1. 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

2. Outline Temporal Characteristics of Events Temporal Constraints Between Intervals A Temporal Model for Cyclic Events Cyclic Temporal Constraints

3. 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

4. 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, )

5. 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

6. 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)

7. 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

8. Temporal Constraints Between Cyclic Events University policy: whenever possible there is at least one bus running on the campus t centered

9. 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

10. 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

11. t period of equivalence A Model of Temporal Relations for Cyclic Events

12. t overlappedBy overlaps meets contains metBy t period of equivalence

13. All Possible Characteristic Sets of Correlations {contains, meets, overlappedBy, overlaps, metBy} {startedBy, overlaps, overlappedBy, overlaps} {contains, overlaps, overlappedBy, overlaps} {finishedBy, overlappedBy, overlaps, overlappedBy}

14. 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

15. 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

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

17. 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

18. 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}

19. {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

20. Future Work Definition of a weight for each temporal relation Incoporation of some metric information Incorporation of more abstract temporal relations in our reasoning