Crash-Proofness of the Lexicon and Bare Phrase Structure
Miyoko Yasui
Dokkyo University
myasui@dokkyo.ac.jp

1.

Crash-Proof Selection Versus Initial Lexical Choice

Frampton and Gutmann (2000, henceforth F&G) propose a very interesting theory of syntax
that is claimed to be 'crash-proof': an optimal derivational system from a computational pointof view is the one that does not generate ill-formed objects at any stage of derivation. If thederivation starts with some lexical items that are chosen arbitrarily from the lexicon as in
Chomsky (1995,1999,2000,2001), it is quite likely to crash.

F&G's theory thus dispenses

with initial lexical choices and adopts a few syntactic constraints to make lexical items
introduced one by one from the lexicon in the 'correct' order.

I will discuss that the crash-

proofness F&G intend to achieve cannot be efficiently guaranteed within narrow syntax but
should be deduced from a native speaker's vast knowledge of lexical items.

Instead of

pursuing F&G's crash-proof selection or Chomsky's approach with initial lexical choices, I willattempt to replace the standard syntactic tree with a strictly minimalistic graphicalrepresentation that can straightforwardly inherit the crash-proofness from the lexicon.

2.

Crash-Proof Selection

One of F&G's main points is the 'correct' order of selection. The system guarantees the correct
order crucially depending on the following assumptions:(1) a.
b.

Only a lexical item which selects nothing can start the derivation.
Satisfaction of selectional requirement is given priority over that of agreement inPage 1

2002.9.4

introducing lexical items.

Specifically, given three lexical items X, Y and Z, where

X has already been introduced into the derivation, while Y and Z are not, Y is to be
introduced into the derivation before Z if a selectional relation holds between X andY, and an agreement relation holds between X and Z.
Consider the derivation of (2a), which consists of the four lexical items in (2b):1(2) a.

Men arrived.

b.

{men, [past], v, arrive}

Arrive selects nominal, [past] selects v, v selects verbal, and men selects nothing. Given (1a),men is the first lexical item to be introduced into the derivation. Men can be selected by theverb arrive and it can agree with (or valuate the unvalued f-features of) the tense [past].
Given (1b), arrive is to be introduced next. Arrive can be selected by v, and this is the only
option at this stage. The tense [past] can select v and agree with men.
introduced as the head selecting men.

Given (1b), [past] isFinally, the agreement requirement of [past] is satisfied

by the internal merger of men into its specifier position.
Note that (1a) is necessary in blocking the derivation from starting with [past] or v rather
than men.

If v is introduced into the derivation first, it merges with arrive next, forming

structure (3a):(3) a.

vv

b.
arrivevv

arrivemenarriveThen, cyclicity precludes men from being introduced into the derivation as in (3b).
One obvious problem with this account is that (2b) does not exist in F&G's system;
lexical items are to be freely chosen from the whole lexicon at each stage of derivation.

1

Forexpository convenience,Iassum e w ith Chom sky (1999)thatthere are tw o lightverbs v
and v* selecting intransitive and transitive verbs,respectively,though F& G analyze (2a)w ithoutv. The difference does notaffectthe discussion here.
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Lexical items that satisfy (1a) are mostly nouns.2 Thus, the first step is not selecting men
from the set in (2b) but selecting some noun non-deterministically from the whole set of nouns.
Similarly, the next step is not selecting arrive from (2b) but selecting some verb nondeterministically from the lexicon. The verb in question need not be intransitive; merging
men with a transitive verb such as hit can lead to a well-formed structure if one more
appropriate noun is introduced into the derivation. It is true that (2a) is derivable in one'correct' order but only on the basis of accidental and time-consuming selections of the four
lexical items from the whole lexicon.
The situation seems no better than the massive overgeneration of initial lexical arrays in
Chomsky's system, most of which are doomed to fail, as pointed out by F&G. In F&G's
system, several (and often a great number of ) lexical items are searched as a candidate for eachlexical item that will eventually constitute a sentence, but none of them are actually chosen
except for one.

