An algorithm for efficiently generating summary paragraphs using
tree-adjoining grammara0
Bruce Eddy, Diana Bental and Alison Cawsey
Department of Computing and Electrical Engineering
Heriot-Watt University
Edinburgh
EH14 4AS
UK
a1 ceebde1,diana,alison
a2 @cee.hw.ac.uk
Abstract
We present an algorithm which im-
proves the efficiency of a search for the
optimally aggregated paragraph which
summarises a flat structured input spec-
ification. We model the space of possi-
ble paraphrases of possible paragraphs
as the space of sequences of composi-
tions of a set of tree-adjoining grammar
(TAG) elementary trees. Our algorithm
transforms this to a set with equivalent
paraphrasing power but better compu-
tational properties. Also, it identifies an
explicit mapping between input propo-
sitions and their possible surface reali-
sations.
1 Introduction
Summarisation of simply structured data as short
natural language paragraphs has recently been
a focus of interest. Shaw (1998) and Bental
et al. (1999) looked at generating text from
database records. Robin and McKeown (1996)
summarised quantitative data. Shaw’s examples
were drawn from patient medical records; Bental
et al’s from online resource cataloging informa-
tion. A requirement common to all these studies
has been to produce aggregated (Reape and Mel-
lish, 1999) text.
Also in all these studies, the structure of the
input data used was fairly flat. In particular, in
(Shaw, 1998) and (Bental et al., 1999) each record
a3 This work is supported by EPSRC grant GR/M23106.
is associated with a particular entity (e.g. a patient
or an online resource) and is essentially a list of
attribute-value pairs. We refer to pairs as fields,
and to attributes as field names. The relationship
between a value and the entity with which it is
associated is specified by the field name. Most
field names represent “is a” or “has a” relation-
ships and hence most values represent facts about
the entity. Slightly more complex structure may
also be coerced into this form, but we will focus
on this simple case.
For our application (summarising data about
educational resources), we additionally assume
that we are required to be able to summarise any
subset of fields from a given record, and that our
summary must include every member of that sub-
set. The challenge from this sort of summarisa-
tion is to devise a system which satisfies two po-
tentially incompatible constraints. First, it must
be flexible enough to model, for any combina-
tion of fields, the optimally aggregated paragraph
which expresses them. Second, despite the very
large search space that such flexibility probably
implies, it must be capable of finding that para-
graph in a reasonable time.
The contribution the present work makes is a
set of algorithms which prune this search space.
This space is specified in terms of compositions
of elementary trees of a tree-adjoining grammar
(TAG) (Joshi, 1986). The first transforms a TAG
into a lexicalised version of itself which has bet-
ter computational properties with respect to sum-
marising a record. The second removes those
parts of a TAG which are redundant with respect
to summarising a particular record. The third
identifies an explicit mapping from each field to
its possible surface realisations, and hence allows
a desirable surface form to be chosen for each
field. Our partial implementation of these algo-
rithms has produced some promising results.
The rest of the paper is organised as follows. In
section 2 we discuss the problem, our approach
to modelling it, and characteristics of the search
space implied by our approach. In section 3 we
present our algorithms for searching this space.
In section 4 we summarise and discuss.
2 Searching for concise, coherent
paragraphs
2.1 Aggregation is a global optimisation
problem
Our aim is to generate paragraphs which are well
aggregated. This notion should be defined in
terms of conciseness and coherence, which terms
are not formally definable. However, some rea-
sonable approximation to them can be achieved
by specifying preferences for certain types of syn-
tactic constructions over others (Robin and McK-
eown, 1996), possibly by giving each generat-
able construction a score which reflects its rela-
tive preferability. We then define the best aggre-
gated paragraph to be that which achieves the best
sum of its constituent constructions’ preference
scores.
Robin and McKeown’s (1996) system,
STREAK, generates aggregated, fact-rich sen-
tences. It adds facts in order of the preferability
of their best possible realisation. It revises its
syntactic choices every time an extra fact is
aggregated. This is computationally expensive,
and makes multi-sentence generation by the same
means prohibitively slow. They do suggest how
to deal with this when many of the facts occur
in fixed positions, but this is not the case in our
corpus.
