Proceedings of the Workshop on Annotating and Reasoning about Time and Events, pages 9–16,
Sydney, July 2006. c©2006 Association for Computational Linguistics
Local Semantics in the Interpretation of Temporal Expressions
Robert Dale∗ and Paweł Mazur†
Centre for Language Technology
Macquarie University, NSW 2109, Sydney, Australia
∗Robert.Dale@mq.edu.au,
†mpawel@ics.mq.edu.au
Abstract
Work on the interpretation of temporal ex-
pressions in text has generally been pur-
sued in one of two paradigms: the for-
mal semantics approach, where an attempt
is made to provide a well-grounded theo-
retical basis for the interpretation of these
expressions, and the more pragmatically-
focused approach represented by the de-
velopment of the TIMEX2 standard, with
its origins in work in information extrac-
tion. The former emphasises formal ele-
gance and consistency; the latter empha-
sises broad coverage for practical applica-
tions. In this paper, we report on the de-
velopment of a framework that attempts
to integrate insights from both perspec-
tives, with the aim of achieving broad cov-
erage of the domain in a well-grounded
manner from a formal perspective. We
focus in particular on the development
of a compact notation for representing
the semantics of underspecified tempo-
ral expressions that can be used to pro-
vide component-level evaluation of sys-
tems that interpret such expressions.
1 Introduction
Obtaining a precise semantic representation for ut-
terances related to time is interesting both from a
theoretical point of view, as there are many com-
plex phenomena to be addressed, and for purely
practical applications such as information extrac-
tion, question answering, or the ordering of events
on a timeline.
In the literature, work on the interpretation of
temporal expressions comes from two directions.
On the one hand, work in formal semantics (see,
for example, (Pratt and Francez, 2001)) aims to
provide a formally well-grounded approach to the
representation of the semantics of these expres-
sions, but such approaches are difficult to scale
up to the broad coverage required for practical ap-
plications; on the other hand, work that has its
roots in information extraction, while it empha-
sizes broad coverage, often results in the use of
ad hoc representations. The most developed work
in this direction is focused around the TimeML
markup language1 (described, for example, in
(Pustejovsky et al., 2003) and in the collection
edited by Mani et al. (2005)).
Some work attempts to bring these two tradi-
tions together: notable in this respect is Schilder’s
(2004) work on temporal expressions in German
newswire text, and Hobbs and Pan’s (2004) work
on the axiomatisation in terms of OWL-Time. Sa-
quete et al. (2002) present an approach that views
time expressions as anaphoric references.
We take the view that an important step to-
wards a truly broad coverage yet semantically
well-founded approach is to recognize that there
is a principled distinction to be made between the
interpretation of the semantics of a temporal ex-
pression devoid of its context of use, and the fuller
interpretation of that expression when the context
is taken into account. The first of these, which we
refer to here as the local semantics of a tempo-
ral expression, should be derivable in a composi-
tional manner from the components of the expres-
sion; determining the value of the second, which
we refer to as the global semantics of the expres-
sion, may require arbitrary inference and reason-
1Note that with TimeML one can annotate not only tem-
poral expressions, but also events and relations between
events and temporal expressions.
9
ing. Such a distinction is implicit in other ac-
counts: Schilder’s (2004) use of lambda expres-
sions allows representation of partially specified
temporal entities, and the temporary variables that
Negri and Marseglia (2005) construct during the
interpretation of a given temporal expression cap-
ture something of the same notion.
Our proposal here is to reify this level of inter-
mediate representation based on a formalization in
terms of recursive attribute–value matrices. This
has two distinct advantages: it provides a conve-
nient representation of underspecification, and it
leads naturally to a compositional approach to the
construction of the semantics of temporal expres-
sions via unification. We also provide a compact
encoding of this representation that is essentially
an extension of the existing TIMEX2 representa-
tion for temporal expressions. This brings the ad-
vantages that (a) existing tools and machinery for
evaluation can be used to determine how well a
given implementation derives these local semantic
values; and (b) performance in the determination
of local semantics and global semantics can be
tested independently. To ensure breadth of cover-
age, we have developed our representation on the
basis of the 256 examples of temporal expressions
provided in the TIMEX2 guidelines (Ferro et al.,
2005). To make it possible to compare systems on
their performance in producing these intermediate
representations, we make available this set of ex-
amples annotated in-line with the representations
described here.
The rest of this paper is structured as follows. In
Section 2, we describe the architecture of DANTE,
a system which embodies our approach to the de-
tection and normalisation of temporal expressions;
in particular, we focus on the architecture em-
ployed in this approach, and on the particular lev-
els of representation that it makes use of. In Sec-
tion 3, we argue for an intermediate representa-
tional level that captures the semantics of temporal
expressions independent of the context of their in-
terpretation, and introduce the idea of using recur-
sive attribute–value matrices to represent the se-
