A Meta-Level Grammar: 
Redefining Synchronous TAG for Translation and Paraphrase 
Mark Dras 
Microsoft Research Institute 
Department of Computer Science 
Macquarie University, Australia 
markd@±cs, mq. edu. au 
Abstract 
In applications such as translation and 
paraphrase, operations are carried out on 
grammars at the meta level. This pa- 
per shows how a meta-grammar, defining 
structure at the meta level, is useful in 
the case of such operations; in particu- 
lar, how it solves problems in the current 
definition of Synchronous TAG (Shieber, 
1994) caused by ignoring such structure 
in mapping between grammars, for appli- 
cations such as translation. Moreover, es- 
sential properties of the formalism remain 
unchanged. 
1 Introduction 
A grammar is, among other things, a device by 
which it is possible to express structure in a 
set of entities; a grammar formalism, the con- 
straints on how a grammar is allowed to ex- 
press this. Once a grammar has been used to 
express structural relationships, in many ap- 
plications there are operations which act at a 
'meta level' on the structures expressed by the 
grammar: for example, lifting rules on a depen- 
dency grammar to achieve pseudo-projectivity 
(Kahane et al, 1998), and mapping between 
synchronised Tree Adjoining Grammars (TAGs) 
(Shieber and Schabes, 1990; Shieber 1994) as 
in machine translation or syntax-to-semantics 
transfer. At this meta level, however, the oper- 
ations do not themselves exploit any structure. 
This paper explores how, in the TAG case, us- 
ing a meta-level grammar to define meta-level 
structure resolves the flaws in the ability of Syn- 
chronous TAG (S-TAG) to be a representation 
for applications such as machine translation or 
paraphrase. 
This paper is set out as follows. It describes 
the expressivity problems of S-TAG as noted 
in Shieber (1994), and shows how these occur 
also in syntactic paraphrasing. It then demon- 
strates, illustrated by the relative structural 
complexity which occurs at the meta level in 
syntactic paraphrase, how a meta-level gram- 
mar resolves the representational problems; and 
it further shows that this has no effect on the 
generative capacity of S-TAG. 
2 S-TAG and Machine Translation 
Synchronous TAG, the mapping between two 
Tree Adjoining Grammars, was first proposed 
by Shieber and Schabes (1990). An applica- 
tion proposed concurrently with the definition 
of S-TAG was that of machine translation, map- 
ping between English and French (Abeill~ et al, 
1990); work continues in the area, for example 
using S-TAG for English-Korean machine trans- 
lation in a practical system (Palmer et al, 1998). 
In mapping between, say, English and French, 
there is a lexicalised TAG for each language (see 
XTAG, 1995, for an overview of such a gram- 
mar). Under the definition of TAG, a grammar 
contains elementary trees, rather than flat rules, 
which combine together via the operations of 
substitution and adjunction (composition oper- 
ations) to form composite structures--derived 
trees--which will ultimately provide structural 
representations for an input string if this string 
is grammatical. An overview of TAGs is given 
in Joshi and Schabes (1996). 
The characteristics of TAGs make them better 
suited to describing natural language than Con- 
text Free Grammars (CFGs): CFGs are not ad- 
equate to describe the entire syntax of natural 
language (Shieber, 1985), while TAGs are able 
to provide structures for the constructions prob- 
lematic for CFGs, and without a much greater 
generative capacity. Two particular chaxacteris- 
80 
(~1: S 
NP0 $ VP 
V NP1 j. 
I defeated 
a2: NP 
I Garrad 
NP 
I Garrad 
a4: Det I 
the 
(~3: NP 
Det$ N I 
Sumer~ans 
;35: VP 
Adv VP, I 
cunningly 
Figure 1: Elementary TAG trees 
tics of TAG that make it well suited to describ- 
ing natural language are the extended domain of 
locality (EDL) and factoring recursion from the 
domain of dependencies (FRD). In TAG, for in- 
stance, information concerning dependencies is 
given in one tree (EDL): for example, in Fig- 
ure 1,1 the information that the verb defeated 
has subject and object arguments is contained 
in the tree al. In a CFG, with rules of the 
form S --+ NP VP and VP --+ V NP, it is 
not possible to have information about both ar- 
guments in the same rule unless the VP node 
is lost. TAG keeps dependencies together, or 
local, no matter how far apart the correspond- 
ing lexicM items are. FRD means that recursive 
information--for example, a sequence of adjec- 
tives modifying the object noun of defeated--are 
factored out into separate trees, leaving depen- 
dencies together. 