CASPER (Shaw, 1998) delays syntactic
choices until after it has decided where sentence
boundaries should fall. It thereby gains computa-
tional efficiency at the cost of its sentences being
less optimal aggregations.
Our algorithms are an attempt to avoid these
problems and to achieve greater efficiency by pre-
compiling detailed syntactic decisions, the results
of which we store in the form of explicit map-
pings from fields to surface forms. At generation
time, we search for the optimal selection of reali-
sations. This approach deviates from the pipeline
architecture of NLG systems which, it has been
observed, is not wholly suited to the generation
of aggregated texts.
The first author to discuss this was Meteer
(1992), who showed that the microplanning stage
of the pipeline is constrained by surface realisa-
tion in two ways. First, a microplan must be real-
isable in the target language; second, a realisable
microplan must make best use of the capacities
the target language for concise expression.
More generally, in order to generate aggregated
text, constraints imposed by and opportunities af-
forded by the surface form may be taken into ac-
count at any stage in the pipeline. Reape and Mel-
lish (1999) provided examples of different sys-
tems each of which takes aggregation decisions
at a different stage. It may not be easy to deter-
mine what effect a decision taken at an early stage
will have at the surface; and decisions taken at one
stage may preclude at a later stage a choice which
results in a more aggregated surface form. Simi-
larly, it may not be easy to make a decision at an
early stage which makes best use of the surface
possibilities.
Consider the examples of figures 1 and 2. Both
summarise the same set of fields; figure 2 sum-
marises additionally the field “subject = science”.
Both paragraphs summarise their fields in the
most concise and coherent manner possible (al-
though this is, of course, a subjective judgement).
Note that they treat the fields they have in com-
mon differently with respect to ordering and dis-
tribution between the sentences.
Various types of constraints cause this. Syn-
tactic constraints include: “science” may be used
as an adjective to pre-modify “lesson plan”. Se-
mantic constraints include: “Constellations” lasts
4 hours, but ProLog does not. Stylistic constraints
include: ‘Maureen Ryff wrote ...’ is preferable to
‘... was written by Maureen Ryff’. We suggest, as
do Stone and Doran (1997), that integrating these
constraints simultaneously is more efficient then
pipelining them. We additionally suggest that rep-
resenting these constraints in a unified form can
provide further efficiency gains.
“Constellations” is a 4-hour lesson plan pub-
lished by online provider ProLog. Maureen
Ryff wrote it for small group teaching.
Figure 1: A paragraph which summarises the set
of fields of figure 3 in an aggregated manner.
“Constellations” is a science lesson plan
which lasts 4 hours. Maureen Ryff wrote
it for small group teaching and ProLog, an
online provider, is its publisher.
Figure 2: A well aggregated paragraph which
summarises the set of fields of figure 1, together
with field subject = “science”. Notice the non-
linear effect the addition of a single extra propo-
sition can have on the structure of the paragraph.
2.2 Modeling paragraphs with TAG
Our approach uses, as its primary representation,
TAG formalism extended to include unification
based feature structures (Vijay-Shanker and Joshi,
1991). Joshi (1986) describes the advantages
TAG possesses as a syntactic formalism for NLG.
In generation, the TAG model has usually been
applied to generating clauses and sentences. Re-
cently, Webber et al. (1999) outlined the benefits
of modelling longer strings of text by the same
means.
The most important characteristic of TAG for
our purposes is the local definability of dependen-
cies: constraints between the nodes of elemen-
tary trees are preserved under adjoinings which
increase the distances between them. For exam-
ple, in the sentence fragment “Springer published
...”, which might be modelled by a single initial
tree, the object is constrained to be some entity
published by Springer. If an adjunction is made so
that the fragment becomes “Springer, the largest
publishing company in Europe, published ...”, this
constraint is undisturbed.