mantics of temporal expressions. In Section 4, we
provide an encoding of these attribute–value ma-
trices in a compact string-based representation that
is effectively an extension of the ISO-based date–
time format representations used in the TIMEX2
standard, thus enabling easy evaluation of system
performance using existing tools. In Section 5
we discuss how the approach handles construc-
tions that contain one TIMEX embedded within
another. Finally, in Section 6 we draw some con-
clusions and point to future work.
2 The DANTE System
2.1 Processing Steps
In our work, our goal is very close to that for which
the TIMEX2 standard was developed: we want to
annotate each temporal expression in a document
with an indication of its interpretation, in the form
of an extended ISO-format date and time string,
normalised to some time zone. So, for example,
suppose we have the following italicised temporal
expression in an email message that was sent from
Sydney on Monday 10th April 2006:
(1) I expect that we will be able to present this
at the meeting on Friday at 11am.
In the context of our application, this temporal ex-
pression should be marked up as follows:
(2) <TIMEX2 VAL="2006-04-14T01:00GMT">
Friday at 11am</TIMEX2>
We have to do three things to achieve the desired
result:
• First, we have to detect the extent of the tem-
poral expression in the text. We refer to
this process as temporal expression recog-
nition.
• Then, we have to use information from the
document context to turn the recognized ex-
pression into a fully specified date and time.
We refer to this as temporal expression in-
terpretation.
• Finally, we have to normalise this fully spec-
ified date and time to a predefined time zone,
which in the case of the present example is
Greenwich Mean Time. We refer to this as
temporal expression normalisation.2
2Note that this third step is not required by the TIMEX
guidelines, but is an additional requirement in the context of
our particular application. This also means that our use of the
term ‘normalisation’ here is not consistent with the standard
usage in the TIMEX context; however, we would argue that
our distinction between interpretation and normalisation de-
scribes more accurately the nature of the processes involved
here.
10
We observe that, at the time that the extent of a
temporal expression within a text is determined, it
is also possible to derive some semantic represen-
tation of that expression irrespective of the wider
context within which it needs to be interpreted:
for example, by virtue of having recognized an
occurrence of the string Friday in a text, we al-
ready know that this is a reference to a specific day
of the week. Most existing systems for the inter-
pretation of temporal expressions probably make
use of such a level of representation. Schilder’s
(2004) approach captures the semantics here in
terms of a lambda expression like λxFriday(x);
Negri and Marseglia (2005) capture information
at this stage of processing via a collection of tem-
porary attributes.
In our system, each of the three steps above cor-
responds to a distinct processing component in the
DANTE system architecture. These components
communicate in terms of a number of distinct rep-
resentations, which we now describe.
2.2 The Text
This level of representation corresponds simply to
the strings that constitute temporal expressions in
text. These are understood to be linguistic con-
structions whose referents are entities in the tem-
poral domain: either points in time, or periods of
time. In the above example, the text representation
is simply the string Friday at 11am.
2.3 Local Semantics
We use this term to refer to a level of representa-
tion that corresponds to the semantic content that
is derivable directly from the text representation;
in the case of temporal expressions that are argu-
ments to prepositions, this includes the interpreta-
tion of the preposition. Such representations are
often incomplete, in that they do not denote a par-
ticular point or period on the time line; however,
usually they do partially specify points or peri-
ods, and constrain the further interpretation of the
string.
2.4 In-Document Semantics
We use this term to refer to the fully explicit in-
terpretation of the text string, to the extent that
this can be determined from the document itself,
in conjunction with any metadata associated with
the document. This level of representation corre-
sponds to the information encoded in the attributes
of the TIMEX2 tag as defined in the TIMEX
guidelines.
2.5 Global Semantics
The TIMEX guidelines do not have anything to
say beyond the representation described in the pre-
vious section. In our application, however, we
are also required to normalise all temporal expres-
sions to a specific time zone. This requires that
some further temporal arithmetic be applied to the
semantics of the found expressions. To calculate
this, we simply have to determine the difference
between the time zone of the document containing
the temporal reference and the target time zone,
here Greenwich Mean Time. The document may
not always be explicitly marked with information
about the time zone of its creation; in such cases,
this has to be inferred from information about the
location of the author or sender of the message.
3 Representing Temporal Expressions
In this section, we describe a conceptualisation of
the semantics of temporal expressions in terms of
recursive attribute–value matrices.
3.1 Temporal Entities
As is conventional in this area of research, we view
the temporal world as consisting of two basic types
of entities, these being points in time and dura-
tions; each of these has an internal hierarchical
structure. We can represent these in the following
manner:3









