temporal constraints between cyclic geographic events jorge campos 1,2 and kathlenn hornsby 2...
Post on 27-Mar-2015
214 Views
Preview:
TRANSCRIPT
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
Outline
•Temporal Characteristics of Events
•Temporal Constraints Between Intervals
•A Temporal Model for Cyclic Events
•Cyclic Temporal Constraints
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
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, )
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
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)
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
Temporal Constraints Between Cyclic Events
University policy: “whenever possible there is at least one bus running on the campus”
t
centered
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
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”
t
period of equivalence
A Model of Temporal Relations for Cyclic Events
A Model of Temporal Relations for Cyclic Events
t
overlappedBy
overlaps
meets
contains
metBy
t
period of equivalence
All Possible Characteristic Sets of Correlations
{contains, meets, overlappedBy, overlaps, metBy}
{startedBy, overlaps, overlappedBy, overlaps}
{contains, overlaps, overlappedBy, overlaps}
{finishedBy, overlappedBy, overlaps, overlappedBy}
Instances of Cyclic Temporal Constraints
MaximizeRelation
MinimizeRelationwhere Relation is
DisconnectedMeetsOverlappsFinishedByStartsContainsContainedByEqualsFinishesStartedByOverlappedByMetBy
Cyclic Constraint - Select one possible configuration amongall possible representative sets of temporal relations
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
Selecting the “Closest” Configuration
startedBy overlaps overlappedBy overlaps
contains overlaps overlappedBy overlaps
contains meetsoverlappedByoverlapsmetBy
finishedByoverlappedBy overlapsoverlappedBy
maximizeDisconnected
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
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}
{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
Future Work
• Definition of a weight for each temporal relation
• Incoporation of some metric information
• Incorporation of more abstract temporal relations in our reasoning
top related