A Graph-Theoretic Reanalysis of Bare Phrase Structure
Theory and its Implications on Parametric Variation
Miyoko Yasui
Dokkyo University, Soka
Abstract
This paper attempts to offer a minimalistic theory of syntactic structure from a graph-theoretic
point of view with special emphases on elimination of category and projection labels and the
Inclusiveness Condition. A syntactic structure is regarded as a graph consisting of the set of
lexical items, the set of relations among them and nothing more. Operations of internal andexternal MERGE are redefined as applying on graphs. It is claimed that head-initial andhead-final languages share basic syntactic graphs and operations and that differences in theirphonetic realizations such as the positions of heads and wh-phrases are deduced from thenatural extension of traversals of graphs, which are extensively studied in graph theories. A
major consequence of the theory is its explanation for the correlations between the headparameter values, on the one hand, and the types of wh-movement and word order freedom,on the other: head-initial languages such as English exhibit overt wh-movement and position
their specifiers in a fixed position due to their downward traversal, while head-final languages
like Japanese are subject to the upward traversal and hence do not raise wh-phrases obligatorily and their word orders are relatively free.

1. Graph-theoretic Properties of Standard Phrase Structure Diagrams
A representation of phrase structure such as (1) is a kind of directed graph:1
(1)

IP
D’

I’

D

INFL

V’

it

will VV’beVraining

A directed graph G consists of a finite set of nodes (V) and a finite set of ordered pairs of nodes (E) that express immediate domination relations. (1) isnothing more than G= (V, E) defined in (2):Miyoko Yasui(2) V={IP, D’, I’, D, INFL, V’, V, V’, V, it, will, be, raining}
E={<IP, D’>, <IP, I’>, <D’, D>, <I’, INFL>, <I’, V’>, <V’, V>,<V’, V’>, <V’, V>, <D, it>, <INFL, will>, <V, be>, <V, raining>}
Besides the defining properties as a directed graph, a phrase structure diagram has been assumed to have properties such as (3):(3)(i) There is one node, called the root, that is dominated by no nodes andfrom which there is a path to every node.2(ii) Every node other than the root has exactly one node that immediately dominates it.
(iii) The nodes each node immediately dominates are ordered from theleft.3(3i) says that a well-formed sentence needs to constitute a single connected
graph with one special node as its root. (3iii) need not or should not be retained within the minimalist program, where linear order is assumed to play nosignificant syntactic role.
Like (3i), (3ii) has been adopted in virtually every theory of phrase structure,and it specifically excludes a diagram with a closed route such as (4):4
(4)

A
B

C
D

E
F

The offending node is F, which is dominated by two nodes, D and E; thus, (4)violates (3ii).
Whether (3ii) should be assumed or not depends on other assumptions onphrase structure. I will show that a graph-theoretic reanalysis of some of thefundamental assumptions in the minimalist program, specifically of bare phrase
structure theory, leads to the rejection of (3ii). In the alternative theory to be

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

proposed below, the output of external MERGE is a tree with the property (3ii)but that of internal MERGE (or movement) is a graph that has a closed route.
This distinction will offer a natural explanation for the parametric difference in
wh-movement; the PF requirement of linearizing lexical items forces a graphwith a closed route to be changed into a tree in either of the two possible ways,
which correspond to overt and covert movement.
The organization of the rest of the paper is as follows: In section 2, major assumptions in bare phrase structure theory will be examined from a viewpoint ofgraph theory, with special attention to the Inclusiveness Condition. In section
3, external and internal Merge will be defined according to the alternative
phrase structure theory. Specifically, internal MERGE will be regarded as an
operation forming a closed route; there is no necessary reason to exclude such agraph within syntax. It will be argued in section 4, however, that the PF requirement as to word order leads to the elimination of a closed route without
altering the overall structure; two options are available, corresponding to overt
wh-movement in head-initial languages and covert wh-movement in head-final
languages. It will also be discussed how the nodes of a syntactic graph aretraversed systematically and linearly ordered, from which differences in word
order between these languages will be deduced. Section 6 is a brief discussion
on some of the remaining issues.

2. A Graph-Theoretic Reanalysis of Bare Phrase Structure Theory
One important simplification of phrase structure pursued since Chomsky(1995: Chapter 4) is the elimination of category and projection labels by theextensive use of lexical items themselves, which is motivated by the Inclusiveness Condition. To meet the Inclusiveness Condition, (5) is to be assumed
instead of (1) (=(2)):5
(5)

will
it

V={it, will, will, will, be, be, raining}
E={<will, it>, <will, will>, <will, will>,

will
will

be
be

<will, be>, <be, be>, <be, raining>}
raining(5) contains nodes with the same labels will and be.