point
TIMEANDDATE






TIME


HOUR 15
MINS 00
SECS 00


DATE



DAY
bracketleftbigg
DAYNAME D4
DAYNUM 13
bracketrightbigg
MONTH 5
YEAR 2006









ZONE Z









The example above corresponds to the semantics
of the temporal expression 3pm Thursday 13th
May 2006 GMT; in the ISO date and time format
used in the TIMEX2 standard, this would be writ-
ten as follows:
(3) 2006-05-13T15:00:00Z
3For reasons of limitations of space, we will ignore dura-
tions in the present discussion; their representation is similar
in spirit to the examples provided here.
11
Each atomic feature in the attribute–value struc-
ture thus corresponds to a specific position in the
ISO format date–time string.
3.2 Underspecification
Of course, very few temporal expressions in text
are fully specified. The attribute–value matrix rep-
resentation makes it easy to represent the con-
tent of underspecified temporal expressions. For
example, the content of the temporal expression
Thursday in a sentence like We will meet on
Thursday can be expressed as follows:


point
TIMEANDDATE
bracketleftbigg
DATE
bracketleftBig
DAY
bracketleftbig
DAYNAME D4bracketrightbig
bracketrightBigbracketrightbigg


On the other hand, a reference to 13th May in a
sentence like We will meet on 13th May has this
representation:



point
TIMEANDDATE
bracketleftBigg
DATE
bracketleftBigg
DAY
bracketleftbig
DAYNUM 13bracketrightbig
MONTH 05
bracketrightBiggbracketrightBigg



In the cases just described, the semantic repre-
sentation corresponds to the entire temporal noun
phrase in each case. The same form of represen-
tation is easy to use in a compositional seman-
tic framework: each constituent in a larger tem-
poral expression provides a structure that can be
unified with the structures corresponding to the
other constituents of the expression to provide a
semantics for the expression as a whole. The val-
ues of the atomic elements in such an expression
come from the lexicon; multiword sequences that
are best considered atomic (such as, for example,
idioms) can also be assigned semantic representa-
tions in the same way. The value of a composite
structure is produced by unifying the values of its
constituents. Unifying the two structures above,
for example, gives us the following representation
for Thursday 13th May:4




