Monotonic C-Command:

A New Perspective on Tree Adjoining Grammar

Robert Frank (rfrank@cogsci.jhu.edu)Dept. of Cognitive Science, Johns Hopkins University

Seth Kulick (skulick@linc.cis.upenn.edu)Institute for Research in Cognitive Science, University of Pennsylvania

K. Vijay-Shanker (vijay@cis.udel.edu)Dept. of Computer and Information Sciences, University of Delaware

Abstract.

In this paper we argue for a reconceptualization of the Tree Adjoining Grammar(TAG) formalism, in which the elementary structures are collections of c-commandrelations, and the combinatory operation is substitution. We show how the formalismwe sketch resolves a number of problems for TAG that have been identified in theliterature. Additionally, we demonstrate that our proposal is preferable to otherpreviously proposed extensions to TAG, for example D-tree grammars (Rambowet al., 1995), in that it preserves many of the linguistically desirable aspects ofTAG’s restrictiveness, specifically concerning the derivation of locality constraintson unbounded dependencies.

Keywords: C-Command, Long-Distance Dependencies, Tree Adjoining Grammar

1. Introduction

The Tree Adjoining Grammar (TAG) formalism has a number of prop-erties that make it attractive for use in natural language analysis.Specifically, the use of the adjoining operation allows the specificationof grammatical constraints to be separated from the recursive processesin the grammar. This leads to an elegant analysis of extraction in TAGwhich allows the specification of co-occurrence constraints to remainstated within the local domains determined by the elementary trees(Kroch and Joshi, 1985; Frank, 1992). Over the last 15 years, however,it has been pointed out a number of times that there exist linguis-tic phenomena that pose problems for this elegant analysis. This hasled to a variety of proposed extensions to the basic TAG formalism.The most successful of these extensions with regard to capturing thebroadest range of problematic cases have, unfortunately, also extendedthe formal power of TAG, so much so that grammatical constraintslike Subjacency, that had been found to be derivable from general

c© 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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2 Frank, Kulick and Vijay-Shanker

Y

Y

X

X

Y

Y

Y

(B)(C)

(A)

Figure 1. Adjoining in TAG

architectural properties of the TAG adjoining operation (Kroch, 1987),must now be explicitly stated in the extended formal systems.

In this paper we argue for a reconceptualization of the TAG formal-ism, in which the elementary structures are collections of c-commandrelations and the combinatory operation is substitution, thus refiningand expanding upon a proposal made by Frank and Vijay-Shanker(1998b). This extension turns out to be sufficiently powerful to cap-ture previously problematic cases, though it preserves many of thelinguistically desirable aspects of TAG’s restrictiveness. In section 2we present a brief overview of TAG, in section 3 we discuss a coupleof the empirical problems for the TAG analysis of extraction, and insection 4 we review a pair of proposed solutions. Section 5 presents theoutline of our proposal, and in section 6 we illustrate how it is ableto retain the linguistically relevant restrictiveness of the original TAGderivational system.

2. TAG and Extraction

The separation of recursive processes in TAG is accomplished by localiz-ing the grammatical constraints within small pieces of phrase structure,called elementary trees, which are combined using the adjoining op-eration. The adjoining operation operates by splitting a tree at onenode, which we will call the adjoining site. In the resulting structure,the subtrees above and below the adjoining site are separated by, andconnected with, the auxiliary tree used in the composition, as shown inFigure 1. Trees which can be adjoined into another tree are auxiliary

trees, and have a foot node along the frontier which is of the samecategory as the root node. As illustrated below, recursive structuresare treated as auxiliary trees, which adjoin in to produce non-localdependencies. (In addition to adjoining, tree substitution is also usedas a tree composition operation in TAG.)

TAG is a formal system that combines elementary trees, but it isnot a linguistic theory and imposes no constraints upon the nature of

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Monotonic C-Command: A New Perspective on TAG 3

(a) IP

���

HHH

DPi

Gabriel

I′

��HH

I

to

VP

��HH

ti V′

�� HH

V

eat

DP

gnocchi

(b) I′

��HH

I VP

�� HH

V

seems

I′

Figure 2. Elementary trees for subject to subject raising

these elementary trees. However, it does enforce a particular workinghypothesis for all linguistic work in TAG, namely that the substantivetheory of syntax must be stated over the bounded local domains of theelementary trees. We follow here the characterization of the elementarytrees proposed by Frank (1992), in which the crucial point is that anelementary tree is built around some lexical predicate and includes all ofthe syntactic structure necessary for the realization of all of its semanticarguments, its so-called extended projection (Grimshaw, 1991).

(1) Condition on Elementary Tree Minimality (CETM):Every elementary tree consists of the extended projection ofa single lexical head

Under the CETM, the building blocks of TAG derivations, the el-ementary trees, are larger than individual lexical items or individualphrase structure rules familiar from other formalisms. Rather, theyare themselves phrase structure trees. This extended domain of locality

of TAG allows the expression of lexically imposed constraints to beseparated from the recursive processes involved in the construction ofcomplex phrase markers and creation of long-distance dependencies, asin wh-movement.

A TAG analysis of the subject raising construction (Kroch and Joshi,1985; Frank, 1992) provides a clear demonstration of how the adjoiningoperation can be used to separate local dependencies from recursivegrammatical processes. Consider the raising sentence in (2).

(2) Gabriel seems to eat gnocchi

The tree headed by eat, given in Figure 2(a), is its IP extended projec-tion. Note that the tree for seems, in Figure 2(b), lacks a position forthe matrix subject Gabriel, since seems does not select for a subject.

