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<Paper uid="W04-2613">
  <Title>Generating Linear Orders of Text-Based Events</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 Ordering events
</SectionTitle>
    <Paragraph position="0"> To generate linear orders of events, the set of 13 possible event interval relations is reduced to a set comprising only before or equal relations. Given two event intervals, A and B, for example, if the start point of A is before or equal to the start point of B and the end point of A is before the end point of B, then A is before B in the linear order. This holds for the cases of: A before B, A meets B, A overlaps B, and A starts B (Figure 2a). Event A is also before B in cases where the start point of B is after the start point of A, and the end point of B is before or equal to the end point of A, as in the occurrence of A contains B and A ended_by B.</Paragraph>
    <Paragraph position="1"> Where the start point of A is after the start point of B and the end point of A is before or equal to the end point of B, then B is before A in the linear order. This holds for A during B and A ends B, as well as for cases, A after B, A met_by B, A overlapped_by B, and A started_by B, where the start point of B is before or equal to the start point of A, and the end point of B is before the end point of A (Figure 2b).</Paragraph>
    <Paragraph position="2">  reduced to (a) A before B, (b) B before A, and (c) A equals B.</Paragraph>
    <Paragraph position="3"> Finally, where the start point of A is equal to the start point of B and the end point of A is equal to the end point of B, then A equals B in the linear order (Figure 2c). For these cases, the event intervals are considered to be simultaneous.</Paragraph>
    <Paragraph position="4"> If all possible relations that hold between events are known through the narrative, then only one plausible linear order will result. More commonly, however, it may not be known for certain how each event interval is related to the other intervals. For these cases, partial orders exist, and the events in the narrative may correspond to multiple possible linear orders.</Paragraph>
    <Paragraph position="5"> In these cases, without filtering or abstracting some of the events, the number of possible orders generated can easily become too large for a user to comprehend. A method for filtering or abstracting is necessary. One method of abstraction is to remove any events that occur at the same time as another event with a longer duration, and about which no other information is known. Thus any event that occurs during another event would be discounted if that event has no known relation to another event. In addition, events that start other events are of shorter duration than the events that they start, and may also be abstracted if no other relation exists between the starting event and a third event. An event that ends another event and about which no other information is known would also be abstracted. This filtering will prune many of the orders from the set.</Paragraph>
    <Paragraph position="6"> The next section presents an example scenario where orders of events are abstracted from a short text.</Paragraph>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 Example Scenario
</SectionTitle>
    <Paragraph position="0"> Consider a narrative describing vehicles traveling on a bridge and boat traffic maneuvering in the harbor below the bridge, as well as activities on land in preparation for a ferry's arrival: While the car was crossing over the bridge, a ferry passed underneath and an ambulance went rushing past. A plane flew over as the ferry passed under the bridge. As the ferry reached the dock on the other side of the bridge, a truck arrived to pick up goods from the boat.</Paragraph>
    <Paragraph position="1"> Events described in a narrative can be reduced to a set of event-relation combinations, where two event intervals are related by one relation. There are n event intervals and m relations in the set, where m [?] 13 is the number of possible event interval relations.</Paragraph>
    <Paragraph position="2"> In this example, there are n=6 event intervals including CarCrossesBridge, FerryUnderBridge, AmbulancePassesCar, FerryDocks, and TruckArrives. There are also m=4 (unique) relations generating the following event-relation combinations:  From this set, the event intervals are extracted and combined pairwise (Figure 3) such that a square matrix E is formed with rows i and columns j, where i=1...n-1 and j=1...n-1. Cells in E are denoted as e i,j .</Paragraph>
    <Paragraph position="3"> The matrix E is populated with the m relations that exist between the events in the set. Event-event combinations that do not exist in the set are represented by ~. All inverse relations are included in the matrix, thereby allowing all information about an event to be captured by a single row. The inverse of an equals relation is another equals. If orders are generated from the example matrix at this point, 15 linear orders are possible. To avoid such large result sets, filtering is performed on the matrix. Each row of the matrix is checked for a single during, starts, or ends relation, and these rows are eliminated from the matrix. The row for Ambulance-PassesCar contains only a during relation, so this row and its corresponding column are eliminated. The re- null A key aspect to generating the linear orders is that the result set comprises orders that are plausible, i.e., capture as closely as possible the semantics of the original text. The next section describes a method for invoking additional constraints that increase the plausibility of all orders that are derived. Keeping the plausibility of the automatically generated linear orders as high as possible, has the added benefit of reducing the number of linear orders that are generated.</Paragraph>