point
TIMEANDDATE

DATE

DAY
bracketleftbigg
DAYNAME D4
DAYNUM 13
bracketrightbigg
MONTH 05








So, these structures provide a convenient repre-
sentation for what we have referred to above as the
4For simplicity here we assume that the syntactic structure
of such an expression is captured by the context-free grammar
rule ’NP→NP NP’. Other treatments are possible.
local semantics of a temporal expression, and cor-
respond to the output of the recognition stage of
our processing architecture.
3.3 Interpretation
We can now define the task of interpretation in
terms of the content of these structures. We as-
sume a granularity ordering over what we might
think of as the defining attributes in a temporal
representation:
(4) year > month > daynum > hour >
minute > second
These are, of course, precisely the elements that
are represented explicitly in an ISO date–time ex-
pression.
Interpretation of a partially specified temporal
expression then requires ensuring that there is a
value for every defining attribute that is of greater
granularity than the smallest granularity present in
the partially specified representation. We refer to
this as the granularity rule in interpretation.
In the case of the example in the previous sec-
tion, the granularity rule tells us that in order to
compute the full semantic value of the expression
we have to determine a value for YEAR, but not
for HOUR, MINS or SECS. This interpretation
process may require a variety of forms of reason-
ing and inference, as discussed below, and is quali-
tatively different from the computation of the local
semantics.
In the context of our application, a third stage,
the normalisation process, then requires taking the
further step of adding a ZONE attribute with a spe-
cific value, and translating the rest of the construc-
tion into this time zone if it represents a time in
another time zone.
4 A Compact Encoding
The structures described in the previous section
are relatively unwieldy in comparison to the sim-
ple string structures used as values in the TIMEX
standard. To enable easy evaluation of a sys-
tem’s ability to construct these intermediate se-
mantic representations, we would like to use a rep-
resentation that is immediately usable by existing
evaluation tools. To achieve this goal, we define
a number of extensions to the standard TIMEX2
string representation for values of the VAL at-
tribute; these extensions allow us to capture the
range of distinctions we need. To save space, we
12
also use these representations here to show the
coverage of the annotation scheme that results.
In our implementation, we represent the local
semantic content via an additional set of attributes
on TIMEX elements that mirrors exactly the set of
attributes used by the TIMEX2 standard: thus we
have T-VAL, T-ANCHOR VAL and so on. This
means that markup applied to a text distinguishes
intermediate and final semantic values, making it
possible to evaluate on just intermediate values,
just final values, or both. In what follows, we will
also use these intermediate attributes to make clear
which level of representation is under discussion.
4.1 Partially Specified Dates and Times
As noted above, many references to dates or times
are not fully specified in a text, with the result that
some parts will have to be computed from the con-
text during the interpretation stage. Typical exam-
ples are as follows:
(5) a. We’ll see you in November.
b. I expect to see you at half past eight.
In the recursive attribute–value notation intro-
duced above, the missing information in each case
corresponds to those features that are absent in the
structure as determined by the granularity rule in-
troduced in Section 3.3.
In our string-based notation, we use lowercase
xs to indicate those elements for which a value
needs to be found, but which are not available at
the time the local semantics are computed; and
we capture the granularity requirement by omit-
ting from the string representation those elements
that do not require a value.5 Table 1 provides a
range of examples that demonstrate various forms
of underspecification.
A lowercase x thus corresponds to a variable.
By analogy with this extension, we also use a low-
ercase t instead of the normal ISO date–time sep-
arator of T to indicate that the time may need fur-
ther specification: consider the third and fourth ex-
amples in Table 1, where it is not clear whether the
time specified is a.m. or p.m.
For partially-specified dates and times, the
string-based encoding thus both captures the local
5Note that this does not mean the same thing as the use
of an uppercase X in the TIMEX2 guidelines: an uppercase
X means effectively that no value can be determined. Of
course, if no value can be found for a variable element during
the interpretation process, then the corresponding lowercase
x will be replaced by an uppercase X.
String Representation
9 pm xxxx-xx-xxT21
11:59 pm xxxx-xx-xxT23:59
eleven in the morning xxxx-xx-xxT11:00
ten minutes to 3 xxxx-xx-xxt02:50
15 minutes after the hour xxxx-xx-xxtxx:15
the nineteenth xxxx-xx-19
January 3 xxxx-01-03
November xxxx-11
summer xxxx-SU
’63 xx63
the ’60s xx6
Table 1: Underspecified Dates and Times
semantic content of the temporal expression, and
provides a specification of what information the
