FACTORING RECURSION AND DEPENDENCIES: AN ASPECT OF TREE ADJOINING GRAMMARS (TAG) AND 
A COMPARISON OF SOME FORMAL PROPERTIES OF TAGS, GPSGS, PLGS, AND LPGS * 
Aravind K. Joshi 
Department of Computer and Information Science 
R. 268 Moore School 
University of Pennsylvania 
Philadelphia, PA 19104 
I.IWrRODUCTION 
During the last few years there is vigorous 
activity In constructing highly constrained 
grammatical systems by eliminating the 
transformational component either totally or 
partially. There is increasing recognition of 
the fact that the entire range of dependencies 
that transformational grammars in their various 
incarnations have tried to account for can be 
satisfactorily captured by classes of rules that 
are non-transformational and at the same Clme 
highly constrlaned in terms of the classes of 
grammars and languages that they de fine. 
Two types of dependencies are especially 
important: subcategorlzatlon and filler-gap 
dependencies. Moreover,these dependencies can 
be unbounded. One of the motivations for 
transformations was co account for unbounded 
dependencies. The so-called 
non-transformational grammars account for the 
unbounded dependencies in different ways. In a 
cree-adJoinlng grammar (TAG), which has been 
introduced earlier in (Joshi,1982), 
unhoundedness is achieved by factoring the 
dependencies and recursion in a novel and, we 
belleve, in a linguistically interesting manner. 
All dependencies are defined on a finite set of 
basic structures (trees) which are bounded. 
Unhoundedness is then a corollary of a 
particular composition operation called 
ad~olnlng. There are thus no unbounded 
dependencies in a sense. 
In this paper, we will ~irsC briefly 
describe TAG's, which have the following 
Important properties: (l) we can represent the 
usual transformational relations more or less 
directly in TAG's, (2) the power of TAG's is 
only slightly more than that of context-free 
grammars (CFG's) in what appears to be Just the 
right way, and (3) TAG's are powerful enough to 
characterize dependencies (e.g., 
subcategorlzatlon, as in verb subcategorlzatlon, 
and filler-gap dependencies, as in the case of 
moved constltutents in wh-questlons) which might 
*GPSG: Generalized phrase structure grammar, 
PLG: Phrase linking grammar, and LFG: Lexlcal 
functional grannnar. 
This work is partially supported by the NSF 
Grant MCS 81-07290. 
be at unbounded distance and nested or crossed. 
We will then compare some of the formal 
properties of TAG's, GPSG*s,PLG's, and LFG*s, in 
particular, concerning (I) the types of 
languages, reflecting different patterns of 
dependencies that can or cannot be generated by 
the different types of grammars, (2) the degree 
of free word ordering permitted by different 
grammars, and (3) parsing complexity of the 
different gra--,-rs. 
2.TREE ADJOINING GRAMMAR(TAG) 
A tree adjoining grammar (TAG), G = (I,A) 
consists of two finite sets of elementary trees. 
The trees in I will be called the initial trees 
and the trees in A, the auxiliary trees. A tree 
{~ is an initial tree if the root node of 
is labeled S and the frontier nodes are all 
terminal symbols (the interior nodes are all 
non-termlnals). A tree ~ is an auxiliary tree 
if the root node of ~ is labeled by a 
non-terminal, say, X, and the frontler nodes are 
all terminals except one which is also labeled 
X, the same label as that of the root. The node 
labeled by X on the frontier will be called the 
foot node of ~ . The internal nodes are 
non-terminals. 
~t. ~ermfmJ$ , ,hAl~ 
As defined above, the initial trees and the 
auxiliary trees are not constrained in any 
manner other than as indicated above. The idea, 
however, is that both the initial and the 
auxiliary trees will be minimal in some sense. 
An initial tree will correspond to a minimal 
sententlal tree (i.e., for example, without 
recurslng on any non-terminal) and an auxiliary 
tree, with the root node and the foot node 
labeled X, will correspond to a minimal 
structure that must be brought into the 
derivation, if one recurses on X. 