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4 Frank, Kulick and Vijay-Shanker

IP

���

HHH

DPi

Gabriel

I′

���

HHH

I VP

���

HHH

V

seems

I′

��HH

I

to

VP

��HH

ti V′

�� HH

V

eat

DP

gnocchi

Figure 3. Result of TAG raising derivation

The recursive structure of auxiliary trees, together with the lack of a[Spec, IP] position, requires that seems takes an I′ complement in thetree in Figure 2(b). This auxiliary tree adjoins at the I′ node of theeat tree to form the tree in Figure 3. A distinctive feature of the TAGanalysis is that there is no “movement” from one clause to another.Whatever movement there may be (e.g., that of the subject from itsVP-internal position to [Spec, IP]) is internal to an elementary tree,and the appearance of inter-clausal movement results by segments of atree getting stretched away from the rest of the tree, as illustrated bythe Gabriel portion of the tree in Figure 2(a) being separated from therest of its elementary tree in the resulting structure in Figure 3.

The analysis of wh-movement, as in (3), is similar. The auxiliarytree given in Figure 4(b) is adjoined into the initial tree in (a) (withwhat moved to [Spec, CP]) at the C′ node, thus stretching what awayfrom that Mary saw.

(3) Whati do you think Mary saw ti?

The constrained nature of the adjoining operation (operating ona tree-to-tree basis) also has desirable results with regard to certainwell-known constraints on the locality of various types of inter-clausalmovements. In the context of the raising construction, it has been ob-served that sentences like (4), so-called “super raising”, are impossible,since Gabriel has moved “too far” past one intervening subject positionto the next higher one. Strikingly, nothing needs to be added to theTAG analysis presented above to derive this result.

(4) * Gabriel seems it is likely to eat gnocchi.

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Monotonic C-Command: A New Perspective on TAG 5

(a) CP

���

HHH

Whati C′

���

HHH

C IP

���

HHH

DPj

Mary

I′

�� HH

I VP

�� HH

tj V′

��HHV

saw

ti

(b) C′

���

HHH

C

dok

IP

���

HHH

DP

you

I′

���

HHH

I

tk

VP

�� HH

V

think

C′

Figure 4. Elementary trees for long-distance wh-movement

(a) I′

��HH

I VP

�� HH

V

seems

IP

(b) IP

���

HHH

DP

it

I′

��HH

I

is

AP��HH

A

likely

I′

Figure 5. Elementary trees that can’t produce super raising

Since neither of the trees in Figure 5 have identical foot and root nodes,neither are TAG auxiliary trees. However, under a different conceptionof tree composition operations, it might be possible to combine togetherthe trees from Figure 5 to form an I′ recursive tree for seems it is likely

that could then adjoin into the tree in Figure 2(a), thereby derivingthe super-raising case. However, this derivation is impossible in TAGsince it cannot be expressed by a well-formed derivation tree. Withoutgoing into the technical details, auxiliary trees must be “born”, not“made” (see Frank (1992) for a discussion of this case). Other cases oflocality constraints have been similarly derived (Kroch, 1987; Kroch,1989), providing strong support for the role of adjoining in establishinglong-distance dependencies.

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6 Frank, Kulick and Vijay-Shanker

C′

���

HHH

C IP

���

HHH

DP

Gabriel

I′

��HH

I

to

VP

�� HH

V

eat

DP

gnocchi

Figure 6. Infinitival elementary tree

3. Two Problems for TAG

As attractive as the account of long-distance dependencies just sketchedis, a number of serious problems for this account have been identifiedin the literature. In this section, we focus on two such problems.

The first of these concerns the phenomenon of modifier extraposi-tion, as seen in (5).

(5) A student walked in who Alice had asked about.

Here, the relative clause who Alice had asked about is interpreted asmodifying the subject, in spite of its apparent attachment to the rightof the clause. Even if we assume that the noun phrase a student and itsmodifying relative are generated within a single elementary tree, thereare no linguistically coherent structures that could be assigned to thiselementary tree and the one headed by walked that could derive (5)through an application of adjoining.

A second problem arises from the interaction of the raising construc-tion, discussed earlier, and subject-auxiliary inversion, as in (6).

(6) Does Gabriel seem to eat gnocchi?

The elementary tree for the eat clause in this example is shown inFigure 6. By the CETM, does should originate in the same elementarytree as seems. However, since the raising auxiliary adjoins to the I′ node,there is no way to include the auxiliary verb does within the seems treeso that it ends up in a position preceding the subject DP in the finalsentence. That is, adjoining at I′ “stretches” Gabriel away from to eat

gnocchi, without allowing the type of “interleaving” necessary to derive(6).

This problem arises in an even more severe form when there is si-multaneously wh-extraction of the PP experiencer complement to theraising verb:

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Monotonic C-Command: A New Perspective on TAG 7

DP��HH

DP ti

IP

����

HH

HH

IP CPi

����

��

PPPP

PP

who Alice had asked about

Figure 7. Multi-component tree set for extraposition from subject position

(7) To whomi does Gabriel seem ti to eat gnocchi?

Since to whom is an argument of seem, they should be in the same tree.Here, not only do we have the previous problem of do-support, but to

whom should be in the same elementary tree as seem as well, and theadjoining operation will not allow to whom and does to be distributedproperly to derive (7).

A number of other problems for TAG have also been discussed inthe literature, such as clitic climbing (Bleam, 1994; Kulick, 1997), longdistance-scrambling (Becker et al., 1991; Rambow, 1994), and raising inVSO languages (Harley and Kulick, 1998). While we focus on the casesjust discussed, it is our contention that there is a close relationshipbetween all of these problematic cases (see Kulick (1998) for a detaileddiscussion of this point), and that the analysis we propose here will beadaptable to those other cases.

4. Extensions to TAG

To approach the types of problems discussed in the previous section,a variety of extensions to TAG have been proposed. The first of theseis tree-local multi-component TAG (TL-MCTAG), in which the basicstructures are no longer single trees, but instead sets of trees.1 Allthe elements of the tree sets are required to adjoin (or substitute) atdistinct nodes of a single (underived) elementary tree.

