, overlaps}
{overlappedBy, contains,contains, overlaps}
{overlappedBy,contains, contains, meets}
{overlappedBy,contains, contains}
{overlappedBy. contains,
finishedBy}
{contains, contains,overlaps}
{contains, contains,overlaps, metBy}
{startedBy, contains, overlaps}
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{overlappedBycontainscontainsoverlaps}
{overlappedBy contains contains
meets}
{overlappedBycontainscontains}
{overlappedBy contains
finishedBy}
{overlappedBy contains, overlaps}
{containscontainsoverlaps}
{containscontainsoverlapsmetBy}
{startedBy contains overlaps}
D M O
Fb
C
Sb
E Ob D
S
Cb
F
M
b
Selecting the new “Closest” Configuration
O ObD D
C
Cb
Fb Sb
E
S F
M M
b
maximizeDisconnected
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Future Work
• Definition of a weight for each temporal relation
• Incoporation of some metric information
• Incorporation of more abstract temporal relations in our reasoning