A consequence of the TAG definition is that, un- 
like CFG, a TAG derived tree is not a record of 
its own derivation. In CFG, each tree given as 
a structural description to a string enables the 
rules applied to be recovered. In a TAG, this is 
not possible, so each derived tree has an asso- 
ciated derivation tree. If the trees in Figure 1 
were composed to give a structural description 
for Garrad cunningly defeated the Sumerians, 
the derived tree and its corresponding deriva- 
1The figures use standard TAG notation: $ for nodes 
requiring substitution, • for foot nodes of auxiliary trees. 
S 
vP 
Adv VP 
cunningly V NP 
defeated Det N 
J I the Sumerians 
or2 (1) ;35 (2) or3 (2.2) 
i 
p ~4(1) 
Figure 2: Derived and derivation trees, respec- 
tively, for Figure 1 
tion tree would be as in Figure 2. 2 
Weir (1988) terms the derived tree, and its 
component elementary trees, OBJECT-LEVEL 
TREES; the derivation tree is termed a META- 
LEVEL TREE, since it describes the object-level 
trees. The derivation trees are context free 
(Weir, 1988), that is, they can be expressed by 
a CFG; Weir showed that applying a TAG yield 
function to a context free derivation tree (that 
is, reading the labels off the tree, and substi- 
tuting or adjoining the corresponding object- 
level trees as appropriate) will uniquely specify 
a TAG tree. Schabes and Shieber (1994) charac- 
terise this as a function 7) from derivation trees 
to derived trees. 
The idea behind S-TAG is to take two TAGs 
and link them in an appropriate way so that 
when substitution or adjunction occurs in a tree 
in one grammar, then a corresponding compo- 
sition operation occurs in a tree in the other 
grammar. Because of the way TAG's EDL cap- 
tures dependencies, it is not problematic to have 
translations more complex than word-for-word 
mappings (Abeill~ et al, 1990). For example, 
from the Abeill~ et al paper, handling argument 
swap, as in (1), is straightforward. These would 
be represented by tree pairs as in Figure 3. 
2In derivation trees, addresses are given using the 
Gorn addressing scheme, although these are omitted in 
this paper where the composition operations are obvious. 
81 
o~6: 
sg\] 
Np$~~VP Np$~~~Vp 
V NP$ \[~\] V PP 
misses manque P NP$\[-~ 
I 
d 
or7: I \] as: \] I 
John Jean Mary Marie 
Figure 3: S-TAG with argument swap 
(1) a. John misses Mary. 
b. Marie manque g Jean. 
In these tree pairs, a diacritic (\[-/7) represents 
a link between the trees, such that if a substi- 
tution or adjunction occurs at one end of the 
link, a corresponding operation must occur at 
the other end, which is situated in the other 
tree of the same tree pair. Thus if the tree for 
John in a7 is substituted at E\] in the left tree 
of a6, the tree for Jean must be substituted at 
\[-~ in the right tree. The diacritic E\] allows a 
sentential modifier for both trees (e.g. unfortu- 
nately / malheureusement). 
The original definition of S-TAG (Shieber and 
Schabes, 1990), however, had a greater genera- 
tive capacity than that of its component TAG 
grammars: even though each component gram- 
mar could only generate Tree Adjoining Lan- 
guages (TALs), an S-TAG pairing two TAG 
grammars could generate non-TALs. Hence, a 
redefinition was proposed (Shieber, 1994). Un- 
der this new definition, the mapping between 
grammars occurs at the meta level: there is an 
isomorphism between derivation trees, preserv- 
ing structure at the meta level, which estab- 
lishes the translation. For example, the deriva- 
• tion trees for (1) using the elementary trees of 
Figure 3 is given in Figure 4; there is a clear 
isomorphism, with a bijection between nodes, 
and parent-child relationships preserved in the 
mapping. 