Kroch and Joshi (1987) propose using this approach to handle theextraposition problem illustrated in example (5). They suggest thatthe tree set in Figure 7, containing an adjoined trace and the relativeclause modifier, would be simultaneously adjoined respectively to thesubject and the IP node of an elementary tree corresponding to thesimple clause a student walked in, thereby deriving (5). As Kroch andJoshi note, extraposition may also take place from object noun phrases.

(8) I met the student yesterday who Alice had asked about.

Kroch and Joshi provide evidence that the landing site for extraposi-tion from object is structurally lower than that for extraposition from

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8 Frank, Kulick and Vijay-Shanker

(a) CP

���

HHH

DPi

what

C

C

���

HHH

C IP

���

HHH

DP

Mary

I

�� HH

I VP��HH

V

saw

ti

(b) C

���

HHH

C

do

IP

��HH

DP

you

I

��HH

I VP�� HH

V

think

C

Figure 8. DTG elementary trees for long-distance wh-movement

subject.2 To account for this difference, they suggest that exampleslike (8) must be generated using a slightly different tree set from thatin Figure 7, one in which the auxiliary tree containing the relativeclause adjoins to VP rather than IP. The existence of both tree setsin the grammar now raises the spectre of overgeneration however: wemust now prevent the use of the object tree set in cases of subjectextraposition, improperly adjoining the trace to the subject and therelative clause to the VP.

Kroch and Joshi draw from the TAG literature on multi-componentsets and suggest utilizing a “dominance” link between the foot of oneof the components of the set, in their case the relative clause compo-nent, and the root of the other, the trace component. The effect ofthese dominance links is to restrict adjunction of the two members ofmulti-component set so that the dominance relation specified betweenthem is maintained throughout the derivation. The presence of sucha dominance link will therefore allow the adjunction of the set in (7)to the subject and IP as well as the adjunction of the VP-adjoinedvariant to the object and VP, but will not allow the adjunction of theVP-adjoined form to the subject and VP, as the foot of the relativeauxiliary will not dominate the root of the DP subject adjoined trace.

The idea of incorporating dominance into a TAG-like system is takenconsiderably further in D-tree grammars (DTG) (Rambow et al., 1995),which builds upon earlier work by Vijay-Shanker (1992). DTG rechar-acterizes the notion of a TAG derivation as the monotonic growth ofdominance relations that characterize the structures being composed.The proposal in Vijay-Shanker (1992) rests crucially on the assumption

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Monotonic C-Command: A New Perspective on TAG 9

that the elementary trees are characterized in terms of a dominationrelation among nodes, and that each potential adjoining site is rep-resented by two nodes standing in a domination relation. Under thisproposal, the derivation of (3) uses the structures in Figure 8 to derivethe long-distance wh-movement. To accomplish the analog of adjoiningin this system, the root and foot nodes of the tree depicted in Fig-ure 8(b) are identified with the two C′ nodes standing in a dominationrelation in Figure 8(a) (represented by the dotted line). This domina-tion relation still holds after adjoining, as do all the other dominationrelations stated in defining the trees in Figure 8. (In sentences in whichthere is no adjoining at the C′ node, e.g., I wonder what Mary saw, theseC′ nodes could collapse, preserving domination under the assumptionthat it is a reflexive relation.)

DTG builds upon this idea by using tree sets related by dominationlinks as the elementary components of the system, and adjoining iseliminated in favor of a new operation, subsertion, that allows com-ponents of two structures to combine by substitution, with the othercomponents interleaving with each other. This approach is able tohandle many of the problems that have been pointed out for TAG,including a number that are beyond the reach of TL-MCTAG (butsee Kulick (1998)). Yet, while DTG retains the crucial TAG notionof an extended domain of locality, it abandons the TAG derivationalconstraints on how trees may interact. Thus, DTG analogs of the treesin Figure 5 can be used to derive the the super-raising violation, which,as discussed earlier, is ruled out by the character of TAG derivations.DTG specifies a method of stating constraints on a derivation whichcan be used to prohibit this derivation.3

Both TL-MCTAG and DTG make crucial use of the dominancerelation in extending the expressive power of TAG. However, this struc-tural relation is not always appropriate for characterizing the rela-tion among the various pieces of an elementary structure. Recall theraising/subject-auxiliary inversion example in (6). Frank (1992) pro-posed utilizing the TL-MCTAG approach to resolve this problem, usingthe tree set in Figure 9. The derivation proceeds by adjoining the (b)tree from this set into the elementary tree in Figure 6 at the I′ node,while at the same time substituting the (a) tree from the set into theC node of the same tree. One disadvantage of this approach is thatit requires that the inversion of does is represented rather differentlyhere than in cases in which plain TAG suffices, as in the case of wh-movement (see Figure 4), in which movement of the auxiliary can besimply represented in a single tree. A second disadvantage, and theone pertinent to our current concerns, stems from the fact that thereis no dominance relation between the two components of the multi-

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10 Frank, Kulick and Vijay-Shanker

(a) Ci

does

(b) I′

��HH

I

ti

VP��HH

V

seem

I′

Figure 9. Multi-component tree set for raising with inversion

(a) I��HH

Clitic

loi

I

VP

���

HHH

DP

PRO

V′

�� HH

V

mangiare

ti

(b) IP

����

HH

HH

DPk

Gabriel

I′

���

HHH

I

vuolej

VP

�� HH

tk V′

��HHV

tj

VP

Figure 10. Multi-component elementary trees for clitic climbing and the derivedstructure

component tree set in Figure 9, i.e., between the fronted auxiliary verbthat is substituted into the C position and the root of the I′ auxiliarytree.4,5

Clitic climbing (Bleam, 1994) provides another example of a con-struction in which dominance relations do not provide the right de-scriptive vocabulary for characterizing relations among members ofan elementary structure in a TAG like system. In this construction,illustrated in (9) for Italian, the pronominal object of an embeddedverb appears attached to a higher verb.