Our approach presupposes the existence of a
TAG whose string set is exactly those paragraphs
which are comprehensible summaries of subsets
of fields. We do not discuss the creation of such
a TAG here. We have made progress with design-
ing one; we believe that it is the flatness of the
input data which makes it possible.
Let us restate the problem somewhat more for-
mally. Suppose that we have a set a4a6a5 of a7 fields
whose values we may be required to express.
Suppose that for every a8a10a9a11a4 a5 there is a template
which expresses a8 . A template is a paragraph in
which certain words are replaced by slots. A slot
is a reference to a field-name. A template a12 ex-
presses a set of fields a8 if the name of every ele-
ment of a8 is referenced by a slot, and every slot
refers to an element of a8 . We say thata12 expresses
a8 and that the resulting paragraph is the expres-
sion of a8 with respect to a12 . See figure 3.
Let a13a15a14a16a8a18a17 denote the template which “best” ex-
presses some a8 a9a19a4a6a5 . Suppose also that we
have a TAG a12a20a5 with string set a21a22a14a23a12a24a5a25a17 such that
a26
a13a15a14a16a8a18a17a20a27a28a8a29a9a11a4a30a5a32a31a33a9a34a21a35a14a23a12a24a5a25a17 . The creation of a12a24a5 is
not discussed here. Every string in a21a35a14a23a12a20a5a25a17 is the
yield of a36 , some derived tree of a12a20a5 .
Each of a TAG’s derived trees is represented
by a unique derivation tree. Typically a deriva-
tion tree represents several (differently ordered)
sequences of compositions of (the same set of)
elementary trees, all of which result in the same
derived tree.
Hence, a derived tree a36 of a TAG a12 with el-
ementary trees a37 is the result of some sequence
of compositions of the elements of a37 which is
equivalent to some derivation tree a38 . We write
a36a40a39a41a38a42a14a43a37a44a17 or just a36a45a39a46a38a15a14a23a12a47a17 , Hence, our problem
is, given a12a24a5 and some a8a40a9a48a4a30a5 , find some a38 such
that a38a42a14a23a12a24a5a49a17a50a39a46a13a51a14a16a8a18a17 .
There are two parts to the problem of finding
a13a15a14a16a8a18a17 . First we must recognise a13a51a14a16a8a18a17 , which we
may do, as described in section 2.1, by defining
a13a15a14a16a8a18a17 to be the paragraph which achieves the best
sum of its constituent constructions’ preference
scores. Second, since the search space of deriva-
tion trees grows exponentially with the number of
trees in the grammar, we must find its derivation
in a reasonable amount of time.
For each field to be expressed, the slot which
refers to it may be expressed by means of one of
several different syntactic constructions. So each
slot will contribute one of several possible pref-
erence scores to the paragraph in which it occurs,
depending on the syntactic form in which it is re-
alised. However, the syntactic forms by which a
slot slot slot slotis a published by 
slot slot slot. wrote it for .
Lesson planType
Title "Constellations"
Template Fields
Field name Value
Duration 4 hours
small group teaching
Maureen Ryff
ProLog
online provider
Pedagogy.TeachingMethods
Creator.PersonalName
Publisher.Name
Publisher.Role
Figure 3: A template which expresses a set of fields. The curves indicate the field name to which each
slot refers. The fields’ expression with respect to the template is the paragraph in figure 1.
slot may be expressed are an implicit property of
the grammar: it requires search to discover what
they are, and then further search to find their op-
timal configuration.
2.3 The search space
We model possible paraphrases with a TAG, the
paraphrases being the elements of its string set.
The nodes in the search space are TAG derivation
trees, and an arc from a52 to a53 represents the com-
position into the partial derivation corresponding
to a52 , of an elementary tree, with result the par-
tial derivation corresponding to a53 . The size of
the search space may be reduced by collapsing
certain paths in it, and by pruning certain arcs.
These operations correspond to specific lexicali-
sation and the removal of redundant trees from
the grammar respectively.
