Long-Distance Scrambling and Tree Adjoining 
Grammars* 
Tilman Becker~ Aravind K. Joshi, Owen Rainbow 
University of Pennsylvania, Department of Computer and Information Science, Philadelphia, PA 19104-6389 
t ilman@cs .uni-sb .de~ { joshi ,rainbow} @linc. cis. upenn, edu 
1 Introduction 
Scrambling, both local and long-distance, has recently 
attracted considerable attention among linguists and 
computational linguists. In this paper, we will ex- 
plore the adequacy of the Tree Adjoining Gram- 
mar (TAG) formalism for dealing with long-distance 
scrambling I in German. We will show that TAGs 
cannot capture the full range of constructions derived 
by scrambling. I\[owever, Multi-Component TAGs 
(MC-TAG), an extension of TAGs introduced earlier 
\[Joshi 1987a, Weir 1988\] and utilized for linguistic pur- 
poses (e.g. for extraposition \[Kroch and Joshi 1986\]), 
can indeed capture the full range of constructions de- 
rived by scrambling. We will also present an ID/LP 
variant of TAG to capture the same constructions, and 
then comment on the relationship between the two sys- 
tems. 
2 Some Linguistic Data 
A striking feature of scrambling is its freedom: there 
appear to be no systematic syntactic restrictions on 
the number of verbal arguments that undergo "move- 
ment," nor on the distances over which they may 
move 3. Thus, any ordering of the arguments from all 
clauses is possible. To illustrate this freedom we will 
present two additional examples in which scrambling 
of a more complex nature occurs. 
1. More than one constituent may undergo movement 
into higher clauses. The scrambled constituents need 
not retain their original relative order to each other af- 
ter scrambling. In sentence (2b), two NPs are scram- 
bled out of the embedded clause into the top-level 
clause. 
2. Constituents may be moved over an unbounded 
number of clauses. In sentence (3b), NP die Witwen 
has been moved into its immediately dominating 
clause, while NP der Opfer has been moved from the 
most deeply embedded clause into the top-level clause, 
beyond the intermediate clause. 
In German (and in many other SOV languages, such 
as Korean, Ilindi and Japanese), a constituent of an 
embedded clause may be moved from that clause into 
the matrix clause. Consider, for example, sentences (1) 
in Figure 1. In German, the object of the embedded 
clause can be "moved "2 to any position in the matrix 
clause, as in sentences (lb) and (lc). 
"This work was partially supported by NSF grants DCR-84- 10413, ARO grant DAAL03-89-O031, and DARPA-ONR grant 
N0014-85-K0018. We are indebted to Tony Kroch, Young-Suk 
Lee, Beatrice Santorini, Yves Schabes and David Weir for dis- cussions and clarifications related to this paper. 
t Now at University of Saarbrllcken, Fachbereidt Informatik, D-W6600 Saarbriicken. 
11ntra-clausal scrambling and string-vacuous scrambling will 
not he discussed in tlfispaper, since they do not pose any par- 
tieular problem for the TAG formalism. 
2We use "traces" only to indicate the unmarked order; we 
do not mean to imply any particular theory of movement. In 
fact, analyses have been proposed (going back to \[Evers 1975J} bMid on a proctms of "ver\[~ cluster formatlon n, which avoid 
inter-clausal movement altogether. However, since embedding 
is recursive, the verb clusters ca,mot all be listed in the lexicon. Ilence, from a formal point of view, a lexical or morphological 
analysis of verb cluster formation poses exactly the same prob- lems as scrambling interpreted as syntactic movement. 