(9) GabrielGabriel

loit

vuolewants

mangiareeat-inf

‘Gabriel wants to eat it.’

The most natural syntactic analysis of the tight morphological relation-ship between the “climbed” clitic and the matrix verb is one in whichthe clitic is directly adjoined to this verb. Since this clitic is an argumentof the embedded verb, it must be generated in the same elementary treeset, as in Figure 10(a). The two halves of Figure 10(a) are adjoined andsubstituted into the elementary tree headed by mangiare, depicted inFigure 10(b). Once again, there is no domination relationship betweenthe two halves of this multi-component tree set, in this case between the

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Monotonic C-Command: A New Perspective on TAG 11

I foot node of clitic-hosting structure and the VP root node that is pro-jected from the verb. Thus, some other mechanism must be exploitedto force the clitic to adjoin in the appropriate context.6

5. TAG Derivation as Monotonic C-Command

As we have just seen, the dominance relation that is crucially ex-ploited in TL-MCTAG and DTG is not sufficiently expressive to cap-ture the full range of linguistic phenomena. Furthermore, even in caseswhere dominance does suffice, it is often far from clear what gen-eral grammatical principle motivates the statement of the requisitedominance relations. For example, for the structure in (8a) what iscrucial grammatically is not a statement about duplicate C′ nodesstanding in a domination relation, but rather that the moved elementwhat must stand in a different structural relation with its trace, thatof c-command, both in the the elementary tree and throughout thederivation. Similarly, in the cases of extraposition and clitic climbing,the relevant relation between the extraposed relative and clitic respec-tively and their traces is that of c-command. Instead of compiling outthe crucially important c-command relations into statements aboutdomination, we suggest, following Frank and Vijay-Shanker (1998b),that the centrality of c-command be taken seriously and propose thatc-command as opposed to domination be used in extending TAG.

It turns out that given how adjoining and subsertion have beendefined and the manner in which domination statements have been uti-lized in TL-MCTAG and DTG, this c-command relation will always bepreserved during a derivation. Consequently, Frank and Vijay-Shanker(1998b) propose that this preservation of c-command is the definingproperty of the adjoining operation, and not a residual effect of thespecific choice of dominance relations. Following the line taken in DTG,this leads to a view in which TAG elementary structures are definedby their c-command relations, and where TAG derivations constitutemonotonic additions to a set of c-command relations. That is, instead ofviewing TAG structures being defined in terms of domination relations,we consider any domination relations that will be preserved to ariseor be inferred from the c-command relations used in defining TAGstructures.

5.1. Elementary trees as c-command relations

In characterizing TAG elementary trees, we make use of independentlymotivated assumptions concerning the c-command relations that ex-ist among structural elements. Thus, we assume that the c-command

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12 Frank, Kulick and Vijay-Shanker

(a) CP

���

HHH

DPi

what

C

���

HHH

C IP

���

HHH

DP

Mary

I

�� HH

I VP��HH

V

saw

ti

(b) C′

���

HHH

Cj

do

IP

���

HHH

DP

you

I′

���

HHH

I

tj

VP

�� HH

V

think

C′

Figure 11. C-command-based elementary trees for long-distance wh-movement

relations within elementary trees will be determined by (at least) thefollowing principles (cf. the definitions in Kayne (1994)):

(10) a. A moved element c-commands its trace.b. A head and its complement c-command one another.c. A modifier c-commands the phrase it modifies.d. A specifier c-commands the phrase to which it attaches.

Following these principles leads us to the structure in Figure 11(a) cor-responding to the elementary tree in Figure 8(a) (where arrows indicatec-command relations).7 There are two crucial c-command relations toobserve in this structure: the first between the fronted wh-phrase andits trace, and the second between the wh-phrase and the C′ node, whichserves as the target of movement within the elementary tree. The struc-ture in Figure 11(b) is the c-command analog of the one in Figure 8(b),Let us suppose that derivations proceed as monotonic combinations ofstructures like this one defined in terms of c-command. This meansthat we can perform an operation analogous to adjoining, insertingthe tree from FIgure 11(b) between the fronted wh-element and theC′ of Figure 11(a), by identifying this C′ with the foot node of theauxiliary structure. In the structure that results, all of the c-commandrelations stated in the elementary trees are preserved, most notablythose between the fronted wh-element and both the C′ and its trace.From this perspective, we can now understand why it was necessary inthe framework of Vijay-Shanker (1992) to posit a domination relationbetween the two C′ nodes in the structure in Figure 8(a): as an indirectrepresentation of (at least) the principle requiring that moved elementsc-command their traces.

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Monotonic C-Command: A New Perspective on TAG 13

(a) NP

�� HH

AP

��PP

green

NP

(b) DP

�� HH

D

the

NP

N

idea

Figure 12. C-command-based elementary trees for adjectival modification

5.2. Deriving Constraints on Adjoining

This proposal allows us to explain many previously stipulated proper-ties of TAG elementary trees and constraints on the adjoining opera-tion. Kroch (1989) and Schabes and Shieber (1994) noted structuraldifferences between two classes of auxiliary trees: complement auxiliarytrees on the one hand and modifier or athematic auxiliaries on the other.Modifier auxiliaries have the distinctive property that their foot nodeis the sister of a modifying phrase and is the daughter of the root node.Following the principles in (10), it follows that a modifier c-commandsthe XP phrase it modifies, though not vice-versa. The structure inFigure 12(a) is the c-command representation of a modifier auxiliarytree. The green AP node c-commands the NP it adjoins to, and so ifthe adjoining site is the NP node of Figure 12(b), the adjoining willform the green idea.