A tree in the grammar is redundant if it cannot
contribute to a paragraph which expresses the re-
quired fields; or if it cannot contribute to a ‘best’
paragraph which expresses those fields. We will
expand on redundancy removal after describing
the specific lexicalisation algorithm. The spe-
cific lexicalisation algorithm converts a TAG into
a specific-lexicalised version of itself, in which
certain paths in the search space, which it can
be known will be used in any derivation, are col-
lapsed.
3 The algorithms
3.1 Specific lexicalisation: creating a clausal
lexicon
We begin by introducing some notation, and
defining some properties of TAGs and their ele-
mentary trees. Let a54a43a12a56a55a58a57a60a59 denote a12 , a TAG, and
a57 , some set of elementary trees, not necessarily
in a12 . A leaf node of an elementary tree may be
labelled as a slot, which is a special case of the
lexical anchor.
An elementary tree is specific-lexicalised if at
least one1 of its leaf nodes is a slot. An elemen-
tary tree is a61 -lexicalised if it is specific-lexicalised
or if it has no substitution nodes or foot nodes.
A TAG is specific-lexicalised if all its elementary
trees are a61 -lexicalised.2
Given some a54a62a12a56a55a58a57a63a59 , let a64 be an element of
a12a10a65a66a57 which is not specific-lexicalised. Let a67
be an elementary tree of a12 . Suppose that there is
some composition of a67 into a64 and that the resulting
tree is specific-lexicalised. Then we say that a64 is
single-step-lexicalisable in a54a23a12a56a55a58a57a60a59 . We call any
such resulting tree a single-step-lexicalisation at
a7 of a64 in a54a23a12a56a55a58a57a60a59 , where a7 is the node at which the
composition occurred.
We now present the algorithm for
our transformation Specific Lexicalisa-
tion.
1: a12a68a39a69a12a20a5 is some TAG, a57a70a39a68a71a70a39a41a72 .
2: repeat
3: Add a54a23a12a56a55a58a57a63a59 to a71 .
4: for all a64a74a73a75a12a66a65a76a57 do
5: if a64 is sinlge-step lexicalisable in a54a62a12a77a55a58a57a60a59
1This is an important parameter. It specifies how many
slots each elementary tree in the transformed TAG may have
(and consequently how many times the “derivation tree” of
each of these trees branches).
2This definition is compatible with that used in the liter-
ature. A TAG is lexicalised (Joshi and Schabes, 1991) if it is
specific-lexicalised according to this definition. The impli-
cation does not necessarily hold in reverse.
then
6: if a64a78a73a79a12 then
7: Remove a64 from a12 .
8: Add a64 to a57 .
9: end if
10: For some node of a64 , a7 , add all the
single-step-lexicalisations at a7 of a64 in
a54a62a12a77a55a58a57a60a59 , to a12 .
3
11: end if
12: end for
13: until a54a23a12a56a55a58a57a60a59a78a73a80a71
14: a12 is a specific-lexicalisation4 of a12a24a5 .
To illustrate this procedure, we have provided
some figures. Consider the TAG a12a30a81 , whose el-
ementary trees are shown in figure 4. We have
chosen, for reasons of space and simplicity, not to
show the feature structures attached to each node
of these trees. Their approximate form can per-
haps be deduced by examination of the templates
modelled by a12a6a81 , shown in figure 6. A specific lex-
icalised version of the TAG, a12a20a82 is shown in figure
5. We have named each elementary tree in a12a20a82 by
concatenating the names of its constituents from
a12 a81 . The templates generated by a12 a81 (and hencea12 a82 )
are shown in figure 6.
3.2 Redundancy removal
We can further remove redundancy in a specific-
lexicalisation, a12 , of some TAG. Let a54a23a12a56a55a58a57a63a59 be
a pair as in the previous section. The following
three subsets of the elementary trees of a12 are re-
dundant. First, those trees a64a83a73a68a12 which are not
rooted on the distinguished symbol and for which
there is no a67a84a73a41a12a48a65a63a57 such that a64 can be com-
posed into a67 . Second, those a64a44a73a66a12 which have a
substitution node into which no a67a18a73a75a12a75a65a85a57 can be
substituted. Third, those a64a35a73a80a12 such that for each
tree a86 which is the result of the composition of
some a67a85a73a79a12a87a65a88a57 into a64 , a86a89a73a90a12a91a65a88a57 . Our program
3Note that there is a choice at this step. Our implemen-
tation of this algorithm chooses a92 such that the number of
single-step-lexicalisations at a92 is maximised. But different
choices result in a transformed grammar with different prop-
erties.