* I wish to thank Bob Berwlck, Tim Finin, Jean 
Gallier, Gerald Gazdar, Ron Kaplan, Tony Kroch, 
Bill Marsh, Milch Marcus, Ellen Prince, Geoff 
Pullum, R. Shyamasundar, Bonnie Webber, Scott 
Weinstein, and Takashi Yokomori for their 
valuable comments 
We will now define a composition operation 
called adjoining (or adJunction) which composes 
an auxilia~ tree ~ with a tree ~ • ~t 
tree with a node labeled X and let ~ ~ an 
auxiliary tree ~th the root labeled X also. 
~te Chat ~ ~st ~ve,by definition, a node 
(and only one)labeled X on the frontier. 
~Jolnlng can now ~ defined as follows. If 
Is adjoining to ~ at the node n then the 
resulting tree ~ is as sho~ in Fig.l. 
s 
e 
/ 
FiG, :L. 
The tree t dominated by X in ~ is 
excised, ~ is inserted at the node n in 
and the tree t is attached to the foot node 
(labeled X) of ~ , i.e., ~ is inserted or 
'adjoined' to the node n in ~ pushing t 
downwards. Note that adjoining is not a 
substitution operation in the usual sense. 
Example 2.1: Let G - (I,A) be a TAG where 
m+ b ~ r 
/~ / xb 
o- b 
t+i-- , (Z) +++: db T x(~ 
S 
o,, b <:x,, T b 
The root node and the foot node of each 
auxiliary tree is circled for convenience. Let 
us took at some derivations in G. 
~ wlll be adjoined to ~/o at the 
indicated node in ~ . The resulting tree 
Is then ~ 
b ~-r o 
$ 
(~.T. b 
b 
We can continue the derivation by 
ad~olnlng, say /@@, at S as indicated ing£ . 
The resulting tree ~fX is then 
. sL"  
• P4 F • ~ "\[ 4''z'" 
@- b 
Note that ~o is an initial tree# a 
sententiat tree. The derived trees yi and MR 
are also sentential trees, 
We will now define 
T(G): The set of all trees derived in G 
starting from the initial Crees in I. This set 
will be called the tree setof G. 
LCG): The set of all terminal strings of 
the trees in TCG). This set will be called the 
strln~ language(or language) of G. 
The relationship between TAG's CFG's and 
the corresponding string languages can be 
summarized as follows (Joehl, Levy, and 
Takahashl, 1975). 
Theorem 2.1: For every CFG, G', there is 
an equivalent TAG, G, both weakly and strongly. 
Theorem 2.2: For every TAG, G, one of the 
following statements holds: 
(a)there is a cfg, G', that is both weakly 
and strongly equivalent to G, 
(b)there is a cfg,G', that is weakly 
equivalent to G but not strongly equivalent to 
G, Or 
(3) there is no cfg, G', that is weakly 
equivalent to G. 
Parts (a) and (c) appear in (Joshl, Levy, 
and Takahashl, 1975). Part (b) is implicit in 
that paper, but it is important to state It 
explicitly as we have done here. For the TAG, 
G, in Example 2.1, it can be shown that there is 
a CFG, G', such that G" Is both weakly and 
strongly equivalent to O. Examples 2.2 and 2.3 
below illustrate parts (b) and (c) respectively. 
Example 2.2: Let G - (I,A) be a TAG where 
I: 
A 
e 
S 
o-'I" 
$ 
-r 
~z" II 
i", i~ 
"T" 
Some derivations in G. 
t 
e. 
¥~ : -'/I 
/ O, "1" ~,, 
/,i O. "I" 
|"b 
$ ! 
e 
i O. "3".,, .t 
! 
e. 
/ndi'u~ili aide ~i ¢a~i 
3 
.... 