If nodes with the same

Miyoko Yasuilabel are to be identified as one, the set V in (5) is non-distinct from {it, will, be,raining}.6 Then, (5) is forced to be replaced by (6):
(6)

will
it

V={it, will, be, raining}beE={<will, it>, <will, will>, <will, will>,raining<will, be>, <be, be>, <be, raining>}(6) contains three loops, <will, will>, <will, will> and <be, be>, which express
nothing other than intermediate projections. Therefore, (7) is to be finally assumed here:
(7)

will
it

V={it, will, be, raining}beE={<will, it>, <will, be>, <be, raining>}

raining(7) might not look like a syntactic tree, but the set of nodes V is essentiallythe numeration in the sense of Chomsky (1995: 225-227), and E seems to best
meet the Inclusiveness Condition in that no projection and category labels areadded. Moreover, the order pair <α, β> is generally defined as {{α}, {α, β}},and it looks quite close to Chomsky's (1995:244-245) definition of the object
formed from α and β of the type α: {α, {α, β}}. For expository convenience,
Chomsky continues to employ graphical representation such as (5), acknowledging that they are more complex than are absolutely necessary. If {{α},{α, β}} is adopted instead of {α,{α, β}} as the definition of the object formed
from α and β , the discrepancy between the formal definition and its graphicalrepresentation will disappear, which seems to be a desired result.
3. External and Internal Merge
How can the operations of internal and external MERGE be defined here?
First, let’s consider external MERGE, which is applied to two substructures α
and β and produces a larger structure only if some syntactic relation holds between α and β. To paraphrase it in the alternative theory here, MERGE is akind of union operation on two graphs, with a new ordered pair added to theunion. It is formally defined as (8):A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation(8)

Theory and its

Given two graphs G1 =(V1, E1) and G2=(V2, E2), MERGE (G1, G2)
produces a graph G=(V, E) such that(i) V=V1V2 and(ii) for some v1 V1, v2

V2, E=E1 E2 {<v1, v2>} or

E=E1 E2 {<v2, v1>}(8i) is straightforward; the resulting set of nodes is simply the union of the nodesets of the two input graphs. (8ii) essentially says that some node in one graphenters into a local syntactic relation with some node in the other graph, whereby
the two graphs are combined. I assume the first member of each ordered pair toselect the second member or to agree with it with its EPP feature.
A derivation starts with a set of minimal graphs, each of which consists of asingle lexical item. (5), for example, starts with (9):7
(9)

it

will

be

raining

G1=(V1, V2): V1={it}, E1=
G2=(V2, E2): V2={will}, E2=
G3=(V3, E3): V3={be}, E3=
G4=(V4, E4): V4={raining}, E4=
Since the aspectual auxiliary be selects the progressive verb raining, the ordered pair <be, raining> is introduced as in (10):
(10)

it

will

be

MERGE(G3, G4) = G5=(V5, E5)raining

V5=V3

V4={be, raining}

E5=E3 E4 {<be, raining>}={<be, raining>}
Will selects verbal and Case-checks nominative; thus, the recursive applicationof MERGE will convert (10) into (11) and then (12) (=(7)):

Miyoko Yasui

(11)

it

will
be

MERGE (G2, G5)=G6=(V6, E6)

raining

V6=V2

V5={will, be, raining}

E6=E2 E5 {<will, be>}={<will, be>, <be, raining>}
(12)

will
it

be

MERGE (G1, G6)=G7=(V7, E7)raining

V7=V1

V6={it, will, be, raining}

E7=E1 E6 {<will, it>}={<will, it>, <will, be>, <be, raining>}
It does not matter which of the ordered pairs in E7 is added first. For example,
it is easy to verify that adding the pair <will, it> before <will, be> or <be, raining> will make the same result.8
MERGE defined in (8) does not prevent a graph from being combined withitself, and it is exactly a case of internal MERGE (or movement). To illustrate
this point, consider (13), a case involving wh-movement:(13)(I wonder) what John will buy.