In translation, it is not always possible to have 
a bijection between nodes. Take, for example, 
(2). 
a\[misses\] a\[man.que ~\] 
s a\[John\] a\[Mary\] a\[Jean\] a\[Marie\] / 
Figure 4: Derivation tree pair for Fig 3 
(2) a. Hopefully John misses Mary. 
b. On esp~re que Marie manque 
Jean. 
In English, hopefully would be represented by a 
single tree; in French, on esp~re que typically 
by two. Shieber (1994) proposed the idea of 
bounded subderivation to deal with such aber- 
rant cases--treating the two nodes in the deriva- 
tion tree representing on esp~re que as singular, 
and basing the isomorphism on this. This idea 
of bounded subderivation solves several difficul- 
ties with the isomorphism requirement, but not 
all. An example by Shieber demonstrates that 
translation involving clitics causes problems un- 
der this definition, as in (3). The partial deriva- 
tion trees containing the clitic lui and its English 
parallel are as in Figure 5. 
(3) a. The doctor treats his teeth. 
b. Le docteur lui soigne les dents. 
A potentially unbounded amount of material in- 
tervening in the branches of the righthand tree 
means that an isomorphism between the trees 
cannot be established under Shieber's specifi- 
cation even with the modification of bounded 
subderivations. Shieber suggested that the iso- 
morphism requirement may be overly stringent; 
82 
o~\[treats\] a\[s~gne\] 
c~\[teeth I a\[lui\] a\[dents\] 
a\[his\] 
Figure 5: Clitic derivation trees 
but intuitively, it seems reasonable that what 
occurs in one grammar should be mirrored in 
the other in some way, and this reflected in the 
derivation history. 
Section 3 looks at representing syntactic para- 
phrase in S-TAG, where similar problems are 
encountered; in doing this, it can be seen more 
clearly than in translation that the difficulty is 
caused not by the isomorphism requirement it- 
self but by the fact that the isomorphism does 
not exploit any of the structure inherent in the 
derivation trees. 
3 S-TAG and Paraphrase 
Syntactic paraphrase can also be described with 
S-TAG (Dras, 1997; Dras, forthcoming). The 
manner of representing paraphrase in S-TAG 
is similar to the translation representation de- 
scribed in Section 2. The reason for illustrating 
both is that syntactic paraphrase, because of its 
structural complexity, is able to illuminate the 
nature of the problem with S-TAG. In a specific 
parallel, a difficulty like that of the clitics oc- 
curs here also, for example in paraphrases such 
as (4). 
(4) a. The jacket which collected the dust 
was tweed. 
b. The jacket collected the dust. It 
was tweed. 
Tree pairs which could represent the elements in 
the mapping between (4a) and (4b) are given in 
Figure 6. It is clearly the case that the trees in 
the tree pair c~9 are not elementary trees, in the 
same way that on esp~re que is not represented 
by a single elementary tree: in both cases, such 
single elementary trees would violate the Con- 
dition on Elementary Tree Minimality (Frank, 
1992). The tree pair a0 is the one that captures 
the syntactic rearrangement in this paraphrase; 
such a tree pair will be termed the STRUCTURAL 
MAPPING PAIR (SMP). Taking as a basic set of 
trees the XTAG standard grammar of English 
(XTAG, 1995), the derivation tree pair for (4) 
would be as in Figure 7. 3 Apart from c~9, each 
tree in Figure 6 corresponds to an elementary 
object-level tree, as indicated by its label; the 
remaining labels, indicated in bold in the meta- 
level' derivation tree in Figure 7, correspond to 
the elementary object-level trees forming (~9, in 
much the same way that on esp~re que is repre- 
sented by a subderivation comprising an on tree 
substituted into an esp~re que tree. 