3 A TAG Analysis 
The TAG formalism (for a recent introduction, see 
\[Joshi 1987a\]) is well suited for linguistic description 
because (1) it provides a larger domain of locality than 
a CFG or other augmented CFG-based formalisms 
such as tlPSG or LFG, and (2) it allows factoring of 
recursion from the domain of dependencies. This ex- 
tended domain of locality, provided by the elementary 
trees of TAG, allows us to "lexicalize" a TAG gram- 
mar: we can associate each tree in a grammar with a 
lexical item \[Schabes et al 1988, Schabes 1990\] 4. The 
tree will contain the lexical item, and all of its syntac- 
3Some verbs allow scrambling out of their Complements 
more freely than others. It appears that all subject-control 
verbs and most object-control verbs governing the dative al- 
low scrambling fairly f~ely, while scrambling with object- control verbs governing the accusative is more restricted (cir. 
\[Bayer and Kornfilt 1989\]). FYom a formal point of view, these 
restrictions are not relevant for the present argument. 
4 The associated lexical item is called the anchort and is either 
the head or the functional head of the tree. 
-21 - 
(la) ...daft ichl dem Kunden \[PROi den Kiihlsehrank 
..that I the client (dat) the refrigerator (ace) 
.. that I have promised the client to repair the refrigerator 
(lb) ...dab ichi \[den Kiihischrank\]j dem Kunden \[PRO/tj zu reparieren\] 
...that I the refrigerator (ace) the client (dat) to repair 
... that I have promised the client to repair the refrigerator 
(lc) ...dab \[den Kiihlschrank\]j ichi dem Kunden \[ PRO/tj zu reparieren\] 
that the refrigerator (ace) I the client (dat) to repair 
that I have promised the client to repair the refrigerator 
(2a) ...dab der Detektiv/ dem Klienten \[PRO/ den VerdKchtigen 
... that the detective (nora) the client (dat) the suspect (ace) 
des Verbrechens zu iiberfiihren\] versprochen hat 
the crime (gen) to indict promised has 
• .. that the detective has promised the client to indict the suspect of the crime 
(2b) ... dab \[des Verbrechens\]k der Detektivi \[den Verd~ichtigen\]j 
... that the crime (gen) the detective (nora) the suspect (acc) 
dem Klienten \[PROi tj tk zu iiberfiihren\] versprochen hat 
the client (dat) to indict promised has 
• .. that the detective has promised the client to indict the suspect of the crime 
(3a) ...da6 der Rat dem Pfarrer \[die Witwen/ \[PI'LOi der Opfer 
...that the council (nom) the priest (dat) the widows (ace) the victims (gen) 
gedenken\] zu lassen\] versprochen hat 
commemorate to let promised have 
... that the council has promised the priest to let the widows commemorate the victims 
(3b) ... dab \[die Witwen\]j \[der Opfer\]i \[dem Pfarrer\]k 
... that the widows (ace) the victims (gen) the priest (dat) 
der Rat tk \[tj \[PROj ti gedenken\] zu lassen\] versprochen hat 
the council (nom) to commemorate let promised have 
. .. that the council has promised the priest to let the widows commemorate the victims 
zu reparieren\] versprochen habe 
to repair promised have 
versprochen 
promised 
versprochen 
promised 
habe 
have 
habe 
h ave 
Figure 1: Example Sentences 
tic dependents. As has been shown previously, certain 
long-distance phenomena such as topicalization and 
wh-movement can be handled naturally within TAG 
\[Kroch and Joshi 1985\]. Ilere, "naturally" means that 
dependencies are stated within the larger domain of lo- 
cality (the elementary tree), i.e., each clausal tree still 
contains a verb and all of its arguments. Thus, in a 
lexicalized TAG, the effects of long-distance movement 
are achieved by adjunction. The word order freedom 
possible in the context of unconstrained scrambling, 
however, eludes the scope of TAGs. In this section, we 
will informally argue this formal result. 