The foot node of a complement auxiliary tree, in contrast, mustbe the sister of the head of which it is a complement. Thus, this footnode will both c-command and be c-commanded by its sister node.The structure from Figure 8(b) is a complement auxiliary tree, and itsc-command analog in Figure 11 shows the mutual c-command relationbetween the V node think and the C′ foot node.

It has sometimes been stipulated that adjoining of complement aux-iliaries is blocked at the foot node of complement auxiliary trees. Asjust noted, since the foot of a complement auxiliary is a complement,this node c-commands the lexical head of the complement auxiliarytree. Adjoining to this foot node by another complement auxiliary treewill have the effect of lowering it, so that it no longer c-commands thehead. This would violate the monotonicity requirement on c-commandrelations during the derivation, and we could therefore reduce the stip-ulation often used in TAG to a more general condition on monotonicity.

Since complement auxiliary trees may not adjoin at a complementnode, the obvious question is where they may adjoin. Clearly, ad-joining at the root of a structure would not require any statementsof c-command relations to be retracted, and thus is permissible. But

grammars-franketal.tex; 11/12/2002; 16:41; p.13

14 Frank, Kulick and Vijay-Shanker

this is not an interesting situation as it can also be considered to besubstitution. Saying that this derivation step is a case of adjoining ismerely an artifact of the TAG formalism which, quite possibly, has nosignificant implications. The interesting cases correspond to adjoiningcomplement auxiliary trees to internal nodes (i.e., non-root nodes). Weadopt here Kayne’s (1994) suggestion that specifier positions should beassimilated to adjuncts, specifically with respect to their c-commandrelations (i.e., they c-command but are not c-commanded by their X′

sister).8 This leads to the previously stated condition (10d), that aspecifier c-commands the phrase to which it attaches.

From this, we are able to derive the result that the only internal(non-root) nodes where complement auxiliary trees can adjoin are X′

nodes that are sister to a specifier. The reason for this is exactly asin our discussion of the tree in Figure 11(a), namely that it is onlyin the context of unidirectional c-command from the specifier to theX′ node that it is possible to insert a complement auxiliary that willhave the effect of lowering the X′ node. Interestingly, this view matchesquite well what has been assumed in previous TAG analyses, wheresuccessive cyclic A′-movement is accomplished by adjoining at C′ asdiscussed earlier, and successive cyclic A-movement by adjoining atI′. Indeed, we believe that this proposal provides a means of explain-ing why unbounded movement uniformly proceeds through specifierpositions.

We also derive contrasts in the use of modifier auxiliaries, as opposedto the complement auxiliaries. First, adjoining at the foot node of amodifier auxiliary will not be ruled out, as the modification relationdoes not entail mutual c-command, and such lowering of the foot doesnot force the retraction of any c-command relations. Second, sincemodifier auxiliary trees introduce an asymmetrical c-command relationwith their foot node, it follows that their adjoining will not disruptany c-command relations that the modified phrase already enters into.Thus, it follows the adjoining of modifier auxiliaries should be quitefree and indeed may occur at any node in an elementary tree. In fact,if the root and foot of the auxiliary tree are considered segments of thesame category (which explains the asymmetrical c-command relationbetween the modifier and modifiee), this would explain the possibil-ity of multiple adjoining by modifier auxiliary trees at a single nodeconsidered by Shieber and Schabes.

grammars-franketal.tex; 11/12/2002; 16:41; p.14

Monotonic C-Command: A New Perspective on TAG 15

(a) IP

���

HHH

DP

Gabriel

I′

��HH

I

to

VP

�� HH

V

eat

DP

gnocchi

(b) C′

����PPPP

C

-

doesj

IP-�

I′!

!!

aaa

I

tj

VP-�

""

bb

V

seem

I′-�

Figure 13. C-command-based elementary trees for raising with inversion

5.3. Returning to the Problematic Examples

We suggest that our recasting of TAG derivations as manipulations ofc-command relations leads to a resolution of the problems discussed inSection 3. Consider sentence (6), repeated here as (11):

(11) Does Gabriel seem to eat gnocchi?

The tree for the eat clause, given in Figure 6, is reinterpreted as a collec-tion of c-command relations, shown in Figure 13(a), along the lines ofthe reinterpretation of tree Figure 4(a) as the one in Figure 11(a).9 Thec-command interpretation for the seem clause is shown in Figure 13(b).Recall that there was a relation between the two components in the treeset used for this derivation under the TL-MCTAG analysis, in Figure 9,in which the complementizer does had to substitute into the tree for eat

at a “higher” position than where the seem tree adjoined in. However,that relationship could not be expressed by domination. Under ourproposal, this relation is easily expressed in c-command terms, i.e., does

must c-command seem. This c-command relation arises as the resultof the movement of does from the I to C node, and does thereforeneeds to c-command its trace in I, as shown. We additionally representthe fact that the target of movement is a complementizer position byintroducing the projection of the complementizer and its correspondingcomplementation relation into this elementary structure. Note thatthe absence of a specifier position means that this IP is essentially“floating” in the tree in Figure 13(b).

The derivation proceeds by identifying the I′ node of the structurein Figure 13(a) with the lower I′ node of Figure 13(b). It is still con-sistent with the original c-command relations for the auxiliary does toc-command Gabriel in its higher position. The structure in Figure 14is therefore compatible with this derivation.

grammars-franketal.tex; 11/12/2002; 16:41; p.15

16 Frank, Kulick and Vijay-Shanker

C′

(((((hhhhh

C

-

doesj

IP-�((((hhhh

DP

Gabriel

I′-((((hhhh

I

tj

VP-�((((hhhh

V

seem

I′-� ```

I

to

VP-��� PP

V

eat

DP-�

gnocchiFigure 14. Result of c-command-based raising with inversion derivation

(a) I��HH

Clitic

loi

I

VP

���

HHH

DP

PRO

V′

�� HH

V

mangiare

ti

(b) IP

����

HH

HH

DPk

Gabriel

I′

���

HHH

I

vuolej

VP

�� HH

tk V′

��HHV

tj

VP

Figure 15. C-command-based elementary tree set and tree for clitic climbing

The tree set (10) for the clitic climbing case (9) is recharacterizedin a similar way. As shown in (15), the clitic loi c-commands its traceti. We additionally represent the fact that the clitic must attach to aninflection node (see footnote 7) by showing the clitic as c-commandingthe inflection node I.