The bare phrase structure analysis of (13) is (14), where the vP structure and the
movement of the subject/object are ignored for expository convenience here:9
(14)

[WH]
what

[WH]
[WH]

will
John

will

will

buy
buy

what

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

In the theory here, (13) has structure (15) before the movement of what:
[WH]

(15)

will
John

buy
what

V={[WH], will, John, buy, what}E={<buy, what>,<will, buy>,<will, John>,<[WH], will>}
MERGE (G, G) will produce (16), where the wh-checking relation of <[WH],what> is added:(16) MERGE (G, G)=G’=(V’, E’):
V=V={[WH], will, John, buy, what}

V’=V

E’=E E{<[WH], what>}={<buy, what>,<will, buy>,<will, John>, <[WH], will>, <[WH], what>}
[WH]
will
John

buy
what

(16) violates one of the defining properties of tree, (3ii): what is immediately
dominated by buy and [WH]. More generally, internal MERGE on a tree always
introduces one closed route, and the result is not a tree by definition (seeBalakrishnan and Ranganathan (2000; 71-72)). (16) might look too outrageous,
given the widely accepted view that a sentence has a tree structure. Nothing,
however, seems to be wrong with (16) as a syntactic structure. I will move on to
discuss the PF interpretation of syntactic graphs in the next section, where aMiyoko Yasui

graph with a closed route such as (16) is to be mapped into two linear orderings
and the so-called overt/covert distinction in wh-movement is subsumed underthese options.
4. PF-interpretation of Graphs and Parametric Differences
4.1 Head-Parameter
Let us examine what conditions have to be imposed on the PF interpretationof a syntactic graph. One obvious requirement is that all the nodes corresponding to overt elements in a syntactic graph be pronounced.10 Furthermore, if
the interpretation is economical, each node is to be pronounced just once.11
This kind of task is known as traversal. To traverse a graph is to perform agiven operation on every node (e.g., to pronounce it) in the graph exactly once.
A node can be traversed more than once but may undergo the operation exactly
once.
A specific type of graph is associated with common orders in which its nodes
undergo a given operation. If a directed graph is linear, the two common orders are forward and backward in its direction. Consider the graphical representations of the phrase "lean against the door to the backyard" and its Japanesecounterpart, which are to be analyzed as (17a,b), respectively:(17) aleanb.

motare (lean)againstni (against)thedoa (door)

door

e-no (to-GEN)touraniwa (backyard)

thebackyard
Each node in (17a) is pronounced before its child; you pronounce the verbal
head lean first, pronouncing the other nodes in the downward direction. The
opposite holds in (17b); the pronunciation starts at the nominal complement

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

uraniwa (backyard) and proceeds in the upward direction. The downward andupward pronunciation options constitute the head-parameter, yielding the headinitial and head-final word orders, respectively.
A syntactic graph typically is a tree and its traversal is not so simple as thatof a linear graph. Traversal of an ordered binary tree is one of the important
issues in graph theories.12 In its commonly-used traversals, the root is thestarting and ending node, and they involve the following three parts:(18) At a given node N:a.

Recursively traverse its left subtree. When this step is finished, goback to N.

b.

Recursively traverse its right subtree. When this step is finished, goback to N.

c. Perform the operation on N.
(18a,b) say that the left subtree of N is traversed before its right subtree.
Traversals can be classified according to whether (18c) is done before, between
or after (18a,b). They are called pre-order, in-order and post-order traversals,
respectively. Let us assume that the operation mentioned in (18c) is to pronounce N. The pre-order traversal of (19) results in the pronunciation A-B-CD-E-F-G-I-H:
(19)

A
B

C

E
D
G

F

H
I

The in-order and post-order traversals yield C-B-D-A-G-F-I-E-H and C-D-BG-I-F-H-E-A, respectively.13(18a,b) make crucial reference to the order of subtrees. Let us illustrate thepoint by traversing (19) in pre-order. You pronounce the nodes A, B and C in