On the other hand, a possible algorithm instantiating Chomsky's system might

be to list up all the possible subsets of the lexicon starting with size n, with size n+1 and so on,where n is the length of a shortest possible sentence.

Derivations from most of them crash,

but adopting some appropriate version of (1a,b) and other auxiliary assumptions could help
restrict overgeneration.
Next, consider the derivation of the transitive sentence in (4a) with its components in(4b):(4) a. Women met men.
b.

{[past], v*, hit, women, men}(4a) has structure (5) at an earlier stage of its derivation:2

Besides nouns,the verb rain,selecting nothing,presum ably satisfies (1a).
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(5)

v*
women

v*
v*

hit
hit

men

In (5), hit selects men, and if the relation between the light verb v*and its external argument isselection, v* selects women.

Both men and women are nouns and thus can start the derivation.

It does not matter which noun does. If hit is introduced after one of the nouns, say men, (5)can be derived without a violation of cyclicity. The problem is that v* can be introduced as
the selector of men before hit.
violate cyclicity.

If men is selected by v*, introducing hit in the next step would

One might try to circumvent this problem by claiming that v* only selectsverbal and its relation with an external argument is something other than selection. This
amounts to adding further complication to (1b).

(1b) or its further extension is almost arestatement of what the correct order of merger is, and if Chomsky's system with initial lexical
arrays is supplemented with similar assumptions, it will become as crash-resistant as F&G's.

3. Violations of Cyclicity and Graphical Representations of Syntactic Structure
We have seen that F&G's system needs (1a) and some appropriate extension of (1b) to makesyntactic derivations proceed in an unambiguous manner without violating cyclicity. The
unwanted violations of cyclicity are illustrated again below:(6) a.

vv

b.
arrive==>vv

arrivearrivePage 4men

2002.9.4

(7) a.

v*
women

v*
v*

==>

women

v*

v*

hit
hit

men

Once (6a) and (7a) are formed, cyclicity disallows the circled part to be expanded as in (6b)and (7b), respectively.
Let's find out which part of the circled structures is problematic.

Introducing a new

lexical item into the structure already formed should be allowed since it is indispensable part ofstructure-building. Thus, men in (6b) and the lower hit and men in (7b) are not problematic at
all. Moreover, the lower arrive in (6b) and lower v* have been present as the lexical heads in(6a) and (7a), respectively.

Offending are the upper arrive in (6b), and the upper v* and hit in(7b), all of which are non-terminal symbols. If these offending non-terminal nodes are
somehow eliminable on principled grounds, the violations of cyclicity found in (6) and (7)probably will cease to be an issue; so will the crash-proofness of selection.
Note, first of all, that non-terminal symbols have been postulated, by definition, in
rewriting rules/merging operations and their graphical representations upheld since thebeginning of generative grammar: the combination of constituents is represented as a nodedistinct from them, as in (8):(8) a.

・α

・β

・γ

b.
・α

・β

α and β in (8a) are inputs to merger (or the righthand part of a rewriting rule).

Merging α

and β has been assumed to result in (8b), where the new node γ is introduced along with two
directed edges connecting it with α and β.

Chomsky (1995) argues that the label of γ can be

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identified with that of a or that of b in a principled manner; still, γ is a node distinct from α and
β.3
The above representation of syntactic structure is not mandatory. Alternative andsimpler graphical representations are (9a,b) corresponding to the two cases of (8b) with thehead being a and b, respectively:(9) a.

・α

b. ・β

・β

・α

Merging α and β is graphically represented just by drawing a directed edge from one of them
toward the other.