The tree (10) for the mangiare clause is reinterpreted as the c-command relations in Figure 15(b). To derive (9), the VP node ofFigure 15(a) is identified with the lower VP node of Figure 15(b).This allows the I node headed by lo to c-command the I node headedby vuole, resulting in the structure in Figure 16.10 The extrapositionexample is handled in a very similar way, and we leave aside here thedetails.

grammars-franketal.tex; 11/12/2002; 16:41; p.16

Monotonic C-Command: A New Perspective on TAG 17

IP

�����

HH

HHH

DPk

Gabriel

I′

����

HH

HH

I

��HH

Clitic

loi

I

vuolej

VP

���

HHH

tk V′

���

HHH

V

tj

VP

���

HHH

DP

PRO

V′

�� HH

V

mangiare

ti

Figure 16. Result of clitic climbing derivation

6. The Structure of Derivations and Syntactic Locality

The derivation of example (6) proceeds by identifying the I′ node ofFigure 13(a) with the lower I′ node of Figure 13(b). While such anoperation is in part analogous to adjoining, it can also be considered assubstitution of the “subtree”11 rooted by the I′ node in Figure 13(a) intothe lower I′ node of Figure 13(b), with Gabriel “floating” up. We willtake this version of substitution to be the basic operation of the deriva-tion. When a derivation identifies two nodes, we call the node which ison the frontier of an elementary structure before the identification thesubstitution node.12

In general, applications of this substitution operation will not com-pletely determine relative c-command relations among the pieces of thecombined structures. In the particular derivation we have just seen, thesubstitution of one I′ into the other does not determine the relative c-command relation of Gabriel and does. All we know is that both mustc-command the I′ headed by the trace of does: the latter because ofthe c-command properties of movement and the former because thec-command relations of the I′ portion of Figure 13(b) are so tightlybound as not to allow floating within it. This means that either ofGabriel and does may c-command the other and still satisfy the c-command relations determined through the combination of the twostructures. Thus, the structure in Figure 14 is possible, but is not anecessary consequence. If we are to force the inversion of the auxiliary

grammars-franketal.tex; 11/12/2002; 16:41; p.17

18 Frank, Kulick and Vijay-Shanker

I

���

HHH

I

to

VP

��HH

V

be

AP��HH

A

likely

I

Figure 17. C-command-based infinitival raising auxiliary tree

around the subject, something further must be added. The intuitionwe are pursuing here is that a derivational analog of the CETM is ineffect. Specifically, we believe that there is something illicit about thepresence of two floating IP projections: one that includes the float-ing Gabriel and another that is the complement of the fronted does.The effect of the condition on the floating components is to force theidentification of these two IP nodes, resulting in does c-commandingGabriel and not conversely. For space reasons we leave aside here theprecise characterization of the floating components, but we hope thatthe intuition is clear. Roughly put, then, our condition is as follows:

(12) Derivational CETM: After a substitution, the floating compo-nents of a derivation are resolved as part of exactly one extendedprojection.

For sentences with multiple levels of embedding, the range of deriva-tional options increases. Consider, for example, the following examplewith two raising verbs:

(13) Does Gabriel seem to be likely to eat gnocchi?

We assume that the elementary structure headed by likely is as inFigure 17. There are a number of ways we might go about inserting thelikely clause between the seem and to eat clauses while at the same timemaintaining c-command relations during the course of the derivation.We could first combine the two raising predicates together to form acomposite structure for seem to be likely and then combine this resultwith the eat clause. Alternatively, we could first combine the mostembedded clause with the likely structure, adding the seem structureat the conclusion. We will permit only one of these derivations, rulingout the other via the following restriction:13

(14) The structure containing the substitution node must be elemen-tary (that is, not the product of a derivation).

grammars-franketal.tex; 11/12/2002; 16:41; p.18

Monotonic C-Command: A New Perspective on TAG 19

IP�����XXXXX

DP

Gabriel

I′-����XXXX

I

to

VP-�����PPPP

V

be

AP-�����PPPP

A

likely

I′-�����PPPP

to eat gnocchiFigure 18. Intermediate result for c-command-based raising derivation

This condition can be seen as a natural addition to the DerivationalCETM. In particular, it ensures that after each derivational step thestructure above the substitution node (including the floating compo-nents of the substituted tree) will form a single extended projection.14

Given the requirement in (14), the derivation must proceed “bottom-up”, by substituting the I′ node of the Gabriel to eat gnocchi treein Figure 13(a) into the I′ foot node of the to be likely tree in Fig-ure 17. C-command monotonicity will guarantee that the result of thiscombination is as in Figure 18.

The final step in the derivation substitutes the upper I′ node fromthis structure into the foot I′ node of the structure for does...seem inFigure 13(b). Once again, c-command monotonicity coupled with thederivational CETM will result in the desired representation for (13),in this case that in Figure 19. Note that the alternative “top-down”derivation is ruled out by (14), since it would require the substitutionof the I′ node of the Gabriel to eat gnocchi tree in Figure 13(a) into thefoot node of the derived structure formed by the combination of thedoes. . . seem tree and the likely tree.