Note that the nodes corresponding to the left 
tree of the SMP form two discontinuous groups, 
but these discontinuous groups are clearly re- 
lated. Dras (forthcoming) describes the condi- 
tions under which these discontinuous groupings 
are acceptable in paraphrase; these discontinu- 
ous groupings are treated as a single block with 
SLOTS connecting the groupings, whose fillers 
must be of particular types. Fundamentally, 
however, the structure is the same as for clitics: 
in one derivation tree the grouped elements are 
in one branch of the tree, and in the other they 
are in two separate branches with the possibility 
of an unbounded amount of intervening mate- 
rial, as described below in Section 4. 
4 Meta-Level Structure 
Example (5) illustrates why the paraphrase in 
(4) has the same difficulty as the clitic example 
in (3) when represented in S-TAG: because un- 
bounded intervening material can occur when 
promoting arbitrarily deeply embedded relative 
clauses to sentence level, as indicated by Fig- 
ure 8, an isomorphism is not possible between 
derivation trees representing paraphrases such 
as (4) and (5). Again, the component trees of 
the SMP are in bold in Figure 8. 
(5) a. The jacket which collected the dust 
which covered the floor was tweed. 
b. The jacket which collected the dust 
3Node labels, the object-level tree names, are given 
according to the XTAG standard: see Appendix B of 
XTAG (1995). This is done so that the component trees 
of the aggregate (~9 and their types are obvious. The 
lexical item to which each is bound is given in square 
brackets, to make the trees, and the correspondence be- 
tween for example Figure 6 and Figure 7, clearer. 
83 
S 
NP 
NPo ~'~'~S 
Comp S ' 
which NP VP 
, 
I 
collected 
VP A 
V vP 
is V AdjP I I 
e Adj I 
tweed 
S 
S 
NPo ~~VP 
V NP1 $\['~ I 
collected 
Punct I S 
NP VP 
It V VP 
is V AdjP I I 
Adj I 
tweed 
NP NP > 
alo: Det$ N Det$ N I I 
jacket jacket 
Det 
all: t~e 
NP 
Det > I C~12: Det$ N 
the \] 
dust 
NP A 
Det$ N t 
dust 
Figure 6: S-TAG for (4) 
ocnxOAxl \[tweed\] 
~DXD\[the\] /3N0nx0Vnxl\[collected\] 
~COMPs\[which\] c~NXdxN\[dust\] 
i 
c~DXD\[the\] 
3Vvx\[was\] ~NXdxN\[jacket\] ~Vvx\[was\] ~sPUs\[.\] 
* i 
t i 
~DXD\[the\] cmx0Vnxl^\[collected\] s 
c~NXN\[it\] aNXdx,N\[dust\] 
t 
J c~DXD\[the\] 
Figure 7: Derivation tree pair for example (4) 
was tweed. The dust covered the 
floor. 4 
The paraphrase in (4) and in Figures 6 and 7, 
and other paraphrase examples, strongly sug- 
gest that these more complex mappings are not 
an aberration that can be dealt with by patch- 
ing measures such as bounded subderivation. It 
is clear that the meta level is fundamentally not 
just for establishing a one-to-one onto mapping 
between nodes; rather, it is also about defin- 
ing structures representing, for example, the 
4The referring expression that is the subject of this 
second sentence has changed from it in (4) to the dust 
so the antecedent is clear. Ensuring it is appropriately 
coreferent, by using two occurrences of the same diacritic 
in the same tree, necessitates a change in the properties 
of the formalism unrelated to the one discussed in this 
paper; see Dras (forthcoming). Assume, for the purpose 
of this example, that the referring expression is fixed and 
given, as is the case with it, rather than determined by 
coindexed diacritics. 
SMP at this meta level: in an isomorphism be- 
tween trees in Figure 8, it is necessary to re- 
gard the SMP components of each tree as a uni- 
tary substructure and map them to each other. 
The discontinuous groupings should form these 
substructures regardless of intervening material, 
and this is suggestive of TAG's EDL. 