By an argument very similar to Shieber's argument 
for Swiss German \[Shieber 1985\], it can b'e shown that 
the string language of scrambled High German is not 
a context-free language. However, the linguistic facts 
of German do not allow an extension of the argu- 
ment: we cannot show that the string language is not 
a Tree Adjoining Language. From a linguistic perspec- 
tive, the existence of some grammar that generates the 
string language of German scrambling is not in itself 
of much interest. For examl)le ~ if we define a TAG 
grammar that generates the strings of scrambled Ger- 
man in which, however, some trees pair a verb with 
tile arguments of some other verb, then we have not 
adequately described the linguistic facts. We are really 
only interested in linguistically motivated grammars, 
namely those that exploit the extended domain of lo- 
cality and whose trees obey tile constraint of contain- 
ing a lexical item and all of its syntactic dependents 
(and nothing else). We will refer to such restrictions 
as "co-occurrence constraints". We can show that no 
TAG meeting the co-occurrence constraints can gener- 
ate the sentences of German scrambling. We will argue 
this point in two complementary ways. First, we will 
consider the ease of clauses with two overt nominal ar- 
guments. Then, we will consider the case of clauses 
with one overt nominal argument. 
In the first case, the verb of the embedded clause 
subcategorizes for three NPs, one of which is an 
empty subject (PRO). There is no verb in Ger- 
man that subcategorizes for three NPs and an 
S, so in this case a recursively embedded struc- 
ture is impossible, and we have only one level 
of embedding. We show that the language 
{a(NP~, NP~,NP~,NP~)V~VI \[ a a permutation} 
- 22 - 
cannot be generated by a TAG that contains only ele- 
mentary trees obeying the co-occurrence restraints. A 
linguistically plausible set of two such trees is shown in 
Figure 2. Consider the string NP~NP~ NP~NP~V~VI, 
which corresponds to the ordering in sentence (2b). It 
can easily be seen that this string cannot be generated 
by a TAG of the specified sort: after an adjunct,on the 
yield of the adjoined tree is segmented into at most two 
sections, while the yield of both trees would need to be 
segmented into three sections in order to be composed 
into the desired string. 
~: S 
NPI $ 
NP I ve 
NP~ S V t 
S 
NP~ S 
NP / 8 
NP VP I/b, 
,.o i,; i.; v, 
Figure 2: Initial trees with two verbal arguments 
In the second case, the verbs of the embedded clauses 
subcategorize for two NPs, one of which is again an 
empty subject (PH.O), and an S. We will argue that 
the language {a(NPt,..., gPk)Vk... I/1 I k E N and cr 
a permutation} cannot be generated by a TAG which 
obeys the co-occurrence constraints, i.e., whose ele- 
mentary trees have only two (non-vacuous) terminal 
leaves, NPi and ~5. The idea in selecting this lan- 
guage is as follows: we keep the verbs at the end in 
the inverted order required by embedding, and then 
consider all possible permutations of the NPs. For 
k _< 4 TAGs that generate the possible permuta- 
tions can be constructed; for k = 4 the construc- 
tion is not obvious, but we will not give the details 
here. However, for k = 5 it is impossible. Con- 
sider the string w = NP3NP1NP~ NP2 NP4 V5 V4 Va V2 I/i. 
For this string, it can be shown that it is impossible 
to construct a TAG which meets the co-occurrence 
constraints discussed above and that generates the 
string. The proof is fairly involved; for details, see 
\[Becker and Itambow 1990\]. 
In deciding whether scrambling as a linguistic phe- 
nomenon can adequately be described by a TAG or 
a TAG-equivalent formalism, it is crucial to decide 
5Note that the indices are not actua|ly part of the alpha- 
bet over wliich we have deft,led the langoage, wlfich is simply {NP, 
V}. The indlces oldy serve the pt*rpo~e of indicating wlllch 
terminals axe supposed to be col,tributcd by which tree, exploit- ing 
the co-occurrence constraints. 
whether or not sentences corresponding to the strings 
given above are indeed grammatical. In the case of the 
embedded two-argument clauses, examples are readily 
available, as in sentences (2a) and (2b). In the case of 
the embedded one-argument sentences, it is more diffi- 
cult (but not impossible) to construct an adequate ex- 
ample because of the great depth of embedding. How- 
ever, one might argue that there is a limit on the num- 
ber of clauses over which a scrambled NP may move. 
