Generating Linear Orders of Text-Based Events
Kathleen Hornsby
National Center for Geographic
Information and Analysis
University of Maine
Orono, ME 04469-5711
 khornsby@spatial.maine.edu
Suzannah Hall
Department of Spatial Information
Science and Engineering
University of Maine
Orono, ME 04469-5711
shall@spatial.maine.edu
Abstract
Events described in textual narratives do not
always occur in neat, chronological order but
occur, for example, during or overlapping
each other or as simultaneous events. Summa-
rizations of narratives, however, benefit from
a simpler, linear ordering of events. This pa-
per describes an approach for modeling events
in text as event intervals and for generating
linear orders of event intervals, useful for the
summarization of events or as the basis for
question answering systems. Linear orders are
derived through reducing the set of thirteen
possible event interval relations to a set of
only before or equal relations. The mapping
of event interval relations into before/after se-
quences requires the support of additional
constraints in order to preserve the original
semantics of the events presented in the text
and to derive plausible orders of events.
1 Introduction
The world is a dynamic place and the activities and ac-
tions that are part of our everyday experience include
such phenomena as the flow of traffic on the morning
drive to work, a person walking across a street, or the
fluctuation of water bodies due to seasonal change. An
interest in developing computational models that convey
the dynamic aspects of the world has resulted in a more
explicit focus on modeling events, i.e., actions that re-
sult in some change to an entity over time, such as the
creation, elimination, or transmission of entities (Al-
Taha and Barrera, 1994; Claramunt and Theriault, 1995;
Claramunt and Theriault, 1996; Medak, 1999; Hornsby
and Egenhofer, 2000). The segmentation of real-world
happenings into events facilitates the processing and
conveying of natural language information to a user
(Zacks and Tversky, 2001). An understanding of text is
improved if the event structure of the text can be recon-
structed. Alfonseca and Manandhar (2002) extract
events based on verbs that represent actions, verbs asso-
ciated with the verb to be which represent states, and
occurrences of nouns that are specifications of verbs,
such as arrival or accident. Events are anchored in time
relative to either the time the text is written or to the
main event, and reordered based on this anchoring and
verb tenses. Indexing and information retrieval for cur-
rent and historical reports on infectious disease out-
breaks is improved through an approach where events
relating to occurrences of infectious diseases are auto-
matically extracted from news sources on the Internet
(Grishman et al., 2002). These events are then used to
populate a database with the view that coupling the text-
based event extraction with a database approach, offers
better indexing for reports on infectious disease out-
breaks.
Reasoning about events commonly requires assem-
bling the events into a sequence or order of events such
that a temporal pattern of events becomes distinguish-
able (Frank, 1998) and more understandable. For many
reasoning tasks involving events, users require a simple,
total order of events, where for every pair of events, A
and B, either A is before B or B is before A (or both)
(Frank, 1998). The case where A is before B and B is
before A describes the case where A occurs at the same
time as B. This linear sequencing helps us to understand
and communicate in a simpler fashion how events occur
over time.
In a typical database, the values of one or more at-
tributes of data may be ordered through queries to the
database using a database query language such as SQL.
Dynamic scenarios as captured in text-based narratives,
for example, require alternative approaches to ordering,
where orders are based on events or the relations among
events even though the knowledge about these relations
may be incomplete or uncertain (Pustejovsky et al.,
2003). This paper presents methods to generate linear
orders of events from more complex orderings of events
in text. These linear orders provide simpler, summarized
views of the events in a narrative as well as a basis for
event-based question and answer systems. Automatic
text summarization strategies are necessary to support
decision making from large textual narratives as well as
the large number of information resources available via
the Web (Mani and Maybury, 2001). Temporal seman-
tics and events have been considered in the context of
time-based summarization strategies that assist users to
monitor changes in news coverage over time (Allan et
al., 2001).
In this paper, entities refer to phenomena in the real
world, and an event results in some change to an entity
over time. Events are assumed to be linear with both a
start point and an end point. Events that are ongoing,
i.e., have no end, are not treated here, nor are pre-
existing events, i.e., those that have no known start
point.
The objective of this paper is to introduce an ap-
proach for automatically generating plausible linear
orders of events from partially-ordered sets of event
intervals drawn from text descriptions. The remainder of
this paper is structured as follows: Section 2 describes
events modeled as event intervals and the relations that
hold between event intervals. Section 3 presents an ap-
proach to generating linear orders of event intervals
where the set of 13 possible event interval relations are
reduced to either before or equals. In Section 4 an ex-
ample is introduced to demonstrate this approach. The
next section further refines the ordering process by in-
corporating constraints derived from the semantics of
the original event interval relations, and Section 6 uses
the example scenario to illustrate the use of these  se-
mantics in the ordering process. Section 7 presents the
conclusions and discusses future work.
2 Events and relations among events
Events are often modeled as being instantaneous such
as, for example, an update to a bank account or the
transmission of an electronic message, i.e., changes of
state having no duration (Hinze and Voisard, 2002).
Alternatively, events may be modeled as occurring over
a period of time and therefore have duration. These
