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Temporal Constraints Between Cyclic Geographic Events Jorge Campos 1,2 and Kathlenn Hornsby 2 {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: Ev i =(S i,E i ) Convex intervals as the temporal construct representing the 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: Ev i =(S i =3, E i =5) Ev i =(S i =2 S i =3, E i >5 E i <7) (Ev i, Ev j, )

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Examples of Binary Temporal Constraints Triples of Temporal Constraints Endpoints Relation (Ev i, Ev j, before ) S i <S j E i <E j (Ev i, Ev j, meets ) S i <S j E i =E j (Ev i, Ev j, startTogether ) S i =S j (Ev i, Ev j, centered ) (S i + E i )/2=(S j + E j )/2

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Events of an Aircrafts Operation refuel tires pressuretaxiing 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 CycEv i =(S i,E i,D) CycEv i =({...,S i n-1, S i n, S i n+1...},{...,E i n-1, E i n, E i n+1...}) t CycEv i n CycEv i n-1 CycEv i n-2 CycEv i n+1 CycEv i n+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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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 MinimizeRelation where Relation is Disconnected Meets Overlapps FinishedBy Starts Contains ContainedBy Equals Finishes StartedBy OverlappedBy MetBy Cyclic Constraint - Select one possible configuration among all 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 meets overlappedBy overlaps metBy finishedBy overlappedBy overlaps overlappedBy

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Selecting the Closest Configuration startedBy overlaps overlappedBy overlaps contains overlaps overlappedBy overlaps contains meets overlappedBy overlaps metBy finishedBy overlappedBy overlaps overlappedBy maximizeDisconnected

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Selecting the Closest Configuration startedBy overlaps overlappedBy overlaps contains overlaps overlappedBy overlaps contains meets overlappedBy overlaps metBy finishedBy overlappedBy overlaps overlappedBy maximizeDisconnected DM O Fb C Sb E Ob D S Cb F MbMb DDM MbMb

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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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{overlappedBy contains overlaps} {overlappedBy contains meets} {overlappedBy contains contains} {overlappedBy contains finishedBy} {overlappedBy contains, overlaps} {contains contains overlaps} {contains contains overlaps metBy} {startedBy contains overlaps} DM O Fb C Sb E Ob D S Cb F MbMb Selecting the new Closest Configuration OOb DD C Cb FbSb E SF M MbMb 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

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