If this were true, the number of resulting structures 
would be finite, so that they could be handled triv- 
ially by simple formalisms. Sentences (3a) and (3b) 
show scrambled NPs can move over two clauses, and 
we know of no evidence that convincingly establishes 
such a limit for higher numbers. The reluctance that 
some native speakers show to accept the more com- 
plex sentences is due mainly to processing difficulties, 
rather than to tim ungrammaticality of the sentences. 
A similar phenomenon occurs when native speakers re- 
ject multiply center-embedded sentences as "ungram- 
matical". 
In summary, long-distance scrambling provides lin- 
guistic evidence that shows that scrambling is beyond 
the formal generative capacity of TAGs. In the next 
two sections, we will investigate two ways of extending 
the TAG formalism in order to achieve the necessary 
power. In the first approach, we will relax the imme- 
diate dominance relation of the elementary trees. In 
the second approach, we will relax the linear prece- 
dence relations of the elementary trees. In both cases, 
our concern will be to preserve the key properties of 
'FAGs, namely their extended domain of locality, and 
the factoring of recurs,on from dependencies. 
4 A Multi-Component TAG (MC-TAG) Approach: Re- 
laxed ID 
One approach is to relax the ID (Immediate Domi- 
nance) relation within one elementary tree. Even in 
a standard TAG, the ID relation between a mother 
and a daughter node is not necessarily an immediate 
dominance relation because of the possibility of ad- 
joining another tree at the daughter node. We pro- 
pose to relax some of the ID relations of the auxiliary 
tree when it is adjoined. This can be seen as splitting 
up tile auxiliary tree into parts, while still keeping a 
dominance constraint between the parts. As we will 
show, such a splitting of the elementary trees, interest- 
ingly, leads to a previously defined extension of TAGs: 
namely, that of Multi-Component TAGs (MC-TAG) 
- 23 - 
\[Joshi 1987a, Weir 1988\]. 6 
As shown in Section 3, a TAG meeting the 
co-occurrence constraints cannot derive the string NP~NpINP~NP21V2VI. 
It is obvious that in order 
to get this variation from the trees in Figure 2, the 
yield of the adjoined tree/~ has to be broken up into 
three segments, which means that/~ has to be broken 
up into two parts that are then adjoined to different 
nodes of a. This is exactly what relaxation of the ID 
relation can achieve. If the tree/~ in Figure 2 is split 
at the interior S node, i.e. by relaxing the ID relation 
between the two S nodes, we can construct a pair of 
auxiliary trees as shown in Figure 3, where the dashed 
line indicates a dominance relation. 
e Ne I S V~ 
Figure 3: Splitting an elementary tree into two parts. 
$ 
.... .... 
/\ 
NP VP 
PRO 
Figure 4: Adjunction of an MC-TAG tree set 
Sets of trees are exactly what the MC-TAG formal- 
ism introduces. In an MC-TAG, instead of auxiliary 
trees being single trees we have auxiliary sets, a set 
containing more than one (but still a fixed number) 
oMC-TAGs have already beenused by Kroch and Joshi \[Kroch and Joshi 1986\] for the analysis of extraposition. It is 
interesting to note that the additional requirement that the foot node of one of the components of an auxiliary set dominate 
the root node of tile other component i. tile same auxiliva'y set was 
also used by them. 
of auxiliary trees. For details of tile definition of MC- 
TAG see \[Joshi 1987a, Weir 1988\]. In an MC-TAG, 
adjunction is defined as the simultaneous adjunction 
of all trees in a set to different nodes. It is not possi- 
ble to adjoin trees from the same set into each other. 