Miyoko Yasui

this order since B is the root of A's left subtree and C is the root of B's left subtree. Then, you come back to B and should visit D rather than go back to C.
You never make a mistake at B since you know you have visited its left subtree.
If subtrees are not ordered from left to right, the 'left' subtree does not exist, andwe are not sure at a branching node which way to go.
As has been discussed in connection with (3iii) in Section 1, a syntactic tree
has no distinction of right and left subtrees; thus, (18a-c) cannot be adopted asthey are. Note that in the traversal of (19) under the assumption that it is ordered, the branching node B is traversed three times. When B is traversed forthe first time, its two children are still not pronounced; one of them has beenpronounced when B is traversed second time, and both of them have been pronounced at the point of B's last traversal. In this way, the number of unpronounced/pronounced nodes B immediately dominates changes each time B istraversed, and the same holds of branching nodes in general. The three typesof traversal can be reformulated along this line.
Originally, each node immediately dominates no pronounced nodes.14 If thenode is pronounced at this stage, it is before any of its subtrees has been traversed; this is a pre-order traversal. If it is pronounced when it immediately
dominates no unpronounced nodes, it is a post-order traversal. An in-order
traversal is slightly more complicated; each node is pronounced at the stage
where it immediately dominates no more than one unpronounced node. Pendant nodes such as C,D and G in (19) immediately dominate no nodes and they
are pronounced when they are first traversed. Branching nodes like B are pronounced after one of its children has been pronounced. In this way, we canidentify three kinds of traversal based of the number of unpronounced or pronounced nodes dominated by the node to be pronounced: no pronounced nodes(pre-order), no more than one unpronounced node (in-order), and no unpronounced nodes (post-order).
The upward pronunciation of the linear graph (17b) falls under the version of
post-order traversal sketched above. Starting from motare (lean), you move tothe pendant node uraniwa (backyard) without pronouncing the nodes en route;the latter immediately dominate an unpronounced node at this state. You pronounce uraniwa, which immediately dominates no (unpronounced) nodes, goback to e-(no) (to-GEN) and pronounce it since its only child has been pronounced. Doa (door), ni (against), and motare (lean) are pronounced in thisorder.

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

The downward pronunciation of the linear graph in (17a) can be subsumed
under the pre-order for an obvious reason, but it also can be captured by the inorder traversal formulated here; the verbal head lean is pronounced first since it
immediately dominates just one unpronounced node at the initial stage, its childnode against is pronounced next for the same reason, and the pendant nodebackyard, which immediately dominates no unpronounced node, is pronounced
after all its higher nodes have been pronounced.
Obviously, the English word order of specifier-head-complement is not obtainable in the pre-order. If the possibility of pre-order is excluded for somereason in natural languages, the head-parameter applying to binary syntactic
trees is the option of in-order versus post-order. Applying the in-order traversal method to appropriate linear subparts of binary trees results in the downward or head-initial pronunciation pattern; nodes nearer to the root are pronounced earlier. The head-final pattern is deducible from the post-order traversal: nodes more distant from the root are pronounced earlier. The headparameter will be discussed further in Section 4.3.
4.2 Overt Wh-movement and Wh in-situ
If a node is directly dominated by a single node as in (19), these nodes are
simply to be pronounced in the neighborhood; one of them is pronounced immediately before or after the other according to a head-parameter value. This
simple ordering is not applicable to a result of internal MERGE such as (20a)and its Japanese counterpart in (20b):(20) a[WH]b.

ka (Q)[past]
John

buy
what

[past]Johnkaw (buy)nani (what)

What/nani are immediately dominated by two nodes, buy/kaw and [WH]/ka,
which would mean that what/nani should be pronounced in the positions adjacent to buy/kaw and to [WH]/ka. Obviously, pronouncing what/nani in two
distinct positions at the same time is impossible due to the limitation on our
sensory-motor system. Pronouncing what/nani twice is possible but is notMiyoko Yasui

economical. In brief, it seems necessary to remove a closed route in (20a,b)
and convert them into trees.
Given a connected graph with one closed route, deleting any one branch in
the route will change it into a tree (see Balakrishnan, R. and K. Ranganathan(2000:72)). This operation is minimal in that it removes just one branch without changing the node set. An additional restriction is necessary in choosing abranch to be deleted: the overall structure should not be changed too radically.
For instance, deleting the branch <[WH], [past]> in (20a) can eliminate theclosed route, but [WH] will cease to dominate [past], John and buy, whichmeans that it is no longer the root by definition. To maintain [WH] as the root,
we should remove one of the incoming branches of the doubly-connected node:<buy, what> or <[WH], what>.
Note that the branch <[WH], what> constitutes the shortest path from [WH]to what, while <buy, what> is part of the longer path connecting them. Similarly, in (20b), <ka, nani> forms the shortest path between ka and nani and<kaw, nani> is part of the longer path connecting them. I assume that there
can be constructed a simple algorithm to find out the shortest path from eachdoubly-connected node to the branching root and to mark it, for instance, as
follows:(21) a[WH][past]Johnb.

ka (Q)[past]

buy
whatJohn kaw (buy)nani (what)

In the downward pronunciation, nodes nearer to the root are to be pronounced earlier. Then, it is natural to pick up the shorter path from what to theroot in (20a). On the other hand, (21b) is subject to the upward pronunciation,according to which nodes more distant from the root are pronounced earlier; thelonger path from nani is to be chosen. Then, (21a,b) are to be modified as(21a,b), respectively:

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation(22) a[WH][past]
John

buy

b.

