Proceedings of the Workshop on Annotating and Reasoning about Time and Events, pages 23–29,
Sydney, July 2006. c©2006 Association for Computational Linguistics
A Pilot Study on Acquiring Metric Temporal Constraints for Events 
Inderjeet Mani and Ben Wellner 
The MITRE Corporation 
202 Burlington Road, Bedford, MA 01730, USA 
and 
Department of Computer Science, Brandeis University 
415 South St., Waltham, MA 02254, USA 
{imani, wellner}@mitre.org 
  
 
Abstract 
Previous research on temporal anchoring 
and ordering has focused on the annota-
tion and learning of temporal relations 
between events. These qualitative rela-
tions can be usefully supplemented with 
information about metric constraints, 
specifically as to how long events last. 
This paper describes the first steps in ac-
quiring metric temporal constraints for 
events. The work is carried out in the 
context of the TimeML framework for 
marking up events and their temporal re-
lations. This pilot study examines the fea-
sibility of acquisition of metric temporal 
constraints from corpora.  
1 Introduction 
The growing interest in practical NLP applica-
tions such as question-answering and text sum-
marization places increasing demands on the 
processing of temporal information. In multi-
document summarization of news articles, it can 
be useful to know the relative order of events so 
as to merge and present information from multi-
ple news sources correctly. In question-
answering, one would like to be able to ask when 
an event occurs, or what events occurred prior to 
a particular event. A wealth of prior research by 
(Passoneau 1988), (Webber 1988), (Hwang and 
Schubert 1992), (Kamp and Reyle 1993), (Las-
carides and Asher 1993), (Hitzeman et al. 1995), 
(Kehler 2000) and others, has explored the dif-
ferent knowledge sources used in inferring the 
temporal ordering of events, including temporal 
adverbials, tense, aspect, rhetorical relations, 
pragmatic conventions, and background knowl-
edge. For example, the narrative convention of 
events being described in the order in which they 
occur is followed in (1), but overridden by means 
of a discourse relation, Explanation in (2).  
 
(1) Max stood up. John greeted him.  
(2) Max fell. John pushed him. 
 
While there has been a spurt of recent research 
addressing the event ordering problem, e.g., 
(Mani and Wilson 2000) (Filatova and Hovy 
2001) (Schilder and Habel 2001) (Li et al. 2001) 
(Mani et al. 2003) (Li et al. 2004) (Lapata and 
Lascarides 2004) (Boguraev and Ando 2005) 
(Mani et al. 2006), that research relies on qualita-
tive temporal relations. Qualitative relations (e.g., 
event A BEFORE event B, or event A DURING 
time T) are certainly of interest in developing 
timelines of events in news and other genres. 
However, metric constraints can also be poten-
tially useful in this ordering problem. For exam-
ple, in (3), it can be crucial to know whether the 
bomb landed a few minutes to hours or several 
years BEFORE the hospitalization. While hu-
mans have strong intuitions about this from 
commonsense knowledge, machines don’t. 
 
 (3) An elderly Catholic man was 
hospitalized from cuts after a Prot-
estant gasoline bomb landed in his 
back yard.  
 
Fortunately, there are numerous instances such 
as (4), where metric constraints are specified ex-
plicitly: 
 
 (4) The company announced Tuesday 
that third quarter sales had fallen. 
  