$ 
Clearly, L(G)=L= { a'~e be/ n ~/ 0}, which 
Is a cfl. Thus there must exist a CFG, G', 
which ts at least weakly equivalent to G. It 
can be shown however that there Is no CFG, G', 
which Is strongly ,equivalent to G,l.e., 
T(G)=T(G'). This follows from the fact that 
T(G), the tree set of G, is 
"non-recogntzab\]e',i.e., there is no finite 
state bottom to top automaton that can recognize 
precisely T(G). Thus a TAG may generate a cfl, 
yet assign structural descriptions to the 
strings that cannot be assigned by any CFG. 
Example 2.3: Let C - (I,A) be a TAG where 
"\[: o<d = S 
I 
e 
A; 
", d3 O- "1-" /1~ 
11~ b "I" c 
It can be shown that L(C) - L1 = { w e cn/ 
n ~ 0}, w is a string of a's and b's such that 
(1) the number of a's = the number of b's and 
(2) for any initial substrlng of w, the number 
of a's ~ the number of b's.} 
Ll can be characterized as follows. We 
start with the language L = ( (ba)"e c~/ n ~ 0 
}. L! is then obtained by taking strings in L 
and moving (dtslocsttng) some a's to the left. 
It can be shown that L! is a strictly 
context-sensitlve language (csl), thus there can 
be no CFG that is weakly equivalent to G. 
TAG's have more power than CFG's, however, 
the extra power is quite limited. The language 
Ll has equal number of a's ,b's had c's; 
however, the a's and b's are mixed in a certain 
way. The Language L2 ={a~b~e cn/ n O} is 
similar to Li, except that all a's come before 
all b's. TAG's are not powerful to generate L2. 
The so-called copy inguage L3 ~ {w e w /w 6{a,b} P 
} also cannot be generated by a TAG. 
The fact that TAG's cannot generate L2 and 
L3 is important, because it shows that TAG's are 
only slightly more powerful than CFG's. The way 
TAG's acquire this power is linguistically 
significant. With some modifications of TAG's 
or rather the operation of adjoinlnR, which Is 
linguistically motivated, it is possible to 
generate L2 and L3, but only in some special 
ways. (This modification consists of allowing 
for the possibility for checking ieft-riRht tree 
context(In terms of a proner analysis) as well 
as top-bottom tree context (in terms of 
domination) around the node at which adiunctlon 
is made. Thls is the notion of local 
constraints in (Joshi and Levy,1981)). Thus L2 
and L3 in some ways characterize the limiting 
cases of context-sensitlvlty that can be 
achieved by TAG's and TAG's with local 
constraints. 
In (JoshI,Levy, and Takahashi,1975) it is 
also shown that 
CFL's C TAL's C IL's ~ CSL's. 
where IL's denotes indexed languages. 
3. We will now consider TAG's with links. 
The elementary trees (initial and auxlliar-~ "-=- 
trees) are the appropriate domains for 
characterizing certain dependencies. The domain 
of the dependency is de fined by the elementary 
tree itself. However, the dependency can be 
charaeCerlzed explicitly by introducing a 
special relationship between certain specLfled 
pairs of nodes of an elementary tree. This 
relationship is pictorially exhibited by an arc 
(a dotted line) from one node to the oti,er. For 
example, in the tree below, the nodes labeled B 
and q are linked, 
A 
~- c 
I-, ,, l'- c ~: F G 
' I ~/~ 
"~ ~ .- -~ ~=. 
We will require the following conditions to 
hold for a llnk In an elementary tree. If a 
node n\[ is tlnked to a node n2 then (1) n2 
c-commands nl and (2) nl dominates a null string 
(or a temi.al symbol in the non-linguistic 
formal grammar examples). 
The notion of a link introduced here is 
closely related to that of Peters and Rltchie 
(1982). 