interpretation process has to add. If the temporal
focus is encoded in the same form of representa-
tion, then producing the final interpretation is of-
ten a simple process of merging the two structures,
with the values already specified in the interme-
diate representation taking precedence over those
in the representation of the temporal focus. Ex-
pressions involving references to named months
require a decision as to whether to look for the
next or previous instance of the month, typically
determined by the tense of the major clause con-
taining the reference.
4.2 Representing Weekdays
In recognition that the year-based calendar and
the week-based calendar are not aligned, our in-
termediate representation embodies a special case
borrowed from the TIMEX2 notation for days of
the week that require context for their specifica-
tion. Consider example (6a), uttered on Friday
14th April 2006; the intermediate semantic repre-
sentation is provided in example (6b), and the final
interpretation is provided in example (6c).
(6) a. We left on Tuesday.
b. T-VAL="D2"
c. VAL="2006-04-11"
This is not as convenient as the ISO-like encod-
ing, and requires special case handling in the inter-
preter; however, a more comprehensive single rep-
resentation would require abandoning the ISO-like
encoding and the benefits it brings, so we choose
to use the two formats in concert.
13
String Representation
today +0000-00-00
tomorrow +0000-00-01
yesterday −0000-00-01
five days ago −0000-00-05
last month −0000-01
last summer −0001-SU
two weeks ago −0000-W02
this weekend +0000-W00-WE
this year +0000
three years ago −0003
the next century +01
Table 2: Relative dates in ISO-like format.
The same notation supports references to parts
of specific days, as presented in example (7).
(7) a. We left on Tuesday morning.
b. T-VAL="D2TMO"
c. VAL="2006-04-11TMO"
4.3 Relative Dates and Times
A relative date or time reference is one that re-
quires a calendar arithmetic operation to be carried
out with respect to some temporal focus in the text.
Typical examples are as follows:
(8) a. We’ll see him tomorrow.
b. We saw him last year.
c. We’ll see him next Thursday.
d. We saw him last November.
We distinguish three subtypes here: relative dates
and times whose local semantics can be expressed
in an ISO-like format; relative references to days
and months by name; and less specific references
to past, present and future times.
For the first of these, we extend the ISO format
with a preceding ‘+’ or ‘−’ to indicate the direc-
tion from the current temporal focus. Some exam-
ples of dates are provided in Table 2, and some ex-
amples of date–time combinations are provided in
Table 3. Note the both the date and time elements
in a relative reference can be independently either
absolute or relative: compare the representations
for in six hours time and at 6am today.
This representation leads to a very intuitive
coordinate-based arithmetic for computing the fi-
nal semantic interpretation of a given expression:
the interpreter merely adds the temporal focus and
String Representation
sixty seconds later +0000-00-00T+00:00:60
five minutes ago +0000-00-00T−00:05
in six hours time +0000-00-00T+06:00
at 6 a.m. today +0000-00-00T06:00
last night −0000-00-01TNI
Table 3: Relative times in ISO-like format.
String Representation
last Monday <D1
next Wednesday >D3
last March <M03
next March >M03
Table 4: Relative References to Days and Months
the intermediate value element-by-element from
the smallest unit upwards, using carry arithmetic
where appropriate.
Relative references to named days and months
require a different treatment, in line with the no-
tation introduced in Section 4.2. Table 4 shows
the intermediate values used for a number of such
expressions.
A further variation on this notation also allows
us to specify a local semantics for expressions like
the first Tuesday in temporal expressions like the
first Tuesday in July, or like the last year in the last
year of the millenium; see Table 5. To produce
final interpretations of these, the interpreter has to
construct the set of elements that correspond to the
head noun (for example, a list of the ISO dates that
correspond to the Tuesdays in a given month), and
then select the nth element from that set.
5 Handling Embedded Constructions
The TIMEX specification allows for the embed-
ding of one TIMEX within another. Consider an
example like the following:
String Representation
the first Tuesday 1D2
the second day 2D
the last Tuesday $D2
the last day $D
Table 5: Ordinally-specified Elements
14
Figure 1: The syntactic structure of an embedded
TIMEX
(9) <TIMEX2>the first Tuesday
in<TIMEX2>July</TIMEX2></TIMEX2>
The bulk of the embedded TIMEXs provided as
examples in the TIMEX guidelines are, like this
one, of the form [NP PP], where the head NP
contains a TIMEX, and the PP contains another
TIMEX that is modified by the head NP. Syntac-
tically, these structures are of the form shown in
Figure 1.
For our purposes, it is convenient to first think
of these structures as consisting of three, rather
than two, TIMEXs, corresponding to the three
subscripted NP nodes in this tree. The outermost
TIMEX, corresponding to NP0, is the one whose
value we are ultimately interested in; this is com-
puted by combining the semantics of the two con-