Theory and its

ka (Q)

what[past]Johnkaw (buy)nani(what)

In (22a), we go downward from [WH] directly to what rather than through[past] and buy. This means that what is pronounced immediately after [WH]rather than buy. In (22b), in contrast, we backtrack from the object nani andgo upward to ka (Q) through the verb kaw and [past]; nani is pronounced immediately before the verb selecting it rather than before ka (Q). In brief, a whphrase is pronounced in the neighborhood of the [WH]-COMP attracting it inhead-initial languages such as English but it is pronounced in its original position in head-final languages such as Japanese.
We have just deduced an important correlation between word order and whmovement. This generalization has been pointed out by Bach (1970) andBresnan (1972). In particular, Bresnan (1972: 42) observes that only languages with clause-initial COMP permit a COMP-attraction transformation. Logically possible but non-existent are languages with a clause-final COMP that
attracts a wh-phrase rightward. Ikawa (1996: Chapter 4) extends this correlation to NP-movements: English and a number of other head-initial languages
exhibit obligatory overt leftward movements, but no comparable rightward
movements are attested in head-final languages. The theory advocated here
offers one natural account of the leftwardedness of overt movement.
To recapitulate the discussion so far, a doubly-connected node in a graphcauses a PF problem and one of its incoming branches needs to be ignored
during the PF interpretation of the graph. When the graph is minimally modified, the head-parameter value is respected: the shorter path is chosen in a headinitial language, where a node nearer to the root is pronounced earlier, and the
opposite holds in a head-final language. The idea behind this is Fukui's(1993:400) Parameter Value Preservation (PVP) measure cited in (23):(23) A grammatical operation (Move α, in particular) that creates a structurethat is inconsistent with the value of a given parameter in a language isMiyoko Yasui

costly in the language, whereas one that produces a structure consistent
with the parameter value is costless.
Using (23), Fukui explains scrambling phenomena in Japanese; Japanese ishead-final, and moving a constituent to the left does not alter the head-finality,
hence scrambling is costless. If a grammatical operation in (23) covers deletion of a branch exemplified in (22a,b), that operation is costless.15
4.3 IP-Specifiers
It is illustrated by (21) and (22) in the previous section that the shortest pathfrom a wh-specifier to a [WH]-COMP attracting it is retained in English but isremoved in Japanese on the PF side. The same is true of IP specifiers:16(24) a.

[past]b.

[past]

v*
John

v*

love

John(-ga)

Mary

ais
Mary

<[past], John> constitutes the shortest path from John to the root in both cases,
and it is retained in (24a) but is removed in (24b); the nearness to the root has
significance in the former. Japanese has a syntactic specifier just like English
but, in some sense, loses it in the PF interpretive processes. Then, it is naturalthat a specifier occupies a special position only in the word order of English.
More generally speaking, the root of (25) is branching and it produces pathambiguities:
(25)

R
A
B

C
D

F

E

G
H

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

Choosing either A or C at R yields distinct subtraversals such as (25a, b), respectively, where the initial step is highlighted by a heavy dotted line:(26) a

R

b

A
B

C

R
C

A

D

F

E

G
H

B

D

F
E

G
H

If the subgraph rooted by A is the specifier of R and the one rooted by C is its
complement, applying the in-order/downward pronunciation to the subtraversalin (26a) will give the correct order in English: Specifier-Head-Complement.
The subtraversal in (26b) will yield the order Head-Complement-Specifier. If
Specifier-Head-Complement is the only order (of head-initial languages) as
claimed by Kayne (1994), a specifier needs to be distinguished from a complement, which is possible thanks to its nearness to the head. Specifically, thenode A has initially been connected to R and also to some other node; at the(post-)syntactic level, the incoming branch from R has been marked by the algorithm mentioned in Section 4.2 and the other branch has been removed. If
the specially marked branch is given priority at any branching node, the orderof Specifier-Head-Complement can be properly obtained for English.
A specifier created by movement or internal MERGE is directly connectedwith the head triggering that operation. An expletive like it is also directly
connected with a finite tense by external MERGE. Its incoming branch, however, is not specially marked since only a doubly-connected specifier created byinternal MERGE has been assumed to be subject to the algorithm at stake.
Still, an expletive stands out naturally in always being the nearest pendant node
to the root. Compare the expletive in (27a) with the doubly-connected IPspecifier in (27b):

Miyoko Yasui(27) a.

will
it

b.