A TAG with links is a TAG where some of the 
elementary trees ~y have links as defined 
above. Henceforth, we may often refer to a TAG 
with links as just a TAG. Links are defined on 
the elementary trees. However, the important 
idea is that the composition operation of 
adjoining will preserve the links. Links 
defined on the elementary trees may become 
stretched as the derivation proceeds. 
\[n a TAG the dependencies are defined on 
the elementary trees(which are bounded) and 
these dependencies are then preserved by the 
ad~olnlng(recurslve) operation. This is how 
rectlrsion and dependencies are factored in a 
TAG. This is in contrast to transformational 
grammars (TC) where recursion is defined in the 
base and the transformations essentially carry 
out the checking of the dependencies. The PiG's 
and LFG's share this aspect'of TG,i.e., 
tee.talon builds up a set of structures, some of 
which are filtered out by transfotn~atlons in a 
TG, by the constraints on linking in a PiG, and 
by the constraints introduced via functional 
structures in LFG. In a GPSG on the other hand, 
recurslon and the checking of the dependencies 
go hand in hand in a sense. In a TAG, 
dependencies are defined initially on bounded 
structures and recurslon simply preserves chem. 
In the APPENDIX we have given some examples 
to show how certain sentences could be deirved 
in a TAG. 
Example 2.4: Let G = (I,A) be a TAG with 
links where 
I 
e, 
IX 
i'-,b 
I S/ 
/I o.." S 
l--r: 
Some derivations in G: 
! 
e. 
.'I t "" .,,i-,. B. • OL_'- "%= • f"i 
/t 
',.L.',. 
5 
%,,/ = o,. o,. e. b b 
• s O-'; I" ~, 
' i.'"l.- Io ' o 
1 
e., 
w-- o, e b 
i..,....,.I 
Y~" S 
/i 
/O.", .% 
/ i , \ ' ., 
-.:,_."I=. ..... 
"" - .L":-'~ 
S 
c,,*" I ' "l" 
s 
-'-.1.~ b 
5 I 
e. 
%J : ct~s~e-4 
l0 
~¢ andes each have one link. ~%and ~63 
show how the linking is preserved in 
adjoining. In ~ one of the links is 
stretched. It should be clear now, how, in 
general, the links will be preserved during the 
derivation. We note in this example that in ~¢ 
the dependencies between the a's and the b's as 
reflected tn the terminal string are properly 
nested, while in ~ two of them are properly 
nested, and the third one is cross-serlal and it 
is crossed with respect Co the nested ones. The 
two elementary trees /~ and Ps have only one 
link each. The nesttngs and crossings in ~ 
and ~3 are the result of adjoining. There are 
two points Co note here: (I) TAG's with links 
can characterize certain cross-serial 
dependencies as well as, of course, nested 
dependencies. (2) The cross-serial dependencies 
as well as the nested dependencies arise as a 
result of adjoining. But this is not the only 
way they can arise. It is possible to have two 
links in an elementary tree which represent 
crossed or nested dependencies, which will then 
be preserved during the derivation. 
It is clear from Example 2.4 that the 
string language of TAG with links is not 
affected by the links. Thus if G is a TAG with 
links. Then L(G)-L(G') where G" is a TAG which 
is obtained from G by removing all the links in 
the elementary trees of G. The links do not 
affect the weak generative capacity. However, 
they make certain aspects of the structural 
description explicit, which is implicit in the 
TAG without the links. 
TAG's (or TAL's) also have the following 
three impor~ant properties: 
(l) Limited cross-serial dependencies: 
Although TAG's permit cross-serial dependencies, 
these are restricted. The restriction is that 
if there are two sets of crossing dependencies, 
then they must be either disjoint or one of them 
must be properly nested inside the other. 
Hence, languages such as the double copy 
language, L4 - {w e w e w / w ~ {a,b} ~} or L5 = 
{anb "@dne~/ n ~ \[} cannot be generated by 
TAG's. For details, see (Joshi,1983). 