    <Paragraph position="5"/>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
5 Applying additional constraints based
</SectionTitle>
    <Paragraph position="0"> on semantics of relations Each event interval relation is associated with particular semantics that should be maintained in order to generate plausible linear orders. For example, the meet relation describes a scenario in which two event intervals, A and B, occur such that the start time of B is simultaneous with the end-time of A. No other events would be expected to occur between these two events in a resulting linear order. Combine A meets B with A before C, however, and one resulting linear order of events is A before C before B, in which event C occurs between A and B. Incorporating the semantics of the relations offers a way to increase the plausibility of linear orders of events. Based on this work, mapping rules are defined that reduce the thirteen event interval relations to either before or equals, and constraints are applied to allow the preservation of key semantics associated with any given event interval relation. These constraints provide the basis for mapping event intervals and relations to a linear order of events.</Paragraph>
    <Paragraph position="1"> 5.1Semantics involving during and contains relations The semantics associated with during and contains relations capture cases where one event begins and ends within the time that another event is occurring.</Paragraph>
    <Paragraph position="2"> Applying the mapping rules to a case where, for example, A before B and C during B, with no regard to the semantics of the during relation, returns A before B and B before C, i.e., the linear order, A before B before C. If, in addition, D after A, one linear order becomes A before B before D before C and the events that are originally related by during are no longer together. In order to preserve the semantics relating to during and contains for a linear order of events, therefore, a constraint is applied where any events related by during, are always sequential in the resulting linear order of events and no intermediate events can occur between them, i.e. A during</Paragraph>
    <Paragraph position="4"> A, read A during B leads to B before A and there does not exist a C such that B before C before A. For cases where A contains B, A contains BAEA</Paragraph>
    <Paragraph position="6"> For cases where more than one event occurs during another event interval, for example if C during A and A during B, the events can be put in order and the semantics preserved. C during A reduces to A before C and A during B reduces to B before A, resulting in the order B before A before C. If it is also known that event D occurs before A and during B, the linear order then becomes B before D before A before C. In this case, B and A are separated by event interval D since both A and D are during event B but both events cannot immediately follow B. Formally, A  started_by, ended_by, and ends Applying the mapping rules to any of the relations meets, starts, or ended_by results in the relation being replaced by before. I.e., A meets B AE A before B, A starts B AE A before B, and A ended_by B AE A before B. In all of these cases, it is implausible that a third event would occur between events A and B in a linear order. A constraint is applied to prevent this, and thus when R = meets, starts or ended_by, A R B AE A</Paragraph>
    <Paragraph position="8"> It is equally implausible that a third event would occur between two events related by an inverse of one of the above three relations, and a similar constraint is applied: when R = met_by, started_by or  the constraints for during take precedence over those for all other relations, some exceptions to the above constraints are necessary. In the case of meets and met_by, if, in addition to an event-relation pair that meets, for example A meets B, there are events that occur during A, additional rules are necessary. For these cases we allow events that meet to be separated by other events in the resulting linear order. For example, given A meets B and D during A, these event-relation pairs are mapped to A before B and A before D. Two linear orders result, A before D before B, and A before B before D. The latter order is implausible, however, because event B occurs between two during-events, D and A. To prevent this type of implausible order, an addition is made to the meets</Paragraph>
    <Paragraph position="10"> A, or if $ E | A during E and not B during E, then B</Paragraph>