events are typically associated with a specific point in
time (Motakis and Zaniolo, 1995), usually the point at
which the event finishes (Galton and Augusto, 2002). In
linguistics and cognitive psychology, an event is most
often modeled as occurring over a period of time
(Larson, 1999; Pedersen and Wright, 2002), and human
perceptions of this event time are of particular interest
to researchers. For example, in a court case, a suspect’s
claim about events during a particular time period ver-
sus a witness’ perception of the same events may affect
the jury and make a difference to the outcome of a trial
(Pedersen and Wright, 2002).
The events described in this paper are treated as in-
tervals with a start point and end point, and are assumed
to have some duration. For example, LowPressure-
Moves refers to an event–the movement of a low pres-
sure system–modeled as an interval. Text, such as a
paragraph describing the weather over the past twenty-
four hours, can be processed to yield a set of event-
relation combinations. Our focus in this paper is not so
much on event extraction from text but rather the meth-
ods to automatically generate a plausible linear order of
events. As event intervals are assumed to be linear, Al-
len’s temporal interval relations (Allen, 1983) describe
the set of possible relations that hold among event inter-
vals (Figure 1). For example, scattered showers occur
this afternoon before drier air arrives from the west
relates two events, ScatteredShowersOccur and Dri-
erAirArrives, by the temporal interval relation before.
This approach assumes an underlying linear model of
time and excludes cyclic or branching time (Frank,
1998; Hornsby et al., 1999).
Figure 1. Thirteen event interval relations (after
Allen 1983).
Retrieving information about event intervals that
shows how events relate to each other is required for an
understanding of how entities described in a narrative
evolve over space and time. Generating orders of events
is necessary such that useful information about events is
presented for users, either as a summarization tool for
large information resources or as a method for question
answering.
3 Ordering events
To generate linear orders of events, the set of 13 possi-
ble event interval relations is reduced to a set compris-
ing 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 occur-
rence of A contains B and A ended_by B.
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).
A before B
Æ
A before B
A meets B Æ A before B
A overlaps B Æ A before B
A starts B Æ A before B
A contains B Æ A before B
A ended_by B Æ A before B
(a)
A during B
Æ
B before A
A ends B Æ B before A
A after B Æ B before A
A met_by B Æ B before A
A overlapped_by BÆ B before A
A started_by B Æ B before A
(b)
A equals B Æ A equals B
(c)
 Figure 2. The set of event interval relations are
reduced to (a) A before B, (b) B before A, and (c)
A equals B.
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.
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 corre-
spond to multiple possible linear orders.
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 an-
other 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 infor-
mation is known would also be abstracted. This filtering
will prune many of the orders from the set.
The next section presents an example scenario
where orders of events are abstracted from a short text.
4 Example Scenario
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 ar-
rived to pick up goods from the boat.
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. 
In this example, there are n=6 event intervals in-
cluding CarCrossesBridge, FerryUnderBridge, Ambu-
lancePassesCar, FerryDocks, and TruckArrives. There
are also m=4 (unique) relations generating the following
event-relation combinations:
FerryUnderBridge during CarCrossesBridge
AmbulancePassesCar during CarCrossesBridge
FerryDocks after FerryUnderBridge
FerryUnderBridge overlaps PlaneFliesOver
FerryDocks meets TruckArrives
 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
 .
The matrix E is populated with the m relations that
exist between the events in the set. Event-event combi-
nations 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 exam-
ple 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-
vised matrix E
1
 (Figure 4) becomes the foundation for
computing the orders.
Applying the mappings to before for the relations in
the matrix E
1
 now yields a total of 3 possible orders:
(1) CarCrosseBridge before FerryUnderBridge before
Ferry-Docks before TruckArrives before PlaneFli-
esOver
(2) CarCrossesBridge before FerryUnderBridge before
Ferry-Docks before PlaneFliesOver before
TruckArrives
(3) CarCrossesBridge before FerryUnderBridge before
Plane-FliesOver before FerryDocks before
TruckArrives
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 origi-
nal text. The next section describes a method for in-
voking 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.
FerryUnderBridgeCarCrossesBridgeAmbulancePassesCarFerryDocksPlaneFliesOverTruckArrives
FerryUnderBridge~ during~ beforeoverlaps~
CarCrossesBridgecontains~ contains~ ~ ~
AmbulancePassesCar~ during~ ~ ~ ~
FerryDocksafter ~ ~ ~ ~ meets
PlaneFliesOveroverlapped_by~ ~ ~ ~ ~
E=
TruckArrives ~ ~ ~ met_by~ ~
Figure 3. Matrix based on a set of event-relation pairs
FerryUnderBridgeCarCrossesBridgeFerryDocksPlaneFliesOverTruckArrives
FerryUnderBridge~ duringbeforeoverlaps~
CarCrossesBridgecontains~ ~ ~ ~
FerryDocksafter ~ ~ ~ meets
PlaneFliesOveroverlapped_by~ ~ ~ ~
E
1 
=
TruckArrives~ ~ met_by~ ~
Figure 4. Matrix of events and relations after abstraction
5 Applying additional constraints based
on semantics of relations
Each event interval relation is associated with par-
ticular 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 seman-
tics of the relations offers a way to increase the plau-
sibility 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 inter-
val relation.  These constraints provide the basis for
mapping event intervals and relations to a linear or-
der of events.
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.
Applying the mapping rules to a case where, for ex-
ample, 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 re-
sulting linear order of events and no intermediate
events can occur between them, i.e. A during
BÆB
  