In (4), the falling of sales occurred over the 
three-month period of time inferable from the 
speech time. However, while the announcement 
is anchored to a day inferable from the speech 
23
time, the length of the announcement is not 
specified.  
These examples suggest that it may be possi-
ble to mine information from a corpus to fill in 
extents for the time intervals of and between 
events, when these are either unspecified or par-
tially specified. Metric constraints can also po-
tentially lead to better qualitative links, e.g., 
events with long durations are more likely to 
overlap with other events.  
This paper describes some preliminary ex-
periments to acquire metric constraints. The ap-
proach extends the TimeML representation 
(Pustejovsky et al. 2005) to include such con-
straints. We first translate a TimeML representa-
tion with qualitative relations into one where 
metric constraints are added. This representation 
may tell us how long certain events last, and the 
length of the gaps between them, given the in-
formation in the text. However, the information 
in the text may be incomplete; some extents may 
be unknown. We therefore need an external 
source of knowledge regarding the typical ex-
tents of events, which we can use when the text 
doesn’t provide it. We accordingly describe an 
initial attempt to bootstrap event durations from 
raw corpora as well as corpora annotated with 
qualitative relations.   
2 Annotation Scheme and Corpora 
TimeML (Pustejovsky et al. 2005) 
(www.timeml.org) is an annotation scheme for 
markup of events, times, and their qualitative 
temporal relations in news articles. The TimeML 
scheme flags tensed verbs, adjectives, and nomi-
nals with EVENT tags with various attributes, 
including the class of event, tense, grammatical 
aspect, polarity (negative or positive), any modal 
operators which govern the event being tagged, 
and cardinality of the event if it’s mentioned 
more than once. Likewise, time expressions are 
flagged and their values normalized, based on an 
extension of the ACE (2004) (tern.mitre.org) 
TIMEX2 annotation scheme (called TIMEX3).  
For temporal relations, TimeML defines a 
TLINK tag that links tagged events to other 
events and/or times. For example, given sentence 
(4), a TLINK tag will anchor the event instance 
of announcing to the time expression Tuesday 
(whose normalized value will be inferred from 
context), with the relation IS_INCLUDED. This 
is shown in (5). 
 
(5) The company <EVENT even-
tID=e1>announced</EVENT> <TIMEX3 
tid=t1 value=1998-01-08>Tuesday 
</TIMEX3> that <TIMEX3 tid=t2 
value=P1Q3 beginPoint=t3 end-
Point=t4>third-quarter</TIMEX3> 
sales <EVENT eventID=e2> had 
fallen</EVENT>.  
<TLINK eventID=e1 relatedToEven-
tID=e2 relType=AFTER/> 
<TLINK eventID=e1 relatedToTimeID=t1 
relType=IS_INCLUDED/> 
<TIMEX3 tid=t3 value=1997-07/> 
<TIMEX3 tid=t4 value=1997-09/> 
 
The representation of time expressions in Ti-
meML uses TIMEX2, which is an extension of 
the TIMEX2 scheme (Ferro et al. 2005). It repre-
sents three different kinds of time values: points 
in time (answering the question “when?”), dura-
tions (answering “how long?”), and frequencies 
(answering “how often?”)
1
.  
TimeML uses 14 temporal relations in the 
TLINK relTypes. Among these, the 6 inverse 
relations are redundant. In order to have a non-
hierarchical classification, SIMULTANEOUS 
and IDENTITY are collapsed, since IDENTITY 
is a subtype of SIMULTANEOUS. (An event or 
time is SIMULTANEOUS with another event or 
time if they occupy the same time interval. X and 
Y are IDENTICAL if they are simultaneous and 
coreferential). DURING and IS_INCLUDED are 
collapsed since DURING is a subtype of 
IS_INCLUDED that anchors events to times that 
are durations. (An event or time INCLUDES an-
other event or time if the latter occupies a proper 
subinterval of the former.) IBEFORE (immedi-
ately before) corresponds to MEETS in Allen’s 
interval calculus (Allen 1984). Allen’s OVER-
LAPS relation is not represented in TimeML.  
The above considerations allow us to collapse 
the TLINK relations to a disjunctive classifica-
tion of 6 temporal relations TRels = {SIMUL-
TANEOUS, IBEFORE, BEFORE, BEGINS, 
ENDS, INCLUDES}. These 6 relations and their 
inverses map one-to-one to 12 of Allen’s 13 ba-
sic relations (Allen 1984).  
Formally, each TLINK is a constraint of the 
general form x R y, where x and y are intervals, 
and R is a disjunct ∨
i=1,..,6
(r
i
), where  r
i
 is a rela-
tion in TRels. In annotating a document for Ti-
                                                 