    <Paragraph position="12"> One exception to the constraints for starts and started_by occurs if, given A starts B or B started_by A, an event (e.g., C) or a set of events occurs during event A. Here the resulting order is A before C before B. Another exception is in the case where event B is during a third event. Given A starts B and D contains B, the resulting order is A before D before B. Thus A  An exception is made in the case of ends and ended_by if, given A ends B or B ended_by A, a set of events occurs during the event that is ended_by the other. In this case these events occur between the two events related by ends in the linear order. For exam- null ple, consider A ends B and C during B. These map to B before A and B before C, and the resulting plausible order is B before C before A. Event interval C falls between B and A because C is related to event B by during. Thus A ends B AE B  The semantics involving overlaps and overlapped_by probably pose the most challenges for automatically generating a linear sequence of events. When one event interval overlaps another, the duration of the overlap is not always known. It is possible that two events almost coincide, approximating an equals relation. It is also possible that the overlap is very small, such that one event is almost before the other, or that the two event intervals almost meet. In this work, two event intervals, A and B, that overlap are reduced to A before B. No additional constraint is applied because it is assumed that the relation will hold even if there are intermediate events between the events that overlap, and therefore, A overlaps B</Paragraph>
  </Section>
  <Section position="7" start_page="0" end_page="1" type="metho">
    <SectionTitle>
AE A
</SectionTitle>
    <Paragraph position="0"> + pB. Overlapped_by is represented as A overlapped_by B AE B + pA.</Paragraph>
    <Paragraph position="1"> 5.4Semantics involving before and after When one event is before another event, this order should be preserved in the linear order of events. In contrast to the other relations, it is acceptable to have additional events occurring between any beforeevents, since the relation before continues to hold regardless of the number of events between the two events. Therefore, no constraints are necessary and A before B AE A + pB. This same reasoning holds for any event intervals related by after, such that A after B AE</Paragraph>
    <Section position="1" start_page="0" end_page="1" type="sub_section">
      <SectionTitle>
5.5 Semantics involving equals
</SectionTitle>
      <Paragraph position="0"> If two events are equal to each other this relation is preserved in the ordering of events. As orders are built, the events that are equal will remain together.</Paragraph>
      <Paragraph position="1"> Events that are not equal in the initial set of events and relations will not be equal in the final linear orders. null  is the basis for generating linear orders. The events are arranged in a linear order using the constraints and mapping rules presented in the previous section. Parsing each row of E  ) represents either a relation linking the two event intervals or is an empty cell, ~. Empty cells obviously do not contribute to any linear order. In this example, there is no valid relation for e  returns FerryUnderBridge during Car-CrossesBridge, and based on the mapping rules, an order is instantiated, CarCrossesBridge before FerryUnderBridge. null The next cell encountered, e  , contains FerryUnderBridge before FerryDocks, and the order is updated to CarCrossesBridge before FerryUnderBridge before FerryDocks. Cell e  contains FerryUnderBridge overlaps PlaneFliesOver, and because the relation between PlaneFliesOver and FerryDocks is unknown, two possible orders result:  , there is no valid relation and no updates are made to the orders. The next event-event combination considered is e  , i.e., CarCrossesBridge contains FerryUnderBridge. This is redundant since FerryUnderBridge during CarCrossesBridge has already been considered, and so no changes are necessary to the orders. No valid relations are present in the remainder of the second row, and the next relation encountered is e  , FerryDocks after FerryUnderBridge. The inverse of this relation has also already been considered and no changes are made. However, e  contains FerryDocks meets TruckArrives, which does result in an update to each of the orders. Adding the event TruckArrives such that the constraints of meets are satisfied returns two orders:  The remaining two event interval relations extracted from the matrix (PlaneFliesOver overlapped_by FerryUnderBridge in e  ) are redundant because their inverses have already been considered, and thus require no additional changes to the orders. When all relations have been processed, the result is a set O of all possible orders that are plausible and maintain as closely as possible the original semantics of the relations: O= { CarCrossesBridge before FerryUnderBridge before PlaneFliesOver before FerryDocks before TruckArrives, CarCrossesBridge before FerryUnderBridge before FerryDocks before TruckArrives before PlaneFliesOver } Using the semantics of the relations, both orders generated are plausible. PlaneFliesOver always occurs after the ferry is under the bridge, as does FerryDocks. FerryDocks is always directly before TruckArrives with no intermediate events between them. If the result set O is compared to the set of orders generated in section 4, i.e., before the semantic constraints were applied, O is shown to consist of a smaller number of orders. These correspond to the most plausible orders given the original set of event-relation combinations present in the text. Orders that do not meet the constraints based on semantics are eliminated and not presented to a user.</Paragraph>
    </Section>
  </Section>
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