stituent TIMEXs, corresponding to NP1 and NP2,
and the preposition indicates how this combination
should be carried out.
Structurally, the recognizer may first determine
that there are two separate TIMEXs here:
(10) <TIMEX2>the first
Tuesday</TIMEX2> in
<TIMEX2>July</TIMEX2>
Each of these TIMEXs can be given the appro-
priate local semantics by the recognizer; the rec-
ognizer then reorganizes this structure to mirror
the embedding required by the TIMEX guidelines,
to produce the structure shown in example (10)
above; effectively, NP1 disappears as a distinct
constituent, and its intermediate semantics are in-
herited by NP0.
We then leave it to the interpreter to combine the
intermediate semantics of NP0 with the intermedi-
ate semantics of NP2 to produce a final semantics
for NP0: schematically, we have
(11) NP0(VAL) = NP0(T-VAL) ∗ NP2(T-VAL)
where ‘∗’ is the combinatory operation that corre-
sponds to the preposition used. The operation re-
quired is specified by the recognizer as the value of
the temporary attribute T-REL, which represents
the semantics of the preposition.
The following three examples demonstrate a va-
riety of possibilities, showing both the intermedi-
ate (T-VAL) and final (VAL) semantic interpreta-
tions in each case:
(12) <TIMEX2 VAL="1999" T-VAL="$Y"
T-REL="OF">the last year of
<TIMEX2 VAL="1" T-VAL="+0">this
millennium</TIMEX2></TIMEX2>
(13) <TIMEX2 VAL="1998-01-31"
T-VAL="$D" T-REL="OF">the last
day of <TIMEX2 VAL="1998-01"
T-VAL="xxxx-01">January
</TIMEX2></TIMEX2>
(14) <TIMEX2 VAL="1998-01-31"
T-VAL="$D" T-REL="OF">the last
day of <TIMEX2 VAL="1998-01"
T-VAL="1998-01">January
1998</TIMEX2></TIMEX2>
Note that, when the embedded TIMEX is fully
specified, as in the last example here, it would be
possible for the recognizer to calculate the final
value of the whole expression; however, for con-
sistency we leave this task to the interpreter.
The semantics of the indicated T-REL depend
on the types of its arguments. In the cases above,
for example, the operation is one of selecting an
ordinally-specified element of a list; but where the
entity is a period rather than a point, as in the first
six months of 2005, the operation is one of delim-
iting the period in question.
Of course, other forms of embedding are pos-
sible. In appositions, the syntactic structure can
be thought of as [NP NP]; as in the case of em-
bedded PPs, the TIMEX representation effectively
promotes the semantics of the first NP to be the se-
mantics of the whole. Again, we show both VAL
and T-VAL values here, and the relevant T-REL.
(15) <TIMEX2 VAL="1998-12-29"
T-VAL="xxxx-xx-xx"
15
T-REL="EQUAL">my birthday,
<TIMEX2 VAL="1998-12-29"
T-VAL="xxxx-12-29">December
twenty-ninth</TIMEX2></TIMEX2>
(16) <TIMEX2 VAL="196" T-VAL="196"
T-REL="EQUAL">the 1960s, <TIMEX2
VAL="196" T-VAL="PXD">the days of
free love</TIMEX2></TIMEX2>
Here, the fact that the T-REL is EQUAL causes
the interpreter to combine the values of the two
TIMEXs, with points taking precedence over du-
rations.
6 Conclusions
In this paper, we have argued that, in the context of
interpreting temporal expressions, there is value in
identifying a level of semantic representation that
corresponds to the meaning of these expressions
outside of any particular document context. This
idea is not in itself new, and many existing sys-
tems appear to make use of such representations.
However, we have proposed that this level of rep-
resentation be made explicit; and by providing an
encoding of this level of representation that is an
extension of the existing TIMEX2 annotations in
terms of element attributes and their values, we
make it possible to assess the performance of sys-
tems with respect to intermediate values, final val-
ues, or both, using standard evaluation tools.
We have developed the representation described
here on the basis of the set of 265 examples pro-
vided in the TIMEX2 guidelines (Ferro et al.,
2005), and this set of annotated examples is avail-
able to the community.6 The approach described
here is implemented in DANTE, a text process-
ing system which produces normalised values for
all TIMEXs found in a document. The recogni-
tion component of the system, which constructs
the intermediate representations described here, is
implemented via just over 200 rules written in the
JAPE language:7 time expressions are thus recog-
nised using finite state patterns, but we then ap-
ply a syntactic check, using the Connexor parser,
to ensure that we have identified the full extent of
each temporal expression, appropriately extending
the extent when this is not the case.
6See www.clt.mq.edu.au/timex.
7JAPE is provided as part of the GATE tools (Cunning-
ham et al., 2002).
We are currently testing this representation and
its means of derivation against the data from the
2004 TERN competition. Our results are broadly
comparable to those achieved by other systems
(for example, Chronos or TempEx), though they
can not be compared directly since the reported
evaluations at the TERN competition use data
which are not public and therefore not available
to us.
7 Acknowledgements
We acknowledge the support of the Defence Sci-
ence and Technology Organisation in carrying out
the work described here.

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