Let us examine (8b) and (9a,b) from a graph-theoretic point of view. A

graph, denoted G=(V, E), consists of a set of nodes V and a set of ordered pairs of nodes E.4(8b), (9a,b) are defined as follows:(10) (8b): G1=(V1, E1) V1= {α, β, γ}. E1 ={<γ, α>, <γ, β>}the label of γ is equal to that of α or β.
(9a):G2=(V2, E2) V2={α, β}E2={<α, β>}(9b):G3=(V3, E3) V3={α, β}E3= {<β, α>}.

(8b) and (9a,b) differ in their representation of headedness. In (8b), a non-terminal node
γ is added to the node set V1, two ordered pairs <γ,α> and <γ,β> constitute the edge set E1,
and the label of γ is identified either by that of α or β. In (9a,b), on the other hand, the nodesets V2 and V3 are minimal, containing just α and β, and either of the two possible orderedpairs <α, β> and <β, α> constitutes the edge set. Note that <α, β> is generally defined as
3

Chomsky (1995: 245) recognizes the necessity to distinguish a label for a lexical item and thesame label for the structure headed by the lexical item in terms of subsctipts as follows:
.(i)
・α1
・α2

・β

α1 and α2in (i) are distinct nodes with distinct labels.
4
Instead of using arrows to express ordered pairs, downward lines have been used in standard
tree diagrams such as (8b), and this tradition is followed here.
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{{α}, {α, β}}, and it looks rather similar to Chomsky's (1995:244-245) definition of the object
formed from a and b of the type α: {α, {α, b}}. For expository convenience, Chomsky
continues to employ the graphical representation of the form (8b) for the object {α, {α, β}},acknowledging that (8b) is more complex than is absolutely necessary.

If {{α}, {α, β}} isadopted instead of {α, {α, β}} as the definition of the object formed from α and β , thediscrepancy between the formal definition and its graphical representation will disappear,
which seems to be a desired result.
If the strictly minimalistic system of graphical representation is taken along the aboveline, introducing a new lexical item will not distort the structure already formed, and hence theorder of lexical introduction will become a trivial issue.

Graphically, it just adds a new edge

(the bold line in (11)) connecting the new lexical item α and one of the nodes in the graphalready formed (β) : the graph consisting of the solid lines is retained as a subgraph of thegraph formed by the introduction of α:
・

(11)
・

・β
・

α・
・

・

Set-theoretically, α is added to the node set of the graph already formed, and <α, β> (or<β, α> ) is added to the edge set. Going back to the case of cyclic violation described in (6),the strictly minimalistic system depicts (6a,b) as (12a,b), respectively:(12) a.

・v*

b.

・v*

・women・women ・hit
・men(12b) retains (12a) as its subgraph.

It is easy to verify that introducing the four lexical items

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in any order will inherit the graph already form as its subgraph.

In this way, the alternative

system succeeds in eliminating (1a).
To see if the priority of selection over agreement stated in (1b) can be likewise
eliminated, consider the derivation from (12b) to (13a), where [past] is introduced as theselector of v*:(13) a.

・[past ]・ [past]

b.

・v*

・v*

・women ・hit

・women ・hit

・men

・men

Women should agree with [past]. Suppose that this relation is expressed by the downward
edge from [past] to women as in (16b).

(16b) inherits (16a) as its subgraph, and(16b) will be

produced if its derivation starts with [past] and women rather than men, which might suggestthat (1b) be given up.

Nevertheless, I will retain (1b) in a different form , arguing in Section 5

for the conception of initial syntactic structures as subgraphs of the lexicon, which is claimed
to be a huge connected graph expressing the selectional properties of lexical items.

4.

Preference of Merge over Move and the Full Use of Lexical Items

Chomsky (MI) argues for the phase-based initial lexical choice based on (14) and (15):(14) a. There is likely to be a proof discovered.
b. *there is likely a proof to be discovered(15)

It was decided [ PRO to be executed at dawn ]](14a) has had (16) at an earlier stage of its derivation:(16)[todef [ be a proof discovered ]]The EPP-feature of the defective infinitive tense requires that something occupy its specifier
position. Two options are available: merge there or move a proof.
Page 8Here, (17) comes into
2002.9.4

play, forcing (16) to expand into (18a) rather than (18b):(17)

Simple operations (Merge) preempt more complex ones (Mmove or Merge plus Agree)(18) a.