6.1. Maintaining Locality Constraints

We believe that the derivational CETM as stated in (12), together withthe condition on derivations given in (14), brings back into our systemmuch of the restrictiveness of TAG in that it allows the combinationof only simple structures or recursive combinations of them. Arbitrarystructural combinations, along the lines allowed in DTG, are not per-mitted by the architecture of the formalism, and need not be ruled outby stipulated coherence constraints. It is a welcome result, therefore,that these derivational conditions also have the effect of ruling outcertain cases of illicit long distance movement, such as super raising(as in (4), repeated here as (15)), without additional stipulation.

grammars-franketal.tex; 11/12/2002; 16:41; p.19

20 Frank, Kulick and Vijay-Shanker

C′

����

HH

HH

C

doesj

IP

���

HHH

DP

Gabriel

I′

���

HHH

I

tj

VP

���

HHH

V

seem

I′

���

HHH

I

to

VP

���

HHH

V

be

AP

���

HHH

A

likely

I′

����

PPPP

to eat gnocchi

Figure 19. Result of c-command-based multi-clausal raising with inversion

(a) I′

""

bb

I VP-�

""

bb

V

seems

IP-�

(b) IP����PPPP

DP

it

I′-����PPPP

I

isi

VP-�!

!!

aaa

V

ti

AP-�

""

bb

A

likely

I′-�

Figure 20. C-command-based elementary trees that cannot derive super raising

(15) * Gabriel seems it is likely to eat gnocchi

Consider the structures in Figure 20, which might be used for sucha derivation using our c-command approach, and which are in factc-command reinterpretations of the TAG trees in Figure 5. These struc-tures are different from those assigned earlier to seems and likely in acouple of crucial respects: the foot node of the seems tree is IP ratherthan I′ while the root node for the likely tree is IP as opposed toI′, a result of the present of the expletive subject it. Because of theconstraint from (14), this derivation must proceed by substituting theI′ node of a tree for Gabriel to eat gnocchi, i.e., Figure 13(a), into the I′

grammars-franketal.tex; 11/12/2002; 16:41; p.20

Monotonic C-Command: A New Perspective on TAG 21

IP

������

HH

HH

HH

DP

Gabriel

DP

it

I′

���

HHH

I

is

VP

�����

PPPP

P

likely to eat gnocchi

Figure 21. “Capture” of raised subject in c-command-based derivation

foot node of Figure 20(b), allowing Gabriel to “float up”. At this pointin the derivation, there will be two distinct floating IP nodes withno c-command relations between them, one projected from the lowerclause and one from the higher, each housing the subject of these twoclauses. In this context, the derivational CETM will apply, forcing thesetwo IP nodes to be identified, since otherwise these would constitutetwo distinct extended projections. The resulting structure will then beas in Figure 21. This identification of IPs does not yield any orderor obligatory c-command relation between the two floating subjects it

and Gabriel.15 However, the fact that there is no node “between” themthat could substituted into some higher clause prevents Gabriel frombeing raised out of this clause, and indeed prevents the two subjectsfrom being separated later on in the derivation. We assume that sucha configuration with multiple specifiers of IP is ruled out, at least inEnglish, for reasons that will depend on decisions, not relevant here,about representation of the analog of adjunction constraints in oursystem.16

One can imagine other ways of ruling out the super-raising casewithout recourse to our derivational constraints in (12) and (14). Forexample, one could simply stipulate that trees such as those in Figure 20do not exist. Our very general derivational conditions have the advan-tage that, just as in the original TAG system, they also block other casesin which floating must be constrained, such as islands for extractionof wh-phrases and clitic climbing.17 For example, without going intodetails, in a wh-island violation like that in (16), why will be unable tofloat up past the middle clause, as it will be stuck together with when

in the intermediate [spec, CP] for reasons essentially identical to thosein the super raising case.

(16) * Whyi do you wonder when John said [that Bill left ti]?

Note that this is accomplished without any sort of resort to parochialconstraints on floating nodes, as in DTG. We feel that this contrast

grammars-franketal.tex; 11/12/2002; 16:41; p.21

22 Frank, Kulick and Vijay-Shanker

highlights a difference between our proposal and the DTG approach.DTG’s subsertion-insertion constraints in effect use the elementarystructures in that system as a place to impose a global constraint onthe final structure of the derivation. In contrast, our approach definesconstraints on nodes present in the elementary structures, like in TAGand TL-MCTAG, and defines the composition operation in such a waythat it, together with the locally defined constraints in the elementarystructures, will derive the locality constraints. In that sense what weare doing is more like TAG and TL-MCTAG, as opposed to the DTGapproach.

7. Conclusion

We have discussed a reconceptualization of the elementary structuresand corresponding derivations in TAG. By treating the fundamentalrelationship as one of c-command, we achieve the following results:

1. We have a better understanding of where the necessary dominancerelations derive from in the systems of Rambow et al. (1995) andVijay-Shanker (1992).

2. We explain a variety of constraints on the interaction of TAG el-ementary structures during adjoining or substitution. The same istrue for related formalisms such as DTG, which need to stipulatewhy structures can only be substituted at certain places.

3. We resolve certain problematic cases for TAG, that had previouslynecessitated the use of TL-MCTAG or even more powerful systems

4. A pair of natural constraints on derivations, one a derivationalanalog of the CETM (12) and the other a translation of a TAGconvention on adjoining (14), allows us to derive the effects ofcertain locality conditions on extraction.

Notes

1 If the tree sets have just one member, then it reduces to the case of basic TAG.2 One argument for this conclusion comes from contrasts involving VP fronting,

in which a relative extraposed from the subject may not be moved, but one fromthe object must, indicating that the latter but not the former are within VP Baltin(1981)):

(i) a. Speak politely though people may who are from Boston, he still thinksthey’re all a bunch of bums.

grammars-franketal.tex; 11/12/2002; 16:41; p.22

Monotonic C-Command: A New Perspective on TAG 23

b. * Call people up though he may who are from Boston, he’s generallypretty cheap about long distance phone calls.

(ii) a. * Speak politely who are from Boston though people may, he still thinksthey’re a bunch of bums.

b. Call people up who are from Boston though he may, he’s generallypretty cheap about long distance phone calls.