(2)Constant. ~rowth property: In a TAG,G,at 
each step of the derivation, we have a 
sententlal tree with the terminal string which 
is a string in L(G). As we adjoin an auxiliary 
tree, we augment the length of the terminal 
string by the length of the terminal string of 
(not counting the single non-terminal symbol 
in the frontier of ~ ).Thus for any string, w, 
of L(G), we have 
where wgls the terminal string of some 
initial tree and wg,l ~ i~ m, the terminal 
string of the \[-th auxiliary tree, assuming 
there are m auxiliary trees. Thus w is a linear 
combination of the length of the terminal string 
o~ some Inltial tree and the lengths of the 
terminal strings of the auxiliary trees. Th~ 
constant growth property severely restricts the 
class of languages generated by TAG's. 
Hence,languages such as L6 = { a ~" / n ~ l} or 
L8 ~{a n% /n ~ \[} cannot be generated by TAG's. 
(3)Polynomial parstn~:TAL's can be parsed 
in time O(n~ )(Joshi and Yokomori, 1983). 
Whether or not an O(n5 ) algorithm exists for 
TAL's is not known at present. 
3. A COMPARISION OF GPSG's,TAG's,PFG's,and 
LFG's WITH RESPECT TO SOME OF THEIR FORMAL 
PROPERTIES 
TABLE I lists (i) a set of languages 
reflecting different patterns of dependencies 
Chat can or cannot be generated by the different 
types of grammars, and (li) the three properties 
Just mentioned ahove. 
As regards the degree of free word order 
permitted by each grammar, the languages 
1,2,3,4,5, and 6 In TABLE I give some idea of 
the degree of freedom. The language in 3 in 
TABLE I is the extreme case where the a's, 
b's,and c's can he any order, as long as the 
number of a's =the number of b's=the number of 
c'S. GPSG~and TAG's cannot generate this 
language (although for TAG's a proof is not in 
hand yet), LFG's can generate this language. 
In a TAG for each elementary tree, we can 
add mare elementary trees, systematically 
generated from the given tree to provide 
additional freedom of word order (tn a somewhat 
simllar fashion as in (Pullum,1982)). Since the 
adjoining operation in a TAG gives some 
additional power to a TAG beyond chat of a CFG, 
this device of augmenting the set of elementary 
trees should give more freedom, for example, by 
allowing some limited scrambling of an item 
outside of the constituent it belongs co. Even 
then a TAG does not seem co be capable of 
generatlng the language in 3 in TABLE I. Thus 
there is extra freedom but it is quite limited. 
lwl., i'~.l~" al.lw~i+ %~w~l+ ---.a,.lw.l 
iI 
TABLE I 
GPSG TAG 
(and CFG) (with or 
without local 
constraints) 
PLC LFG 
no yes yes yes 
to Language obcalned by 
starting with 
L={(ba)n~n/n ~ 1} and 
then dislocating some a's 
to the left. 
2o Same as I above except 
that the dislocated a's are 
to the left of all b's.. 
3. L={w / w is string of 
equal number of a's,b's and no 
c's but mixed in any order} 
4° L={x ~y/ n~l, x,y are 
strings of a's and b*s such that 
the number of a'sin x and y = 
the number of b's in x and y- n} 
5. Same as above except that the 
length of x = length of y. 
6. L={w ~/ n~ t, w is string of 
a's and b's and the number of a's 
in w = the number of b's in w - n} 
7. L={a ~b" c" In~l) 
8. Lf{a n b ~ c n d"/n~t} 
9. L={a~b ~ ~ d" ~ e/n 7 1} 
IO. L= {w w/ w is string 
of a's and b's}(copy language) 
11. L=(w w wl w is string of 
a's and b's}(double copy language) 
12. L=ia ~ c TM b ~ d m /m ~ l,n ~ 1} 
13. L={a ~ ~ c W /n ~1, p ~ n) 
14. L-{a ~ In~ It 
15. L-{a nz /n~ 1} 
16. Limited cross-serial 
dependencies. 