† 
pA and 
† 
/ $ C | B
  
† 
pC
  
† 
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 BÆA
  
† 
pB and 
† 
/ $ C | A
  
† 
pC
  
† 
B.
For cases where more than one event occurs dur-
ing 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 or-
der 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
during B Æ B 
  
† 
p A except if $ D |D during B, D be-
fore A then B
  
 D 
  
 A.
5.2Semantics involving meets, met_by,  starts,
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 Æ A before B, A
starts B Æ A before B, and A ended_by B Æ 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 Æ
A  
† 
p
B and 
† 
/ $ C | A  
† 
p
C  
† 
B.
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 con-
straint is applied: when R = met_by, started_by or
ends, A R B Æ B  
† 
p
A and 
† 
/ $ C | B  
† 
p
C  
† 
A. Because
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 ex-
ample, 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 dur-
ing-events, D and A. To prevent this type of implau-
sible order, an addition is made to the meets
constraint, if $ D | D during A then A
  
† 
pD
  
† 
B, or if $
E | B during E and not A during E, then A
  
pE
  
† 
B.
Similarly, A met_by BÆB
  
† 
pA and 
† 
/ $ C | B
  
† 
C
  
A,
except if $ D | D during B then B
  
pD
  
A, or if $ E |
A during E and not B during E, then B  
† 
E  
† 
p
A.
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
starts B Æ A  
† 
p
B except if $ D | D contains B then
A  
† 
p
D  
† 
B. For A started_by B, A started_by B Æ
B  A and 
† 
/ $ C| B  
† 
p
C  
† 
A, except if $ D | D during B
then B  
† 
p
D  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-
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 Æ B  
† 
p
A and 
† 
/ $ C | B  
† 
p
C  
† 
A,
except if $ D | D during B then B  
p
D  A, or if $ E |
A during E and not B during E, then B  
† 
E  
† 
p
A. In the
case where A is ended_by B, A ended_by B Æ A  
† 
p
B
and 
† 
/ $ C | A  
† 
p
C  
† 
B, except if $ D | D during A then
A  
p
D  B, or if $ E | B during E and not A during E,
then A  
† 
p
E  
† 
B.
5.3Semantics involving overlaps and over-
lapped_by
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 re-
lation. 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
Æ A
  
† 
pB. Overlapped_by is represented as A over-
lapped_by B Æ B
  
† 
pA.
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 before-
events, 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 Æ A
  
† 
pB. This same reasoning holds for any
event intervals related by after, such that A after B Æ
B
  