1
 Our representation (using t3 and t4) grounds the fuzzy 
primitive P1Q3 (i.e., a period of one 3
rd
-quarter) to specific 
months, though this is an application-specific step. In ana-
lyzing our data, we normalize P1Q3 as P3M (i.e., a period 
of 3 months). For conciseness, we omit TimeML EVENT 
and TIMEX3 attributes that aren’t relevant to the discus-
sion. 
24
meML, the annotator adds a TLINK iff she can 
commit to the TLINK relType being unambigu-
ous, i.e., having exactly one relType r. 
Two human-annotated corpora have been re-
leased based on TimeML
2
: TimeBank 1.2 (Puste-
jovsky et al. 2003) with 186 documents and 
64,077 words of text, and the Opinion Corpus 
(www.timeml.org), with 73 documents and 
38,709 words. TimeBank 1.2 (we use 1.2.a) was 
created in the early stages of TimeML develop-
ment, and was partitioned across five annotators 
with different levels of expertise. The Opinion 
Corpus was developed recently, and was parti-
tioned across just two highly trained annotators, 
and could therefore be expected to be less noisy. 
In our experiments, we merged the two datasets 
to produce a single corpus, called OTC. 
3 Translation 
3.1 Introduction 
The first step is to translate a TimeML rep-
resentation with qualitative relations into one 
where metric constraints are added. This transla-
tion needs to produce a consistent metric repre-
sentation. The temporal extents of events, and 
between events, can be read off, when there are 
no unknowns, from the metric representation. 
The problem, however is that the representation 
may have unknowns, and the extents may not be 
minimal. 
3.2 Mapping to Metric Representation 
Let each event or time interval x be repre-
sented as a pair of start and end time points <x1, 
x2>. For example, given sentence (4), and the 
TimeML representation shown in (5), let x be 
fall and y be announce. Then, we have x1 = 
19970701T00, x2 = 19970930T23:59, y1 = 
19980108Tn1, y2 = 19980108Tn2 (here T repre-
sents time of day in hours). 
To add metric constraints, given a pair of 
events or times x and y, where x=<x1, x2> and 
y=<y1, y2>, we need to add, based on the quali-
tative relation between x and y, constraints of the 
general form (xi-yj) ≤ n, for 1 ≤ i, j ≤2. We fol-
low precisely the method ‘Allen-to-metric’ of 
(Kautz and Ladkin 1991) which defines metric 
constraints for each relation R in TRels. For ex-
ample, here is a qualitative relation and its metric 
constraints: 
 
(6) x is BEFORE y iff (x2-y1) < 0.  
                                                 
2
More details can be found at timeml.org. 
 
In our example, where x is fall and y is the 
announce, we are given the qualitative relation-
ship that x is BEFORE Y, so the metric con-
straint (x2-y1) < 0 can be asserted. 
Consider another qualitative relation and its 
metric constraint:  
 
(7) z INCLUDES y iff (z1-y1) < 0 and 
(y2-z2) < 0. 
 
Let y be announce in (4), as before, and let 
z=<z1, z2> be the time of Tuesday, where z1 = 
19980108T00, and z2 = 19980108T23:59. Since 
we are given the qualitative relation y 
IS_INCLUDED z, the metric constraints (z1-y1) 
< 0 and (y2-z2) < 0 can be asserted. 
3.3 Consistency Checking 
We now turn to the general problem of check-
ing consistency. The set of TLINKs for a docu-
ment constitutes a graph, where the nodes are 
events or times, and the edges are TLINKs. 
Given such a TimeML-derived graph for a 
document, a temporal closure algorithm (Verha-
gen 2005) carries out a transitive closure of the 
graph. The transitive closure algorithm was in-
spired by (Setzer and Gaizauskas 2000) and is 
based on Allen’s interval algebra, taking into 
account the limitations on that algebra that were 
pointed out by (Vilain et al. 1990). It is basically 
a constraint propagation algorithm that uses a 
transitivity table to model the compositional be-
havior of all pairs of relations in a document. The 
algorithm’s transitivity table is represented by 
745 axioms. An example axiom is shown in (8):  
 
(8) If relation(A, B) = BEFORE && 
   relation(B, C) = INCLUDES 
then infer relation(A, C) = BEFORE. 
 