[ there todef [ be a proof discovered ]]b.

[ a proof todef [ be (a proof) discovered ]]Hence, (14a) is derivable from (18a), but (14b) is not. (17), however, incorrectly blocks the
movement of PRO to the specifier of the control to in (15) since the expletive it is available; itshould merge with to be executed RPO at dawn. To overcome this difficulty, Chomsky
introduces the idea of phase-based lexical choice: from the set of lexical items initially chosen
to build a whole sentence, some subset is extracted and placed in active memory for building
up a phase of the sentence.

Given the phase-based lexical choice, it is not available in theembedded phase of (15); and it is derivable.
Note that a subset of lexical items placed in active memory needs to be used up before
the computation proceeds, as Chomsky (2000) says. This condition, however, appears to
weaken the motivation for (17).

Going back to (16), there is in active memory and it must be

used before the computation goes on to the next phase. Simply for this reason, a poof cannot
move; if it moved, there would go nowhere within the phase. Chomsky (2000:103-104)
argues that (17) is crucial in deducing the order of object-subject in so-called Object Shiftlanguages. Moreover, some amount of look-ahead is involved in the account of (14a,b) basedon the requirement that lexical items be used up in each phase. Still, this requirement reduces
the necessity of (17).

5.

Lexicon as a Graph and Syntactic Structure as its Subgraph

There have been pointed out some problems in F&G's theory of crash-proof selection as wellas in Chomsky's phase-based theory of structure-building.

In this section, I will try toaccommodate their insights into the graph-theoretic approach suggested in Section 3 and to

Page 92002.9.4

work out some of the problems. The important point has been that the graphicalrepresentation adopted here has only lexical items as its nodes. Non-terminal symbols such as
V' have been eliminated since they are largely responsible for cyclicity violations and the issueof lexical introduction.
The question arises how such a graphical representation is obtained

It might be formed

by introducing lexical items one by one from the lexicon as F&G claim, or if the lexicon itself
is a graph with lexical items as its nodes and their selectional relations as its edges, which isplausible, the graphical representation of syntactic structure can be regarded as someappropriate subgraph of the lexicon.5

By definition, the lexicon is about lexical items only;

there are no entries for non-terminal symbols. Each lexical item is related to some otherlexical items; if a lexical item were totally dissociated, it would never be selected in syntactic
derivation. The relation at stake might be semantic (s-selection) or categorial (c-selection).
It might also include valuation of some uninterpretable feature (agreement), but I will assume itdoes not here, and I come back to this issue shortly.

In this way, it is reasonable to represent

each lexical item as a node of the graph L(exicon) and its selectional relations with otherlexical items in terms of directed edges.
For instance, arrive selects nominal and is selected by the light verb v. Then, the graph
L involves the following as one of its numerous subgraphs:
(19)

○ v

○ arrive○ men ○ women ○ people

○ ...

5

The form erview is taken in Yasui(to appear),w hich is an attem ptto explain the correlation
betw een the head-param eterand the overt/covertdistinction in w h-m ovem ent. The accountis
com patible w ith the latterview.
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2002.9.4

I will not go into the question of whether arrive is connected to all nominals or somesemantically appropriate nominals, which is a matter of convergence or gibberishness.
Arrive is connected indirectly with other lexical items in L as follows:(20)● [declarative]○ wonder○ believe○ [alternate Q]○ [WH]○ that●[past]● v● arrive● men ○ women ○ people○ ...

Note that the subgraph of (20) consisting of the filled circles and bold arrows is the graphicalrepresentation of (2a) before the movement of men.