In the TAG definition, the derivation trees are 
context free (Weir, 1988), and can be expressed 
by a CFG. The isomorphism in the S-TAG def- 
inition of Shieber (1994) reflects this, by effec- 
tively adopting the single-level domain of local- 
ity (extended slightly in cases of bounded sub- 
derivation, but still effectively a single level), in 
the way that context free trees are fundamen- 
tally made from single level components and 
grown by concatenation of these single levels. 
This is what causes the isomorphism require- 
ment to fail, the inability to express substruc- 
tures at the meta level in order to map between 
them, rather than just mapping between (effec- 
84 
............... y Nx¢~\] 
~DXDI, h0\] ~l\[:o~I~dJ 
/~COMPs\[which\] aNXdxN\[dust\] 
aDXD\[the\] /~N0nx0Vnxl \[covered\] 
aDXD\[t he\] 
flVvx\[~s\] .. _ %~xdx~lNf~c~ ~Vvx\[is\] /~sPUs\[.\] 
~DXD\[the\] ~N0nx0Vnx l\[coliect ed\] anxOVnxl \[covered\] 
~COMPs\[which\] aNXdxN\[dust\] aNXN\[it\] oNXdxN\[floor\] 
~DXD\[the\] aDXD\[the\] 
Figure 8: Derivation tree for example (5) 
tively) single nodes. 
To solve the problem with isomorphism, a meta- 
level grammar can be defined to specify the 
necessary substructures prior to mapping, with 
minimality conditions on what can be consid- 
ered acceptable discontinuity. Specifically, in 
this case, a TAG meta-level grammar can be 
defined, rather than the implicit CFG, because 
this captures the EDL well. The TAG yield 
function of Weir (1988) can then be applied to 
these derivation trees to get derived trees. This, 
of course, raises questions about effects on gen- 
erative capacity and other properties; these are 
dealt with in Section 5. 
A procedure for automatically constructing a 
TAG meta-grammar is as follows in Construc- 
tion 1. The basic idea is that where the node 
bijection is still appropriate, the grammar re- 
tains its context free nature (by using single- 
level TAG trees composed by substitution, mim- 
icking CFG tree concatenation), but where EDL 
is required, multi-level TAG initial trees are 
defined, with TAG auxiliary trees for describ- 
ing the intervening material. These meta-level 
trees are then mapped appropriately; this cor- 
responds to a bijection of nodes at the meta- 
meta level. For (5), the meta-level grammar for 
the left projection then looks as in Figure 9, 
and for the right projection as in Figure 10. 
• Figure 11 contains the meta-meta-level trees, 
the tree pair that is the derivation of the meta 
level, where the mapping is a bijection between 
nodes. Adding unbounded material would then 
just be reflected in the meta-meta-level as a list 
of/3 nodes depending from the j315/j31s nodes in 
these trees. 
The question may be asked, Why isn't it the 
case that the same effect will occur at the meta- 
meta level that required the meta-grammar in 
the first place, leading perhaps to an infinite 
(and useless) sequence? The intuition is that it 
is the meta-level, rather than anywhere 'higher', 
which is fundamentally the place to specify 
structure: the object level specifies the trees, 
and the meta level specifies the grouping or 
structure of these trees. Then the mapping 
takes place on these structures, rather than the 
object-level trees; hence the need for a grammar 
at the meta-level but not beyond. 
Construction 1 To build a TAG metagram- 
mar: 
1. An initial tree in the metagrammar is 
formed for each part of the derivation tree 
corresponding to the substructure repre- 
senting an SMP, including the slots so that 
a contiguous tree is formed. Any node that 
links these parts of the derivation tree to 
other subtrees in the derivation tree is also 
included, and becomes a substitution node 
in the metagrammar tree. 
2. Auxiliary trees are formed corresponding to 
the parts of the derivation trees that are slot 
fillers along with the nodes in the discon- 
tinuous regions adjacent to the slots; one 
contiguous auxiliary tree is formed for each 
bounded sequence of slot fillers within each 
substructure. These trees also satisfy cer- 
tain minimality conditions. 