17. Constant growth property 
18. Polynomial parsing 
no yes yes yes 
yes no(?) 
no no yes 
no yes no(?) 
no yes yes( ? ) 
no yes no 
no yes no 
no no no 
no yes yes(?) 
no no ? 
no no no ( ? ) 
no yes ? 
no no no ( ? ) 
no no no( ? ) 
no yes ? 
yes yes yes( ? ) 
yes yes ? 
yes 
yes 
yes(?) 
yes(?) 
yes 
yes 
yes 
yes 
yes 
? 
yes<?) 
yes 
yes 
no(?) 
no 
no(?) 
Notation: ?: answer unknown to the author, yes(?): conjectured yes 
no(?): conjectured no. 
12 
REFERENCES 
\[\[\] Gazdar,G.,"Phrase structure grammars" 
in The Nature of Syntactic Representations(eds. 
P. Jacobson and G.K. Pullum),D. Reidel, 
Dordrecht, (to appear). 
\[2\] Joshi, A.K. and Levy, L.S.,"Phrase 
structure trees bear more fruit than you would 
have thought", AJCL, 1982. 
\[3\] Joshl, A.K., Levy, L.S., and Takahashi, 
M.,"Tree adjunct grammars", Journal of the 
Computer and System Sciences,1975. 
\[4\] Josht, A.K.,"How much 
context-sensitivity Is required to provide 
adequate structural descrlpclons ?", in Natural 
language processing: Psycholln~ulstic, -- 
Theoretical, and Computational Perseptives, 
(edso Dowry, O., Karttunen, L., and Zwicky, 
A.), Cambridge University Press, (to appear). 
\[5\] Joshl, A.K. and Yokomorl, T.,"Parsln8 
of tree adjoining grammars", Tech. Rep. 
Department of Computer and Information Science, 
University of Pennsylvanla,1983. 
\[6\] Joshl, A.K. and Kroch, T., "Linguistic 
slgniflcance of TAG's" (tentative title), 
for thcoml ng. 
\[7\] Kaplan R. and Bresnan J.W., "Lexlcal 
functional grammar-s formal system for 
grammatical representation", in The Mental 
Representation of Grammatical Relatlons~ed. 
Bresnan, J.), MIT Press, 1983. 
\[8\] Peters, S. and Ritchte, R.W., "Phrase 
linking grammars",Tech. Rep. University of 
Texas at Austin, Department of Linguistics, 
1982. 
\[9\] Pullum, G.K.,"Free word order and 
phrase structure rules", in Proceeding of NELS 
\[_~2(eds. Puste.|ovsky, J. and Sells, P.), 
Amherst, MA, 1982. 
APPENDIX 
We will give here some examples to show how 
certain sentences could be derived in a TAG. 
For further details about thls TAG and its 
linguistic relevance, see (Joshi,1983 and Joshl 
and Kroch, forthcoming). Only the releva- ~ 
trees of the TAG, G-(I,A) are shown below. The 
following points are worth noting: (1)In a TAG 
the derivation starts with an initial tree. The 
appropriate lexlcal insertions are made for the 
Inltlal tree and the corresponding constraints 
as specified by the lexicon can be checked 
(e.g., agreement and subcacegorizacion). Then 
as the derivation proceeds, as each auxiliary 
tree is brought into the derivation, the 
appropriate lexical items are inserted and the 
constraints checked. Thus in a TAG, lexical 
insertion goes hand in hand with the derivation. 
(2) Each one of the two finite sets, I and A can 
be quite large, but these sets need not be 
expllcltely listed. The crees in \[ roughly 
correspond to all the "minimal' sentences 
corresponding to different subcategorlzation 
frames together with the "transforms" of these 
sentences. We could , of course, provide rules 
for obtaining the trees in I from a given subset 
of I. These rules achieve the effect of 
conventional transformational rules, however, 
these rules can be formulated not as the usual 
transformational rules but directly as tree 
rewriting rules, since both the domains and the 
co-domains of the rules are finite. 