More generally speaking, any well-formed structure before it is subject to movement operations is some subgraph of L. The
converse does not hold, however; not all subgraphs of L will converge in syntax. For one
thing, a subgraph needs to be rooted by one of the specified lexical items: [declarative],[alternative Q] and [WH]. [declarative], denoting the COMP of root declarative clause, is a
special node in that it has no mother node or incoming edge.

[alternate Q] and [WH] canhead root or embedded wh-questions, but that can head only embedded declarative clauses.
Another condition on convergence is that the dead end nodes (those that have no outgoingarrows) of the subgraph must also be dead ends in L. If a dead end node in the subgraph has
outgoing arrows in L, it means that the lexical item the node expresses should select something
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but it does not in the subgraph. As has been mentioned in connection to F&G's assumption(1a), nouns do not select obligatorily; nouns are dead ends in L. (1a) remains in the theory
here in this way, though the necessity to introduce lexical items in a particular order has been
completely eliminated.
Since L is huge, picking up some subgraph from it should be a non-trivial task, but thecondition on the root node might reduce the difficulty to some extent.

Moreover, it is largely

a matter of our thinking rather than syntax. Suppose that a subgraph G=<V, E> is somehow
extracted from L. It is ensured that the selectional requirements of all the lexical items in V
are satisfied since they have been extracted from the lexicon so as to meet this condition. The
remaining job is to satisfy agreement requirements in G if any by Move in syntactic derivation.
In (20), no arrow is assumed to exist between [past] and men.

It is because [past] can agreewith a lot of nouns and if its agreement possibilities are expressed in L by arrows as in (21),something like "*women arrived men" results. :(21)●[past]●v● arrive● men ● women ○ people○ ...

In (21), men, which is the argument of arrive, should agree with [past] but it does not. If thedirected edges of L express only selectional relations among lexical items, excluding
agreement, subgraphs that are doomed such as (21) are never extracted. This architecture of
L has essentially the same function as F&G's assumption (1ii): satisfaction of selectional
requirement is given priority over that of agreement in introducing lexical items.
Page 12It also2002.9.4

corresponds to preference of Merge over Move in Chomsky's theory. The importantdifference is that F&G's and Chomsky's assumptions are part of syntax but it is part of thelexicon here.

In other words, a native speaker's knowledge of the lexical items in his/her

language ensures (1ii) or preference of Merge over Move.
Though nouns are not connected to tenses in L, expletive there and it should be as
follows; otherwise, they would never be introduced into syntactic structure:(22)○[past]○v○it○ there○ men ○ women ○ people○ ...

○ arrive

Going back to (14a,b) and (15) repeated below:(14) a. There is likely to be a proof discovered.
b. *there is likely a proof to be discovered(15)

It was decided [ PRO to be executed at dawn ]]this pattern of data can be explained if extraction of a subgraph is phase-based, as Chomsky
assumes.6 Preference of Merge over Move can be eliminated.

Instead, the condition that all

the lexical items must be used up before the computation proceeds is subsumed under theconception of structure-building here: a subgraph of L is submitted to the syntactic
computation and all the lexical items in it are necessarily used.

6

A sentence often contains m ore than one occurrences ofsom e lightverb and CO M Pl. Ifa
subgraph is extracted to build a phase,itcontains no m ore than one lightverb orCO M P,hence,the phase-based extraction appears to m ake the system sim pler.
Page 132002.9.4

6.

Defining Some Fundamental Structural Relations

How are the two important relations Sister and Immediately-Contain in Chomsky (2000) to be
defined in the alternative theory here? Consider the standard tree diagram of the phrase"believe that this man will hit the woman" in (23a) and its alternative version in (23b):(23) a.

・ believe1・believe2 ・that1・that2・will1・this1・will2・this2 ・man

・will3・v*

・this1・this2 ・man

・v*
・v*

・hit1

・hit2

・the1

・the2 ・woman
・believe

b.