4We claim that a specific-lexicalisation of a TAG is in-
deed specific-lexicalised. Note that there does not neces-
sarily exist a specific-lexicalisation of a TAG. For certain
pathological examples of TAGs, the algorithm does not ter-
minate. Note also that if a specific-lexicalisation exists, it is
not necessarily unique. Further work is required to discover
the properties of the various specific-lexicalisations in these
cases.
which implements the algorithm in fact removes
these redundancies, not only after completion, but
also after every iteration.
3.3 Finding the (approximately) global
optimum
Specific-lexicalisation causes the (previously im-
plicit) grammatical constructions by which an el-
ement of a8 may be expressed to become explicit
properties of the transformed grammar. Specifi-
cally, each element of a8 occurs as the anchor of
each of a number of elementary trees. Let us refer
to the set of elementary trees in the transformed
grammar anchored by a93a60a73a10a8 as a94a24a14a43a93a95a17 .5 Each of
these trees corresponds to a grammatical form in
which the element may be realised. Hence, rather
than performing an exhaustive search of the space
of derivation trees a96a97a14a23a12 a82 a17 , specific-lexicalisation
allows us to instead perform a best first search.
That is, we choose exactly one element of a94a32a14a43a93a95a17
for each a93a47a73a60a8 . Let a93a99a98a101a100a103a102a104a93a99a13a25a67a42a14a16a8a18a17 denote the set of
all sets which contain exactly one element of a94a32a14a43a93a95a17
for each a93a47a73a60a8 . Recall that we may assign to each
syntactic form in which an element of a8 may be
realised a preference score, and that each element
of a94a24a14a43a93a99a17 corresponds to some syntactic form. So,
for each element of a93a99a98a105a100a49a102a106a93a107a13a49a67a15a14a16a8a89a17 we may sum the
preference scores of its elements. Hence, we may
impose an order on the elements of a93a107a98a105a100a103a102a104a93a99a13a25a67a42a14a16a8a18a17
according to their sum of preference scores. We
may then refer to each element of a93a99a98a105a100a49a102a106a93a107a13a49a67a15a14a16a8a89a17 as
a108
a86a109a13a49a110a50a14a16a8a111a55a112a102a113a17 , where a102 is the element’s position in
the order, with a108 a86a109a13a25a110a50a14a16a8a111a55a95a114a25a17 being first.
We then search, in order, the spaces of possible
compositions of the a108 a86a115a13a49a110a50a14a16a8a111a55a112a102a113a17 s combined with
some necessary supporting trees which are not an-
chored by an element of a8 . Call these spaces
a108
a86a109a13a49a110a115a116a95a14a16a8a111a55a112a102a113a17 . In terms of redundancy removal,
a108
a86a109a13a49a110 a116 a14a16a8a111a55a112a102a113a17 is the specific-lexicalised TAG with
those trees which might be redundant with respect
to the search for a13a15a14a16a8a18a17 removed. We begin the
search with a108 a86a109a13a25a110a115a116a99a14a16a8a111a55a95a114a25a17 . It is not guaranteed that
a13a15a14a16a8a18a17 is in this space. If it is not, we repeat the
search using a108 a86a109a13a25a110a115a116a95a14a16a8a111a55a118a117a109a17 , and so on. At worst
(if a13a51a14a16a8a18a17a87a73
a108
a86a115a13a49a110a115a116a95a14a16a8a111a55a112a7a30a17 where a93a99a98a101a100a103a102a104a93a99a13a49a67a15a14a16a8a89a17 has
a7 elements), this procedure exhaustively searches
the space of compositions of the elements of a12a20a82 .
5This is the family (as that term is used by Yang et al.