be
raining

will
a

v

man

talk

from

to

that

Mary

town
The expletive it constitutes a minimal maximal projection and it is the nearest
pendant node to the root.17 The man from New York in (27b) is a phrasal
specifier and its head a is connected to the root directly and indirectly throughthe light verb. Note that the pendant node town is more distant from the root
than Mary. I will assume that the algorithm mentioned above can be extended
to mark the incoming branch from the root to an expletive on a par with theshortest path to a doubly-connected node; the former itself is the nearest pendant node to the root, and the latter retains its shortest path to the root:(28) a.

will
it

be
raining

b.

will
a

v

man

talk

from

to

that

Mary

town
Then, the expletive subject in (28a) can be properly pronounced before the other nodes just like the phrasal subject in (28b) is. Japanese lacks expletives
presumably because it has syntactic specifiers but no phonetic specifiers.
4.4 Word Order Variation
Head-final languages are subject to the post-order/upward pronunciation.

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

In (25) repeated below as (29), let us start at R and visit C as follows:
(29)

R
A

C

B

D

F

E

G
H

Traversing the subtree rooted by D and coming back to C will yield (30):
(30)

R

(31)

A

A

C

B

R

D

F

B

E

G
H

C
D

F

E

G
H

If you visit the other subtree rooted by C as in (31), all the nodes dominated by
C have been visited. Visiting the subtree rooted by A and coming back to theroot results in (32):
(32)

R
A
B

C
D

F

E

G
H

Each branch is traversed once downward and once upward in (32). In the upward pronunciation, each node is pronounced at the point where it immediately
dominates no unpronounced nodes; namely it is pronounced in its backtracking

Miyoko Yasui

traversal. (32) renders the pronunciation E-D-H-G-F-C-B-A-R.
Going back to (30), let us visit R, A, and B before visiting the remaining
nodes within the subgraph rooted by C as in (33a):(33) a.

R

b

A

C

B

R
C

A

D

F

E

G

B

D

F

E

G
H

H

You will be back to R after traversing the remaining unpronounced subtree
rooted by C, as in (33b); the sequence of traversed nodes is R->C->D->E->D>C->R->A->B->A->R->C->F->G->H->G->F->C->R and the pronunciation is
E-D-B-A-H-G-F-C-R. Unlike in (32), the branch <R, C> is unnecessarily
traversed four times. Since a traversal has been assumed to start and end at
the root, the natural economy condition is that each branch should be traversed
downward once and backtracked once, which is the case in (32) but is not in(33b).
Beside (32), there are other traversals of (29) that satisfy the economy
condition just mentioned. (29) has two other pendant nodes, B and H. Visiting one of these nodes before the other pendant nodes yields three distinct sequences of visited nodes: (i) R->A->B->A->R->C->D->E->D->C->F->G->H>G->F->C->R; (ii) R->A->B->A->R->C->F->G->H->G->F->C->D->E->D>C->R; and (iii) R->C->F->G->H->G->F->C->D->E->D->C->R-> A->B->A> R. (i) and (iii) are given below:(34) a.

R

b.

A

C

B

D
E

R
A

F
G
H

B

C
D

F

E

G
H

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

The post-order/upward pronunciations of traversals in (34a,b) result in B-A-ED-H-G-F-C-R and H-G-F-E-D-C-B-A-R, respectively. Choosing F at C before D in (34a) produces (ii) and it is phonetically realized as B-A-H-G-F-E-DC-R . Each branch is traversed downward once and upward once in all thethree traversals.
I assume that any of the three orderings obtained above are basic word orders.
It follows that a head-final language, which takes the post-order/upward option
in the linearization of its syntactic graphs, allows its word order to be quite free.
As is well-known, Japanese confirms this prediction. Besides (35a), for example, (35b-d) are equally acceptable:(35) a. [ John-ga [ Mary-ga
NOM

hon-o

katta

to ]

itta ]

NOM book-ACC bought COMP said

'John said that Mary had bought the book.'b.

[ John-ga [ hon-o Mary-ga katta to ] itta ]Lit. 'John said that the book, Mary had bought.'

c. [ [ Mary-ga hon-o katta to ] John-ga itta ]'That Mary had bought the book, John said.'d.

[ [ hon-o Mary-ga katta to ] John-ga itta ]Lit. That the book, Mary had bought, John said.'