3. The remaining metagrammar trees then 
come from splitting the derivation tree 
into single-level trees, with the nodes on 
85 
Ot13: anx0Axl 
~NXdxN ~Vvx 
aDXD ~N0nx0Vnxl 
~COMPs aNXdxN$ 
a14: c~NXdxN 
I aDXD 
J315: aNXdxN 
aDXD ~N0nx0Vnxl 
~COMPs aNXdxN, 
Figure 9: Meta-grammar for (5a) 
these single-level trees in the metagrammar 
marked for substitution if the corresponding 
nodes in the derivation tree have subtrees. 
The minimality conditions in Step 2 of Con- 
struction 1 are in keeping with the idea of min- 
imality elsewhere in TAG (for example, Frank, 
1992). The key condition is that meta-level 
auxiliary trees are rooted in c~-labelled nodes, 
and have only ~-labelled nodes along the spine. 
The intuition here is that slots (the nodes which 
meta-level auxiliary trees adjoin into) must be 
c~-labelled: fl-labelled trees would not need 
slots, as the substructure could instead be con- 
tinuous and the j3-1abelled trees would just ad- 
join in. So the meta-level auxiliary trees are 
rooted in c~-labelled trees; but they have only ~- 
labelled trees in the spine, as they aim to repre- 
sent the minimal amount of recursive material. 
Notwithstanding these conditions, the construc- 
tion is quite straightforward. 
5 Generative Capacity 
Weir (1988) showed that there is an infinite pro- 
gression of TAG-related formalisms, in genera- 
tive capacity between CFGs and indexed gram- 
mars. A formalism ~-i in the progression is de- 
fined by applying the TAG yield function to a 
derivation tree defined by a grammar formalism 
~16; cmx0Axl 
~NXdxN ~Vvx /~sPUs 
I I c~DXD aNXdxN 
c~NXdxN c~NXdxN$ 
cqT: aNXdxN 
I aDXD 
aNXdxN 
c~DXD ~N0nx0Vnxl 
~COMPs c~NXdxN, 
Figure 10: Meta-grammar for (5b) 
0t14 ~15 a17 ~18/ 
Figure 11: Derivation tree pair for Fig 3 
5~i_1; the generative capacity of ~i is a superset 
of ~'i-1- Thus using a TAG meta-grammar, as 
described in Section 4, would suggest that the 
generative capacity of the object-level formal- 
ism would necessarily have been increased over 
that of TAG. 
However, there is a regular form for TAGs 
(Rogers, 1994), such that the trees of TAGs in 
this regular form are local sets; that is, they 
are context free. The meta-level TAG built by 
Construction 1 with the appropriate conditions 
on slots is in this regular form. A proof of this 
is in Dras (forthcoming); a sketch is as follows. 
If adjunction may not occur along the spine of 
another auxiliary tree, the grammar is in regu- 
lar form. This kind of adjunction does not oc- 
cur under Construction 1 because all meta-level 
auxiliary trees are rooted in c~-labelled trees 
(object-level auxiliary trees), while their spines 
consist only of p-labelled trees (object-level ini- 
tial trees). 
Since the meta-level grammar is context free, 
despite being expressed using a TAG grammar, 
this means that the object-level grammar is still 
8{} 
a TAG. 
6 Conclusion 
In principle, a meta-grammar is desirable, as it 
specifies substructures at a meta level, which is 
necessary when operations are carried out that 
are applied at this meta level. In a practical ap- 
plication, it solves problems in one such formal- 
ism, S-TAG, when used for paraphrase or trans- 
lation, as outlined by Shieber (1994). Moreover, 
the formalism remains fundamentally the same, 
in specifying mappings between two grammars 
of restricted generative capacity; and in cases 
where this is important, it is possible to avoid 
changing the generative capacity of the S-TAG 
formalism in applying this meta-grammar. 
Currently this revised version of the S-TAG for- 
malism is used as the low-level representation in 
the Reluctant Paraphrasing framework of Dras 
(1998; forthcoming). It is likely to also be use- 
ful in representations for machine translation 
between languages that are structurally more 
dissimilar than English and French, and hence 
more in need of structural definition of object- 
level constructs; exploring this is future work. 

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