Anti-coreference contrasts point to a similar conclusion. As Kroch and Joshi note,object pronouns may corefer with names in a relative extraposed from subjectposition, as seen in (iiia). However, as seen in (iiib), if the relative is extraposedfrom object position, such coreference is impossible.

(iii) a. Many people visited heri who cheered Maryi up.b. * I told many people about heri who were interested in Maryi.

We take this to indicate that the landing site for object but not subject extrapositionis c-commanded by the object, and hence within VP.

3 The system we propose also requires a constraint on derivations to rule outundesired cases such as the super-raising violation. In section 6 we discuss thedifferent characteristics of our approach and that of DTG.

4 Frank (1992) suggests instead that there should be a c-command link betweenthe members of the tree set in Figure 9. Quite clearly, this is in the spirit of thecurrent proposal.

5 If the analysis of (6) were reworked so that both specifiers and heads in themulti-component set adjoin in, it would be possible to specify the links betweenthe components as domination links. For example, if all the nodes above VP weresimply further projections of VP with appropriate features added, then the trees inFigure 9 could be rewritten as follows (with corresponding changes in the tree forGabriel to eat gnocchi).

(i) a. VP

�� HH

V

does

VP

b. VP

�� HH

V

seem

VP

Here a domination link could be specified between the foot VP node of (ia) andthe root VP node of (ib). So while it is not impossible to use the dominationrelation to characterize a multi-component tree set to derive this particular case,maintaining the restriction to a domination relation forces a linguistic analysis whichwe take to be undesirable. Given that there are other cases in which the dominationrelation becomes increasingly cumbersome, e.g., clitic climbing, we conclude thatTAG extensions resting on the use of domination relationships are inappropriate forlinguistic analysis.

6 The trees in this example are based on an analysis in which the clitic attaches tothe inflection node, and clitic climbing occurs when the lower clause is “defective”,projecting only to VP, thus forcing the clitic to climb. Even if a different analysis isused, as long as the assumption is made that the clitic attaches to the same nodeas the matrix verb, domination will be insufficient to express the relation betweenthe two halves of the elementary tree.

7 The lines indicating direct domination in Figure 11(a) are not intended as partof the representation, but rather as aid to the reader in comparing our proposed

grammars-franketal.tex; 11/12/2002; 16:41; p.23

24 Frank, Kulick and Vijay-Shanker

structure to that standardly assumed. Note that certain implicit c-command re-lations, such as that between C and the subconstituents of IP are suppressed inthis figure, but we assume that they are present. See Frank and Vijay-Shanker(1998a) for extensive discussion of the properties of structures defined in terms ofc-command and the relationship between such structures and those defined in termsof dominance.

8 This raises the interesting possibility that specifiers could be adjoined in theTAG sense as well. Although this would have certain benefits with respect to thetreatment of subject islands, we believe at present that it is not immediately com-patible with our proposal to derive the possible loci of adjoining from c-commandmonotonicity.

9 One difference between the two cases is that the complementizer is not includedin the structure in Figure 13(a). While we are still investigating the exact conditionsunder which it should be included as part of the elementary structure, one promisinghypothesis is that it need not be included when the clause is headed by the defectiveinflectional head present in raising complements.

10 We have left out some of the c-command relations in Figures 15 and 16 to avoidclutter. Also, note the c-command relation in Figure 16 between the I node headedby loi and its trace ti. This is an instance in which the tree representation of thec-command relations is a bit misleading, since the I node headed by loi appears toc-command the I node headed by vuolej , but nothing else. However, loi is simplyadding an asymmetrical c-command relation to the I node headed by vuolej , andso the I node headed by loi c-commands everything that the node headed by vuolej

c-commands, including the trace ti.11 Technically, a subset of the c-command relations of Figure 13(a).12 Analogs to the constraints on adjoining discussed in Section 5 are still derived

when substitution is taken to be the basic operation.13 Note that (13) is not derivable within TL-MCTAG, even ignoring the dominance

problem mentioned earlier. Assuming that the derivation proceeds by the seem tree(set) adjoining to the root of the likely tree, with the result adjoining into the eattree, a locality problem will arise. If does and seem are a multi-component tree set,then does needs to substitute into the eat tree while seems adjoins into the likely tree,thus violating tree-locality. Kulick (1998) notes that this problem can be avoidedby allowing adjoining at a foot node, therefore allowing to be likely to adjoin at thefoot node of the seem tree. While the full implications of this approach are not yetfully understood, such adjoining at a foot has traditionally been prohibited in TAG.Indeed, as discussed in Section 5, the recharacterization of TAG derivation arguedfor in this paper in fact rules out adjoining a complement auxiliary tree at the footnode of a complement auxiliary tree.

14 Alternatively, one could reformulate the Derivational CETM along the followinglines:

(i) Derivational CETM: After a substitution, the structure above the site ofsubstitution must be resolved as part of exactly one extended projection.

Apart from reproducing the effects of the formulation of the derivational CETMin (12), this version would have the additional consequence of allowing the elimina-tion of condition (14).

15 The relative ordering depicted in Figure 21 is thus only one of two possibilities.Both will, however, suffer the same fate.

grammars-franketal.tex; 11/12/2002; 16:41; p.24

Monotonic C-Command: A New Perspective on TAG 25

16 Possibilities include a violation of the extended projection principle or lack ofCase for Gabriel and/or it.

17 The advantage of blocking locality violations by these general derivational con-ditions also extends to more complicated cases of multiple clitic climbing within onesentence. See Kulick et al. (1999) for a detailed discussion of these cases within thecontext of the system discussed here.

Acknowledgments

We are grateful to three anonymous reviewers for their helpful com-ments, as well as to the National Science Foundation for their financialsupport of this work in the form of grants SBR-97-10247, SBR-89-20230, and SBR-97-10411 for the three authors respectively.

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