・that
・will
・v*
・this

・hit

・man

・the
・womenThe movement of this man is expressed as two occurrence of it in (23a) and the additional edge
with this in (23b). The movement of object is ignored here for expository convenience.
The set-theoretic definitions of the edge set of (23b) is (24a) and equivalently (24b).

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Sisterhoood in the standard sense can be defined by adjancent nodes or ordered pair in thealternative theory.

In (16a), believe2 and the subtree rooted by the node that1 are Sisters.7

In (23b), believe and the subgraph rooted by its adjacent node that are Sisters.

One differenceis that the subject this man and will are Sisters in (23b) according to this definition since thisand will are adjacent nodes, but they are not strictly Sisters in (23a) though they m-commandeach other. This might or might not be a problem.
The notion of Immediately-Contain can also be defined in terms of adjacent nodes. In(23a), will2 Immediately-Contains will3and the subtree rooted byhitt1 in (23a).

In (23b), thegraph rooted by hit is a proper subgraph of that rooted by its superjacent node will. The
Immediately-Containing relation between will2 and will3 in (23a) presumably has no
significance; hence, the absence of the corresponding notion in (23b) is not problematic.
The c-command relation holding between this man and the woman in (23a), which isimportant at least in interpretation, can be translated into (23b) in terms of the same definition.
One type of c-command relation that is present in (23a) but absent in (23b) is that holding
between a head and a phrase other than its complement.

In particular, will3 c-command thewoman in (23a), but the corresponding relation does not exist in (23b), which contains only one
instance of will. This is unlikely to be problematic, since the notion of c-command issignificant only for phrases such as a reflexive and its antecedent.
Note that the definition of closest heads such as will and hit in the phrase underconsideration requires some complication in (23a), but they are simply defined as two adjacentnodes in (23b). Actually, an ordered pair (or two adjacent nodes) constitutes the fundamental
structure in the alternative system of graphic representation here.

This appears to be an

7

The asym m etric c-com m and relation holding betw een nodes ratherthan constituents plays acrucialrole in K ayne’sLiniearCorrespondenceA xiom . Itis notclearifrelations holding
betw een nodes ratherthan constituents are syntactically im portant.
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advantage over the standard tree representation since the notion of closest heads is important inhead-movement and searching for relevant f-features by the probe among others.

7.

Concluding Remakrs

References
Balakrishnan, R. and K. Ranganathan (2000) A Textbook of Graph Theory.

Springer.

Chomsky, N. (1995) The Minimalist Program. The MIT Press.
_____ (1999) Derivation by Phase: MIT Occasional Papers in Linguistics no.18.
_____ (2000) "Minimalist Inquiries: The Framework." In Step by Step: Essays on Minimalist
Syntax in Honor of Howard Lasnik, eds. Roger Martin, David Michaels, and Juan
Uriagereka.

MIT Press, Cambridge.

_____ (2001) "Beyond Explanatory Adequacy." ms., MIT.
Frampton, John and Sam Gutmann (1999).
Efficient Minimalist Syntax.""Cyclic Computation, a ComputationallySyntax 2, 1-27.

_____ (2000) "Crash-Proof Syntax. " ms., Northeastern University.
Hopcroft, J. E. and J. D. Ullman (1979) Introduction to Automata Theory, Languages, andComputation. Addison-Wesley.
Kayne, R. S. (1994) The Antisymmetry of Syntax. The MIT Press.
Yasui, M. (2002) "“A Graph-Theoretic Reanalysis of Bare Phrase Structure Theory and its
Implications on Parametric Variation.” ms., Dokkyo University.
(http://www2.dokkyo.ac.jp/~esemi003/publications/graph_v1.PDF)_____ (to appear)“A Graph-Theoretic Reanalysis of Bare Phrase Structure and Wh-

movement." Proceeding of LP2002.

Charles University Press.

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