(1991) and others) of trees anchored on a119 .
s
verb+item+ predication+
s
predication
item+a
predication_a
predication
participleclause+
predication_part
predication
predication* paticipleclause+
adj_pred_partp
participleclause
participle_p+ item+
participleclause
adjective
item+
adjective
item
adjective+ item*
item_adjective_adjoin
verb
is
is
participle_p
published by
publishedby
item
@<duration>
item_duration
item
@<publisher.name>
item_name
item
@<publisher.role>
item_role
item
@<type>
item_type
item
@<title>
item_title
Figure 4: The elementary trees of a small TAG, a12a30a81 . The trees’ names are in bold below them. Substi-
tution nodes are indicated with a ‘+’; foot nodes are indicated with a ‘*’; the distinguished symbol is
‘s’. Slots are shown as ‘@<reference>’, where “reference” is the field to which the slot refers. Note that
the feature structures which are associated with each node, which prohibit certain compositions, are not
shown. Note also that this is not a lexicalised TAG (LTAG). This is somewhat unusual; we intend, as
part of our ongoing work, to apply our techniques to an established LTAG, such as XTAG.
s
item verb+ predication+
@<title>
s:item_title
item
adjective item*
item
@<title>
item_adjective_adjoin:adjective:item_title
predication
participleclause
participle_p+ item
@<publisher.name>
adj_pred_partp:participleclause:item_name
predication*
predication
participleclause
item
@<publisher.name>
predication_part:participleclause:item_name
participle_p+
item
adjective item*
item
@<publisher.role>
item_adjective_adjoin:adjective:item_role
item
adjective item*
item
@<duration>
item_adjective_adjoin:adjective:item_duration
predication
a item
@<type>
predication_a:item_type
verb
is
is
participle_p
published by
publishedby
Figure 5: The elementary trees of the TAG a12a24a82 , a specific-lexicalised version of TAG a12a6a81 in figure 4.
Each tree’s name is below it, in bold. Note that, since the feature structures are not shown, it is not
apparent why certain trees which the algorithm seems to imply do not occur in this set.
1: @<title> is a @<type>.
2: @<title> is a @<type> published by @<publisher.name>.
3: @<title> is a @<type> published by @<publisher.role>@<publisher.name>.
4: @<title> is a @<duration>@<type>.
5: @<title> is a @<duration>@<type> published by @<publisher.name>.
6: @<title> is a @<duration>@<type> published by @<publisher.role>@<publisher.name>.
7: @<title> is published by @<publisher.name>.
8: @<title> is published by @<publisher.role>@<publisher.name>.
Figure 6: The templates modelled by the TAGs of figures 4 and 5. Note that the expression of the fields
in figure 3 with respect to template 6 is the first sentence of the paragraph of figure 1.
In fact, since the a108 a86a109a13a25a110a115a116a25a14a16a8a111a55a112a7a30a17 s do not partition
a96a97a14a23a12 a82 a17 , in the worst cases this procedure is slower
than an exhaustive search. However, a13a51a14a16a8a18a17 is de-
fined in terms of maximal preference scores, so it
is likely to be found ina108 a86a109a13a49a110a50a14a16a8a111a55a112a102a113a17 for “low” a102 .
For illustration, refer again to the specific-
lexicalisation in figure 5. Notice that @<pub-
lisher.name> occurs as the anchor of more
than one tree.6 These trees, predication part:-
participleclause:item name and adj pred partp:-
participleclause:item name which we will refer to
as a64a120a81 and a64a121a82 respectively, represent the forms in
which that slot may be expressed. Hence, @<pub-
lisher.name> may be realised as a predication in
its own right using a64a120a81 , as in templates 7 and 8
in figure 6, or as an adjunct to another predi-
cation using the second, as in templates 2, 3, 5
and 6. Suppose that our preference scores rate a64a121a82
more highly than a64a120a81 , and that we must include all
four slots. Then the system would first search the
space of compositions of the trees of a12a20a82 without
a64a118a81 , and generate template 6. The second choice,
a12a24a82 without a64a121a82 leads to the generation of the con-
catenation of templates 4 and 8, which expresses
the same fields but is less aggregated. This is as
we would wish.