In propagating constraints, links added by clo-
sure can have a disjunction of one or more rela-
tions in TRels. When the algorithm terminates, 
any TLINK with more than one disjunct is dis-
carded. Thus, a closed graph is consistent and 
has a single relType r in TRels for each TLINK 
edge. The algorithm runs in O(n
3
) time, where n 
is the number of intervals.  
The closed graph is augmented so that when-
ever input edges a r
1 
b and b r
2 
c are composed to 
yield the output edge a r
3 
c, where r1, r2, and r3 
are in TRels, the metric constraints for r
3
 are 
added to the output edge. To continue our exam-
ple, since the fall x is BEFORE the Tuesday z 
25
and z INCLUDES y (announce), we can infer, 
using rule 8, that x is BEFORE y, i.e., that fall 
precedes announce. Using rule (6), we can again 
assert that (x2-y1) < 0. 
3.4 Reading off Temporal Extents 
 
Figure 1. Metric Constraints 
 
We now have the metric constraints added to 
the graph in a consistent manner. It remains to 
compute, given each event or time x=<x1, x2>, 
the values for x1 and x2. In our example, we 
have fall x=<19970701T00, 19970930T23:59>, 
announce y=<19980108Tn1, 19980108Tn2>, 
and Tuesday z=<19980108T00, 
19980108T23:59>, and the added metric con-
straints that (x2-y1), (z1-y1), and (y2-z2) are all 
negative. Graphically, this can be pictured as in 
Figure 1.  
As can be see in Figure 1, there are still un-
knowns (n1 and n2): we aren’t told exactly how 
long announce lasted -- it could be anywhere up 
to a day. We therefore need to acquire informa-
tion about how long events last when the exam-
ple text doesn’t tell us. We now turn to this prob-
lem. 
4 Acquisition 
We started with the 4593 event-time TLINKs 
we found in the unclosed human-annotated OTC. 
From these, we restricted ourselves to those 
where the times involved were of type TIMEX3 
DURATION. We augmented the TimeBank data 
with information from the raw (un-annotated) 
British National Corpus.  We tried a variety of 
search patterns to try and elicit durations, finally 
converging on the single pattern “lasted”. There 
were 1325 hits for this query in the BNC. (The 
public web interface to the BNC only shows 50 
random results at a time, so we had to iterate.) 
The retrieved hits (sentences and fragments of 
sentences) were then processed with components 
from the TARSQI toolkit (Verhagen et al. 2005) 
to provide automatic TimeML annotations. The 
TLINKs between events and times that were 
TIMEX3 DURATIONS were then extracted. 
These links were then corrected and validated by 
hand and then added to the OTC data to form an 
integrated corpus. An example from the BNC is 
shown in (9). 
 
(9) The <EVENT>storm</EVENT> 
<EVENT>lasted</EVENT> <TIMEX3 
VAL="P5D">five days</TIMEX3>.   
 
Next, the resulting data was subject to mor-
phological normalization in a semi-automated 
fashion to generate more counts for each event. 
Hyphens were removed, plurals were converted 
to singular forms, finite verbs to infinitival forms, 
and gerundive nominals to verbs. Derivational 
ending on nominals were stripped and the corre-
sponding infinitival verb form generated. These 
normalizations are rather aggressive and can lead 
to loss of important distinctions. For example, 
sets of events (e.g., storms or bombings) as a 
whole can have much longer durations compared 
to individual events. In addition, no word-sense 
disambiguation was carried out, so different 
senses of a given verb or event nominal may be 
confounded together.  
5 Results 
 