Thus, we can interpret TAGs with relaxed dominance 
as MC-TAGs, by identifying subtrees containing only 
ID relations with trees in an MC-TAG tree set. How- 
ever, we need to introduce an additional constraint: 
the foot node of the first tree (~1) in the tree set of 
Figure 3 has to dominate the root node of the second 
tree (~z) after adjoining the tree set. This is indicated 
by the dashed link between the foot node of ~1 and 
the root node of/~2. For example, Figure 4 shows the 
effect of adjoining the tree set of Figure 3 into tree 
(~ of Figure 2, which yields the ordering of scrambled 
sentence (2b), NP~ZNpINP~NP2tV2VI.7 
In defining adjunction for MC-TAGs, an issue arises 
tha¢ is irrelevant in the case of simple TAGs: do 
we restrict adjunction in such a way that members 
of a tree set must be adjoined into the trees of an 
elementary tree set, or do we allow adjunction into 
derived tree sets as well? With the restricted defini- 
tion of adjunction (called "local MC-TAG"), MC-TAG 
has been shown to have a slightly greater generative 
power than TAG; however, local MC-TAGs still be- 
long to the class of Mildly Context Sensitive Gram- 
mar formalisms (MCSG). Weir \[Weir 1988\] has also 
shown that MC-TAGs are equivalent to the Linear 
Context Free Rewriting Systems (LCFRS), which are 
the best known characterization of the MCSG formal- 
ism (though they are not an exhaustive characteriza- 
tion of MCSG). In particular, we know that local MC- 
TAGs are polynomially parsabie. However, it can be 
shown that local MC-TAGs are not adequate for de- 
riving all possible scrambled sentences in German (for 
a detailed discussion, see \[Becker and Rainbow 1990\]). 
In fact, no LCFILS is powerful enough to capture 
scrambling. It is obvious that MC-TAG with the more 
liberal definition of adjunction (called "nonlocal MC- 
TAG") can produce all the possible versions of scram- 
bled embedded sentences for any level of embedding. 
However, nonlocal MC-TAG has not yet been stud- 
ied in detail, and it is currently not known whether 
nonlocal MC-TAGs are polynomially parsable. 
7This particular example can be derived with a weaker for- 
msdism; the point of tile examp..ie is merely to illustrate the proposed formalism. It can easdy be seen 
how it can handle scrambling from arbitrary levels of embedding. 
- 24 - 
$ A Free-Order Approach: tte- 
laxed LP 
An alternative formalism, which we will call FO-TAG 
(Free Order TAG), is closely based on the LD/LP- 
TAG framework presented in \[Joshi 1987b\]. As does 
an LD/LP-TAG grammar, a FO-TAG grammar con- 
sists of a set of elementary structures. Each elemen- 
tary structure is a pair consisting of one linear dom- 
inance (LD) structure (i.e., an unordered tree) and 
corresponding LP rules. The LD structure (which will, 
imprecisely, be referred to as a "tree" in this paper) is 
either an initial or an auxiliary structure. The LP rules 
may relate any two nodes of the tree unless one linearly 
dominates the other, ttowever, these precedence rules 
can only be stated with respect to the nodes of an 
elementary tree; it is impossible to relate nodes in dif- 
ferent trees. When an auxiliary tree fl is adjoined into 
an initial tree et, the nodes of fl are not ordered with 
respect to the nodes of a. However, even in languages 
with relatively free word order there are restrictions on 
movement. In order to capture these, we introduce two 
linguistically motivated constraints, the integrity con- 
straint and the inheritance constraint. The integrity 
constraint, written A, allows us to express the fact 
that German does not allow scrambling into or out 
of certain constituents, such as NPs and CPs (tensed 
clauses). If we have AX for some node X, then any 
node which is not in the subtree rooted at X and which 
does not dominate X must either precede or follow ev- 
ery node in the subtree rooted in X. The inheritance 
constraint, written $, forces inheritance and allows us 
to capture the clause-final position of the verb in Ger- 
man. If we have $X for a node X, then when the tree 
of which X is a node is adjoined into another tree at 
node A, X inherits all LP rules specified for A. 