Introduction of links can ~,~ considered as a 
part of this rewriting. In any case, these 
rules will be abbreviatory in the sense Chat 
they will generate only finite sets of trees. 
Their adoption will be only a matter of 
convenience and does not affect the TAG in any 
essential ~nner. The set of auxiliary trees is 
also finite. Again these trees could themselves 
be "derived" from the corresponding trees in I 
by introducing appropriate tree rewrltlng rules. 
Again these rules will be abbrevlacory only as 
discussed above. It is in this sense that the 
trees in I and A capture the usual 
transformational relations more or less 
directly. 
Some derivations: 
(l)The girl who met 8ill is a senior. 
We start with the inlttal tree ~ with the 
appropriate texlcal insertions. 
S ~--z..-- 
~/P VP 
~r e~ v ~P 
I I ;~ /~ 
-'tk e. ~;~ I 
o.. 
N 
I 
Se..n ,'~ • 
13 
Adjoining 8t (with the appropriate lexical 
insertions) to~ at the indicated node in ~ , 
ve obtain ~I . 
/"\ Z.~ ', /\ 
e V NP ) kip v~' % ~ 
i ~ i 1 /\ ,, INt" 
I I i V Ivp'. 
ltlll ) I I ! 4i--Z._ 
llkl mee I,'il ~ i~llii..-' 
• "rl,,t ~i~i iik,I mlit I;ll {i 0, il~ilr 
(2)John persuaded Bill to invite Hary. 
N9 ,~p 
| /.~, 
tim "To vl ° 
V xP 
I I 
inv;te I 
Ad~otnin~ /~ ro ~".1 at the tndit'~ated node 
in ~.lr, ~ ohtain Yi" 
~JP '4p 
I /\~ 
# 
t,i 
;,,'11 
~ii,~'ll ~el litieiL ll'll 
t I /t~_ \] 
/ I ,"/~_ 
'~ ~'o~'" I ~.; I I\ % / "' t I -'Iril ,~i ~i 
) fro 
.... " V ~P I 
I ~, 
i~l'tt i 
(3)Nho did John persuade Bill to invite ? 
~l ~ o{Ii -.. 3 
44 \.S "/''x'''~ 
v I /\ 
~, ~a To V? 
V ,'SAP 
"~, I ". I 
• "% i'l'lll'fl ~" 
Ad~ointng ~J to ~C% at the indicated node 
in IC~L, we obtain y~.. 
® 
3o NP ~? / ~~ 
I v NP ra 
' t "" ~'a k,, ld 
p~v.fu.,ll ; 
r~¢tl 
.S 
"" ,/{~ - A P 
/,ili~ lle' .,i? ,, a /~--~'~-- : 
I- ~ ~ V ~P , ' 
~ peY~.,~. \[ ', mo v ,'h@ "- GIll ) 
.. , I ", I 
14 
Note the link In ~ is 'preserved' in~ , 
it is "stretched' resultin 8 in the so-called 
unbounded dependency. 
(&)John tried to please Mary. 
i ",._- 
NP vp 
l /~- 
~o 1-o ,,/P' 
V NP 
On the other hand 
(5)john seems to like Mary. could be 
derived as follows. We will start with ~#~. 
/ ~. S z"-z --~" 
~P V? 
-r~ vf 
/\ 
:T~, 4 UP 
\[ i 
I 
AdJ°inin8 J7 ~o ~ at the indicated node 
in Y~ we obtain ~l" 
~'r = 
, 
~4 
I t 
/ 
t Hr" vP ' 
l I /'~ ' 
\ -t.i~'~ j~i'~ f~ "~ 
• ~. . • 
-to VP ~e i\ 
V NP 
AdJoinin~ ~Mto Y~. at the indicated node 
in ~'*t , we obtain ~*~. 
I 
S 
I o /~..! 
m V YP 
I " 
i i !/~ 
wP 
I 
r~A~ 
JaQm~ -to l(ka /,4 o P.~ 
15 
