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