As an example, consider sentences (2a) and (2b) given 
in Section 2. The initial trees along with the LP rules 
and constraints are shown in Figure 5. Adjunction 
yields the structure shown in Figure 6. Note that only 
one of the possible orderings of the nodes, correspond- 
ing to sentence (2b), is shown. 
S b < V~ 
NP~ < V, NP~ < V 2 
sb t vj P.o ANt I ANP 1 S V 2 
Figure 5: The initial trees in the FO-TAG formalism. 
It is easy to sce that FO-TAG can generate all scram- 
bled configurations, while obeying' the co-occurrence 
5 NP~ < S 2 
NP~ <S 2 
S 2 <V~ 
<v d 
ll : < v d 
NP~ < V ! 
NPI <v, 
< 
A PI 
Figure 6: Sentence (2b) in FO-TAG 
constraint. As in the case of nonlocai MC-TAGs, it is 
immediately obvious that FO-TAG is not an LCFRS; 
the question of polynomial parsability remains open, 
as does the question of the generative power of FO- 
TAG. We are currently investigating these issues. 
From a linguistic point of view, it is interesting that 
the same linguistic phenomenon can be handled by 
two very different formalisms. Scrambling is currently 
attracting much attention from syntacticians working 
in the GB framework. One question as yet unresolved 
is whether clause-internal scrambling is the same type 
of syntactic movement as long-distance scrambling. In 
FO-TAG, both types of movement are created by the 
same formal device, namely the underspecification of 
LP rules. In the case of MC-TAG, only long-distance 
scrambling can be simulated by multicomponent ad- 
junction; clause-internal scrambling must be handled 
by some other means (such as metarules, which func- 
tion as an abbreviatory device for listing a finite set of 
elementary trees), since it is impossible to adjoin one 
tree into another tree of the same tree set. There are 
several other syntactic issues which are currently being 
debated in tile linguistic literature, and for which the 
two formalisms make different predictions. For details, 
see \[Rambow and Becker 1990\]. 
- 25 - 
6 Comparison with Other 
Work 
Kroch, Santorini and Joshi's analy- 
sis \[Kroch et al 1990\] of sentences like (2a) and (2b) 
is similar to the approach proposed in section 4. They 
also make use of a splitting of the auxiliary tree fl 
of figure 2, though they split the elementary tree into 
different tree sets. In particular, the verb and its argu- 
ments are no longer contained within the same domain 
of locality, a key requirement of the TAG formalism. 
Their approach is essentially motivated by linguistic 
considerations; however, it is easy to show that their 
analysis can be expressed in our proposed variant of 
MC-TAG, thus supporting our purely formal analy- 
sis, and also showing that the locality of TAGs can be 
preserved. 
The proposed FO-TAG formalism is close in spirit to 
GPSG, in that ID and LP relations are stated sepa- 
rately. IIowever, none of the work done on free word- 
order languages in the GPSG framework that we are 
aware of \[Uszkoreit 1987, Lee 1985\] deals with long- 
distance scrambling. 
7 Conclusion 
We have shown that long-distance scrambling, a syn- 
tactic phenomenon exhibited by German and some 
other languages, cannot be adequately described with 
a TAG. We have proposed two more powerful exten- 
sions of TAG: a variant of the well-studied MC-TAG, 
and a TAG formalism with free node order, FO-TAG. 
We have shown that both are descriptively adequate. 
The linguistic descriptions that these formalisms give 
rise to, however, are quite different, and they make 
different predictions about the nature of long-distance 
scrambling. 
Some key formal properties of the two formalisms are 
still under investigation, in particular the issues of 
polynomial parsability and generative power. We con- 
jecture that FO-TAG and MC-TAG with dominance 
links (or some slight definitional variants of the two 
systems) are weakly equivalent to each other. 