According to the standard analysis, (35a) has the basic word order; clauseinternal scrambling of the embedded object results in (35b) and scrambling of
the embedded clause in front of the matrix subject in (35a,b) produces (35c,d),respectively. (35a-d) are all obtained from the same syntactic graph here
without running counter to the economy condition on traversal. (35a,c), forinstance, are based on the traversals described in (35a,b), respectively:18

Miyoko Yasui(36) a.

ittab.

John-(ga)

itta

to

John-(ga)

to

katta
Mary(-ga)

katta
hon(-o)hon(-o)Mary(-ga)

The traversal in (36a) underlies (35a), which is generally regarded as the basic
word order. (35c), which is deduced from the traversal in (36b), is also treatedas basic here. This accords with the claim by Hale (1980) among others.
Actually, clause-internal scrambling of non-subjects exemplified in (35b,c)does not require any heavy stress on them or special discourses. What is more,most native speakers of Japanese prefer (35c) to (35a) since the latter involves acenter-embedding of the complement clause. If the traversal starts with thefirst-pronounced pendant node rather than the root, which does not affect theresultant pronunciation, the first few steps from the root to the pendant in(36a,b) are removed as follows:(37) a.

ittab.

John-(ga)

to

itta

John-(ga)

to

katta
Mary(-ga)

katta
hon(-o)hon(-o)Mary(-ga)

The total number of branched traversed is 9 in (37a) and 7 in (37b); the word
order of (35c) is obtainable with fewer steps than that of (35a). This is likely tomake (35c) easier to process than (35a). The same contrast holds between thetraversals underlying (35b,d). I will assume that sentences with clause-internal
scrambling are all basic word orders and that those with fewer branches
traversed tend to be preferred at the PF-interface level.19(38a) involves long-distance scrambling of the embedded object in (35a) andis deduced from the traversal described in (38b):(38) a. [ hon-oJohn-ga [ Mary-ga

book-ACC NOM

katta

to ]

itta ].

NOM bought COMP saidA Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its'The book, John said that Mary had bought.'
b.

itta

John-(ga)

to
katta

Mary(-ga)hon(-o)

You first traverse the embedded object and backtrack to the embedded verb
katta (bought). Next, instead of visiting the embedded subject, you go upward
to the matrix verb itta (said) and visit the matrix subject. Then, you backtrack
to the embedded verb to visit the embedded subject and finally go back to theroot. (38b) violates the economy condition of traversal discussed above, with
its superfluous subtraversals expressed by the double arrows. This accords
with the generally accepted view that cases involving long-distance scrambling
such as (38a) do not have basic word order, and specifically with the observation by Saito (1992) and others that long-distance scrambling behaves differently from clause-internal scrambling. We can conclude either that a violationof the economy condition of traversal is allowed by some discourse-level factors such as focus or that (38a) is deduced from a syntactic graph distinct fromthe one underlying (35a-d).
Let us go back to the instances of the in-order/downward pronunciation in
English. The two traversals described in (26a,b) repeated below as (39a,b) areconsistent with the economy condition:(39) a.

R

b

A
B

C

R
A

D

F

E

G
H

B

C
D
E

F
G
H

No branches in (39a,b) are traversed three times. There is one more downward traversal consistent with the condition, which has the sequence of nodes

Miyoko Yasui

R->C->F->G->H->G->F->C->D->E->C->R->A->B and the resultant ordering
F-G-H-C-D-E-R-A-B:
(40)

R
A

C

B

D

F
E

G
H

(39b) and (40) are filtered out by the specifier-first condition discussed in Section 4.3. A violation of the economy condition on traversal in the inorder/downward pronunciation is (41), with the sequences of traversed nodes
R->C->D->E->D->C->R->A->B->A->R->C->F->G->H->G->F->C->Randthe resultant pronunciation D-E-C-R-A-B-F-G-H:
(41)

R
A
B

C
D

F

E

G
H

After going down the left path from C and backtracking to C, the traversal goesup to R and scans its left subtree instead of traversing the right subtree of C.
The branch <R, C> has been traversed four times. The economy condition
blocks the traversal in (41). What is interesting is that the specifier-first condition imposed on the in-order/downward pronunciation is stricter, filtering out(39b) and (40) as well as (41). In this way, English does not exhibit the word
order freedom Japanese does.20
5. Remaining Issues
This paper has been mainly concerned with parametric differences in word
order: phonetic realizations of specifiers such as attracted wh-phrases, argu-

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

mental subjects and expletives if any, and the flexibility or rigidity of basic
word order. One important operation that greatly affects word order but cannot be discussed here is head-movement. Presumably, it can be analyzed aswhat is called edge contraction in graph theories, which deletes a branch andidentifies the two nodes directly connected by the deleted branch. Dependingon which of the two nodes is retained, the overall graphical structure greatly
differs. A analysis along this line appears to be promising. Another issue,
which has not been explored here or solved in other syntactic studies, is thetreatment of adjuncts. It is not clear whether they are introduced by external
MERGE or some comparable operation at the edge of the graph already formed,
or they are inserted into the graph post-cyclically. I leave these problems for
future research.