3.4 Redundancies in the search space
Specific-lexicalisation is a transformation which
operates on a complete TAG a12a6a81 and its result is
another TAG a12a24a82 whose string set is the same as
a12a30a81 ’s. Also, the feature structures on the nodes
of the elementary trees of a12a20a82 contain fewer un-
bound variables. Unbound variables represent
6We are ignoring the tree item adjective adjoin:-
adjective:item title, which is not usable due to its features,
which are not shown.
dependencies between parts of the grammar. A
search of the space of compositions of elemen-
tary trees may make a long chain of compositions
before discovering that the composed structure is
forbidden by such a dependency. The forbidden
chain of compositions is redundant, and specific-
lexicalisation removes it from the search space.
Importantly, specific-lexicalisation may also
take as a parameter a8 , the set of fields to be ex-
pressed. It then removes from a12a6a81 all elementary
trees which are anchored on slots which do not
refer to elements of a8 and operates on this re-
duced TAG, with result a12a20a82 . And if a13a51a14a16a8a89a17a74a73a60a21a22a14a23a12a30a81a122a17
then a13a51a14a16a8a89a17a66a73a123a21a35a14a23a12 a82 a17 . Then, in effect, specific-
lexicalisation, as well as removing general redun-
dant dependencies, is specifically removing some
of those parts of the grammar which are redun-
dant with respect to the search for a13a15a14a16a8a18a17 .
Redundancy occurs in a grammar for two rea-
sons. First, it is written, by hand, with linguis-
tic rather than computational efficiency concerns
in mind. It is too complex for its writer to be
able to spot redundancies arising from long chains
of dependencies between its parts. So specific-
lexicalisation may be regarded as automatic bug
removal. Second, the grammar is written to be
able to model all the templates which express
some a8a10a9a69a4 a5 . So for any particular a8 , the gram-
mar will contain information about how to ex-
press items not in that set. Specific-lexicalisation
highlights this redundancy.
We have conducted some preliminary exper-
iments using several small TAGs in which, for
each TAG and for its specific-lexicalised equiv-
alent, we measured the time our system takes
to generate the modelled sentences. The results
showed a decrease in the generation time after
lexicalisation of orders of magnitude, with the
best observed reduction being a factor of about
3000.
The specific-lexicalisation of a TAG has the
property of having the same string set (and possi-
bly the same tree set) as the original, but a smaller
space of possible compositions. We have not
proved either clause of this statement, but on the
basis of experimental evidence we believe both to
be true. Also, the following argument supports
the case for the second.
Recall that a feature structure attached to a non-
terminal symbol in some rule (tree in the case of
TAG) of a grammar is an abbreviation for several
similar rules. For example, if a node has asso-
ciated with it a feature structure containing three
features each of which may be in one of two states
and none of which are currently instantiated, then
it abbreviates a117a125a124a87a39a127a126 nodes. So each tree in a
TAG with feature structures is an abbreviation for
a7 trees, where a7 is the number of possible con-
figurations of the feature structures on its nodes.
Hence, when we search the space of possible
compositions of some number a128 of trees, we are
in fact searching the space of compositions of a94a51a128
trees, where a94 is some factor related to the number
of possible configurations of the feature structures
on the trees. Specific-lexicalisation identifies ex-
actly which of the (non-featured) trees for which
a tree with feature structures is an abbreviation
are irrelevant to a search by instantiating unbound
variables in its features.
4 Further work and discussion
The precise circumstances under which the tech-
niques described are effective are still to be estab-
lished. In particular, it is our intention to repeat
our experiments with a standard LTAG; and with
TAGs induced automatically from our corpus.
To summarise, we claim that the generation of
an optimally aggregated summary paragraph re-
quires the ability to move facts across sentence
boundaries. A difficulty to achieving this is the
exponential relationship between the number of
possible paraphrases of a summary of a set of
facts and the number of facts in that set. Our al-
gorithm addresses this by transforming a TAG to
better model the search space.

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