References 
\[Bayer and Kornfllt 1989\] Bayer, Josef and Kornfilt, Jak- 
lin, 1989. Restructuring Effects in German. In Para- 
metric Variation in Germanic and Romance, Centre for 
Cognitive Science, University of Edinburgh. 
\[Becket and Rainbow 1990\] Becker, Tilman and Rambow, 
Owen, 1990. Formal Aspects of Long Distance Scram- 
bling. Unpublished Paper, University of Pennsylvania. 
\[Evers 1975\] Evers, Arnold, 1975. The transformational 
cycle in Dutch and German. PhD thesis, University of 
Utrecht. Distributed by the Indiana University Linguis- 
tics Club. 
\[Joshi 1987a\] Joshi, Aravind K., 1987. An Introduction 
to Tree Adjoining Grammars. In Manaster-Ramer, A. 
(editor), Mathematics of Language. John Benjamins, 
Amsterdam. 
\[Joshi 1987b\] Joshi, Aravind K., 1987. Word-Order Varia- 
tion in Natural Language Generation. Technical Report, 
University of Pennsylvania. 
\[Kroch and Joshi 1985\] Kroch, Anthony and Joshi, Ar- 
avind K., April 1985. Linguistic Relevance of Tree Ad- 
joining Grammars. Technical Report MS-CIS-85-18, De- 
partment of Computer and Information Science, Univer- 
sity of Pennsylvania. 
\[Kroch and Joshi 1:986\] Kroch, Anthony and Joshi, At- 
avind K., 1986. Analyzing extraposition in a Tree 
Adjoining Grammar. In tIuck, G. and Ojeda, A. 
(editors), Syntax and Semantics: Discontinuous Con- 
stituents. Academic Press, New York, NY. 
\[Kroch et al 1990\] Kroch, Anthony; Santorini, Beatrice; 
and Joshi, Aravind, August 1990. A TAG Analysis of 
the German Third Construction. In First International 
Workshop on Tree Adjoing Grammars. SchloB Dagstuhl, 
Germany. 
\[Lee 1985\] Lee, Ik-Hwan, 1985. Toward a Proper Treat- 
ment of Scrambling in Korean. In Kuno, Susumo; Whit- 
man, John; Lee, Ik-Hwan; and Kang, Young-Se (edi- 
tors), Harvard Studies in Korean Linguistics. Hanshin 
Publishing Company, Seoul, Korea. 
\[Rainbow and Becker 1990\] Rambow, Owen and Becker, 
Tilman, 1990. Scrambling and Tree Adjoining Gram- 
mars. Unpublished Paper, University of Pennsylvania. 
\[Schabes 1990\] Schabes, Yves, August 1990. Mathemati- 
cal and Computational Aspects of Lezicalized Grammars. 
PhD thesis, University of Pennsylvania, Philadelphia, 
PA. Available as technical report (MS-CIS-90-48, LINC 
LAB179) from the Department of Computer Science. 
\[Schabes et al 1988\] Schabes, Yves; Abeill~, Anne; and 
Joshi, Aravind: K., August 1988. Parsing Strategies 
with 'Lexiealized' Grammars: Application to Tree Ad- 
joining Grammars. In Proceedings of the 12 th Interna- 
tional Conference on Computational Linguistics (COL. 
ING'88). Budapest, Hungary. 
\[Shieber 1985\] Shieber, Stuart B., 1985. Evidence against 
the context-freeness of natural language. Linguistics and 
Philosophy 8:333-343. 
\[Uszkoreit 1987\] Uszkoreit, Hans, 1987. Word Order and 
Constituent Structure in German. CSLI, Stanford, CA. 
\[Weir 1988\] Weir, David J., 1988. Characterizing Mildly 
Contezt-Sensitive Grammar Formalisms. PhD thesis, 
Department of Computer and Information Science, Uni- 
versity of Pennsylvania. 
- 26 - 