Notes

1

Downward lines are used instead of arrows, as has been the convention in syntactic trees.

2

A path is any linear subset of a tree.

A terminology more familiar in graph theories is: α is a predecessor of β and β is a successorof α. See, for example, Balakrishnan, and Ranganathan (2000), and Hopcroft and Ullman(1979).

3

4

A closed route is called ‘cycle’ in the graph theory, but I will reserve the terminology to be
used for ‘cycle’ in rule application and so on.
5vP structure, if any, is ignored in (5).

See note 16.

6

Chomsky (1995: 244) distinguishes nodes with the same label by indices, which is an undesirable departure from the Inclusiveness Condition.
7

Nodes will be expressed with dots henceforth.

8

Thus, the crash-proof selection pursued in Frampton and Gutmann (2000) does not constitutea significant issue here. See Yasui (2002).

9

Following Lopez (2000), I will assume in Section 4 that an object is Case-checked in its
original position.
10

In the theory here, Move does not produce a copy of the moved element, so that phoneti-Miyoko Yasui

cally non-empty elements in a graph can all be pronounced, which is a desirable result.
11

Relaxing this economy condition presumably results in clitic doubling and similar phenomena.
12

A binary tree is a rooted tree where each node immediately dominates at most two nodes(i.e., zero, one or two children). Each child can be identified as either a left or right child. If anode has just one child as in a linear graph, identifying it as left or right does not affect thetraversal if it is pre- or post-order. See Sahni (2001) among others.
13

In any of the three traversals, the nodes are traversed in the same order according to the 'leftfirst' rule: A-B-C-B-D-B-A-E-F-G-F-I-F-E-H-E-A.
14

There are two cases: it immediately dominates just unpronounced nodes or no nodes at all. The
latter case covers pendant nodes.

15

We can assume either that this operation takes place in syntax and its output is subject to the
PF interpretive processes, or that (23) governs PF as well as syntactic operations.

16

Following Lopez (2001), I assume that the object stays in its original position and Casechecked. Given this assumption, we can maintain the generalization that each node has at
most two downward branches. A tense selects a light verb and agrees with D; COMP selects
T (and agrees with a wh-phrase if it is [WH]); D selects N (and agrees with a DP-specifier if itis the genitive marker). Similarly, each lexical category could be analyzed as selecting at
most one category if the object of a predicate taking two arguments such as put is assumed to
be Case-checked in-situ. This generalization collapses if Chomsky's analysis of the transitive
verbal structure is taken, where v* is connected to three distinct categories: the object, theverb it selects, and the subject it selects. The choice does not seriously affect the discussion
here.
17

The expletive in "it will rain" is one of the nearest pendant nodes to the root if the sentence
is analyzed on a par with (28a), or it is the only nearest node if an intransitive verb is selectedby a light verb.

18

The verb stem kaw (buy) and the past tense morpheme are assumed here to constitute a single node. More exactly, the subject is connected to the light verb selecting kaw (buy) byexternal MERGE and doubly connected to the past tense by internal MERGE. Since internal
MERGE has no PF effect in upward pronunciation languages as discussed in Section 4.2, thesimplified analysis in (31a,b) suffices.
19

According to Fukui's PVP, not only clause-internal scrambling but also long-distancescrambling are costless. In the theory here, the former produces equally economical PF realizations but the letter yields less economical PF realizations.

A Graph-Theoretic Reanalysis of Bare Phrase Structure
Implications on Parametric Variation

Theory and its

20

Fukui (1993) claims that English exhibits rightward cost-free movement, which is the counterpart of Japanese scrambling. The present theory denies it.

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Chomsky, Noam (1995) The Minimalist Program. The MIT Press.
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_____ (2000) "Minimalist Inquiries: The Framework." In Step by Step: Essays on Minimalist Syntax in Honor of Howard Lasnik, eds. Roger Martin, David Michaels, and JuanUriagereka. MIT Press, Cambridge.
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_____ (2000) "Crash-Proof Syntax. " ms., Northeastern University.
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DoctoralKayne, Richard S. (1994) The Antisymmetry of Syntax. The MIT Press.
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