† 
pA
5.5 Semantics involving equals
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.
Events that are not equal in the initial set of events
and relations will not be equal in the final linear or-
ders.
6 Using a matrix to generate orders
The matrix E
1
 is the basis for generating linear or-
ders. The events are arranged in a linear order using
the constraints and mapping rules presented in the
previous section. Parsing each row of E
1
, the first
event-event combination (e
1,1
) represents either a re-
lation 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
1,1
.
Cell e
1,2
 returns FerryUnderBridge during Car-
CrossesBridge, and based on the mapping rules, an
order is instantiated, CarCrossesBridge before Fer-
ryUnderBridge.
The next cell encountered, e
1,3
, contains FerryUn-
derBridge before FerryDocks, and the order is up-
dated to CarCrossesBridge before FerryUnderBridge
before FerryDocks. Cell e
1,4
 contains FerryUnder-
Bridge overlaps PlaneFliesOver, and because the
relation between PlaneFliesOver and FerryDocks is
unknown, two possible orders result:
(1) CarCrossesBridge before FerryUnderBridge before
PlaneFliesOver before FerryDocks
(2) CarCrossesBridge before FerryUnderBridge before
FerryDocks before PlaneFliesOver
At e
1,5
, there is no valid relation and no updates
are made to the orders. The next event-event combi-
nation considered is e
2,1
, i.e., CarCrossesBridge
contains FerryUnderBridge. This is redundant since
FerryUnderBridge during CarCrossesBridge has
already been considered, and so no changes are nec-
essary to the orders. No valid relations are present in
the remainder of the second row, and the next rela-
tion encountered is e
3,1
, FerryDocks after FerryUn-
derBridge. The inverse of this relation has also
already been considered and no changes are made.
However, e
2,5 
contains FerryDocks meets TruckAr-
rives, 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:
(1) CarCrossesBridge before FerryUnderBridge before
PlaneFliesOver before FerryDocks before TruckAr-
rives
(2) CarCrossesBridge before FerryUnderBridge before
FerryDocks before TruckArrives before PlaneFli-
esOver
The remaining two event interval relations ex-
tracted from the matrix (PlaneFliesOver over-
lapped_by FerryUnderBridge in e
4,1
 and
TruckArrives met_by FerryDocks in e
5,3
) are redun-
dant because their inverses have already been consid-
ered, 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 plausi-
ble 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 Ferry-
Docks before TruckArrives before PlaneFliesOver }
Using the semantics of the relations, both orders
generated are plausible. PlaneFliesOver always oc-
curs after the ferry is under the bridge, as does Fer-
ryDocks. FerryDocks is always directly before
TruckArrives with no intermediate events between
them. If the result set O is compared to the set of or-
ders 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.
7 Conclusions and future work
This paper introduces a method for abstracting events
from text and generating a linear order of these
events based on the temporal semantics associated
with them. These simpler orders are useful as sum-
maries of the events contained in the textual descrip-
tion. They also provide a basis for reasoning about
the events and performing operations on the orders,
such as returning, for example, all events that hap-
pened before event X, or returning the first event, last
event, etc. The approach presented in the paper mod-
els events as event interval relations and maps the
thirteen possible event interval relations to before and
equals. A system of constraints that preserve the se-
mantics associated with the original event relations
assists in generating orders that are plausible. For
example, when one event is during another, no in-
termediate events will fall between these two events
in a linear order. Since for many cases not all rela-
tions among events are known, it is possible that
there are many candidate linear orders produced for a
given narrative. In an effort to reduce the number of
orders, methods are presented for filtering the orders
based on event relations.
This linear sequencing helps us to understand and
communicate how events described in text occur over
time and serves as the basis for establishing a time-
line of events. Timelines organize events into
chronological order and provide a method of encap-
sulation or summarization where detailed data are
rendered in a simpler, temporally ordered fashion.
Future work will focus on additional approaches for
filtering possible orders, for example, if the narrative
includes the locations of events, this spatial informa-
tion can be used to refine further the orders. Events
that happen beyond a certain distance, or outside a
known area of interest, for example, can be ab-
stracted from the orders.
Acknowledgements
This research is supported by the National Geospa-
tial-Intelligence Agency under grant number,
NMA201-00-1-200. Kathleen Hornsby's research is
further supported by a grant from the National Insti-
tute of Environmental Health Sciences, NIH, under
grant number 1 R 01 ES09816-01.

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