Number of 
durations 
Number of 
Events 
Normalized 
Form of 
Event 
26 1 lose 
16 1 earn 
10 1 fall 
9 1 rise 
8 1 drop 
7 2 decline, in-
crease 
6 4 end, grow, 
say, sell 
5 2 income, 
stop 
4 9 … 
3 17 … 
2 40 … 
1 176 … 
Table 1. Frequencies of event durations 
 
The resulting dataset had 255 distinct events 
with the number of durations for the events as 
shown in the frequency distribution in Table 1. 
The granularities found in news corpora such as 
OTC and mixed corpora such as BNC are domi-
26
nated by quarterly reports, which reflect the in-
fluence of specific information pinpointing the 
durations of financial events. This explains the 
fact that 12 of the top 13 events in Table 1 are 
financial ones, with the reporting verb say being 
the only non-financial event in the top 13.  
The durations for the most frequent event, rep-
resented by the verb to lose, is shown in Table 2. 
Most losses are during a quarter, or a year, be-
cause financial news tends to quantize losses for 
those periods. 
 
Duration Frequency
1 day (P1D) 1 
2 months (P2M) 1 
unspecified weeks (PXW) 1 
unspecified months (PXM) 1 
3 months (P3M) 9 
9 months (P9M) 3 
1 year (P1Y) 6 
5 years (P5Y) 1 
1 decade (P1Y) 1 
TOTAL 26 
Table 2. Distribution of durations for event 
 to lose 
 
Ideally, we would be able to generalize over 
the duration values, grouping them into classes. 
Table 3 shows some hand-aggregated duration 
classes for the data. These classes are ranges of 
durations. It can be seen that the temporal span 
of events across the data is dominated by 
granularities of weeks and months, extending 
into small numbers of years.  
 
Duration Class Count
<1 min 1 
5-15 min 12 
1-<24 hr 20 
1 day 14 
2-14 days 49 
1-3 months 120 
7-9 months 48 
1-6 years 97 
1 decade - < 1 century 30 
1-2 centuries 2 
vague (unspecified 
mins/days/months, continu-
ous present, indefinite fu-
ture, etc.) 
69 
Table 3. Distribution of aggregated durations 
 
   Interestingly, 67 events in the data correspond 
to ‘achievement’ verbs, whose main characteris-
tic is that they can have a near-instantaneous du-
ration (though of course they can be iterated or 
extended to have other durations). We obtained a 
list of achievement verbs from the LCS lexicon 
of (Dorr and Olsen 1997)
3
. Achievements can be 
marked as having durations of PTXS, i.e., an 
unspecified number of seconds. Such values 
don’t reinforce any of the observed values, in-
stead extending the set of durations to include 
much smaller durations. As a result, these hidden 
values are not shown in our data 
6 Estimating Duration Probabilities 
Given a distribution of durations for events 
observed in corpora, one of the challenges is to 
arrive at an appropriate value for a given event 
(or class of events). Based on data such as Table 
2, we could estimate the probability P(lose, P3M) 
≅ 0.346, while P(lose, P1D) ≅ 0.038, which is 
nearly ten times less likely. Table 2 reveals peak-
ing at 3 months, 6 months, and 9 months, with 
uniform probabilities for all others. Further, we 
can estimate the probability that losses will be 
during periods of 2 months, 3 months, or 9 
months as ≅ 0.46. Of course, we would prefer a 
much large sample to get more reliable estimates.  
One could also infer a max-min time range, 
but the maximum or minimum may not always 
be likely, as in the case of lose, which has rela-
tively low probability of extending for “P1D” or 
“P1E”.  Turning to earnings, we find that P(earn, 
P9M) ≅ 4/16 = 0.25, P(earn, P1Y) ≅ 0.31, but 
P(earn, P3M) ≅ 0.43, since most earnings are 
reported for a quarter. 
 
Figure 2. Distribution of durations 
of event to lose 
 
So far, we have considered durations to be 
discrete, falling into a fixed number of categories. 
These categories could be atomic TimeML DU-
                                                 
3
See  www.umiacs.umd.edu/ ~bonnie/ LCS_ Data-
base_Documentation.html. 
27
RATION values, as in the examples of durations 
in Table 2, or they could be aggregated in some 
fashion, as in Table 3. In the discrete view, 
unless we have a category of 4 months, the prob-
ability of a loss extending over 4 months is unde-
fined. Viewed this way, the problem is one of 
classification, namely providing the probability 
that an event has a particular duration category.  
The second view takes duration to be continu-
ous, so the duration of an event can have any 
subinterval as a value. The problem here is one 
of regression. We can re-plot the data in Table 2 
as Figure 2, where we have plotted durations in 
days on the x-axis in a natural log scale, and fre-
quency on the y-axis. Since we have plotted the 
durations as a curve, we can interpolate and ex-
trapolate durations, so that we can obtain the 
probability of a loss for 4 months. Of course, we 
would like to fit the best curve possible, and, as 
always, the more data points we have, the better.  
7 Possible Enhancements 
    One of the basic problems with this approach 
is data sparseness, with few examples for each 
event. This makes it difficult to generalize about 
durations. In this section, we discuss enhance-
ments that can address this problem. 
7.1 Converting points to durations 
More durations can be inferred from the OTC 
by coercing TIMEX3 DATE and TIME expres-
sions to DURATIONS; for example, if someone 
announced something in 1997, the maximum 
duration would be one year. Whether this leads 
to reliable heuristics or not remains to be seen.  
7.2 Event class aggregation 
A more useful approach might be to aggregate 
events into classes, as we have done implicitly 
with financial events. Reporting verbs are al-
ready identified as a TimeML subclass, as are 
aspectual verbs such as begin, continue and fin-
ish. Arriving at an appropriate set of classes, 
based on distributional data or resource-derived 
classes (e.g., TimeML, VerbNet, WordNet, etc.) 
remains to be explored. 
7.3 Expanding the corpus sample 
Last but not least, we could expand substan-
tially the search patterns and size of the corpus 
searched against. In particular, we could emulate 
the approach used in VerbOcean (Chklovski and 
Pantel 2004). This resource consists of lexical 
relations mined from Google searches. The min-
ing uses a set of lexical and syntactic patterns to 
test for pairs of verbs strongly associated on the 
Web in a particular semantic relation. For exam-
ple, the system discovers that marriage happens-
before divorce, and that tie happens-before untie. 
Such results are based on estimating the prob-
ability of the joint occurrence of the two verbs 
and the pattern. One can imagine a similar ap-
proach being used for durations. Bootstrapping 
of patterns may also be possible. 
8 Conclusion 
This paper describes the first steps in acquir-
ing metric temporal constraints for events. The 
work is carried out in the context of the TimeML 
framework for marking up events and their tem-
poral relations. We have identified a method for 
enhancing TimeML annotations with metric con-
straints. Although the temporal reasoning re-
quired to carry that out has been described in the 
prior literature, e.g., (Kautz and Ladkin 1991), 
this is a first attempt at lexical acquisition of 
metrical constraints. As a pilot study, it does 
suggest the feasibility of acquisition of metric 
temporal constraints from corpora. In follow-on 
research, we will explore the enhancements de-
scribed in Section 7. 
However, this work is limited by the lack of 
evaluation, in terms of assessing how valid the 
durations inferred by our method are compared 
with human annotations. In ongoing work, Jerry 
Hobbs and his colleagues (Pan et al. 2006) have 
developed an annotation scheme for humans to 
mark up event durations in documents. Once 
such enhancements are carried out, it will cer-
tainly be fruitful to compare the duration prob-
abilities obtained with the ranges of durations 
provided in that corpus.  
In future, we will explore both regression and 
classification models for duration learning. In the 
latter case, we will investigate the use of con-
structive induction e.g., (Bloedorn and Michalski 
1998). In particular, we will avail of operators to 
implement attribute abstraction that will cluster 
durations into coarse-grained classes, based on 
distributions of atomic durations observed in the 
data. We will also investigate the extent to which 
learned durations can be used to constrain 
TLINK ordering. 

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