Across-the-Board Rule Application

Across-the-Board Rule ApplicationAuthor(s): Edwin WilliamsSource: Linguistic Inquiry, Vol. 9, No. 1 (Winter, 1978), pp. 31-43Published by: The MIT PressStable URL: http://www.jstor.org/stable/4178033 .

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Linguistic Inquiry Volume 9 Number I (Winter, 1978) 31-43.

Edwin Williams Across-the-Board Rule Application*

0. Introduction

My purpose is to develop and formalize Ross's (1967) principle of Across-the-Board (ATB) rule application, and to support the hypothesis that this principle governs the application of all transformations.

Consider two plausible derivations of the following indirect question:

(1) Who John saw and Bill hit.

The first derivation would use Conjunction Reduction (CR) to derive (1) from (2):

(2) Who John saw and who Bill hit.

The second derivation, the ATB derivation, would generate (1) from (3) by a single application of Wh Movement, putting who in the complementizer and simultaneously deleting both of the underlying who's (4):

(3) COMP[[John saw who]s and [Bill hit who]s]s (4) COMP[[John saw t]s and [Bill hit t]]s

who

1. Formalization

In this article I will present evidence that derivations such as (2) -> (1) are to be barred. I will also present the necessary extensions of linguistic theory that are needed to provide for ATB derivations.

1.1. To simultaneously delete the two who's in (3), we must make them both parts of the factor or factors to be deleted by Wh Movement. To achieve this, I propose that

* I would like to thank the members of the University of Amsterdam Linguistics Department, especially Henk van Riemsdijk, the members of the Thursday afternoon seminar at the Maison de Science de l'Homme, especially Richie Kayne and Joseph Emonds, the members of the Spring semester 1977 course in Linguistic Formalism at the University of Massachusetts, and the members of the Linguistics Department at MIT, all of whom heard presentations of the material in this article.



32 EDWIN WILLIAMS

conjuncts in a coordinate structure be written on top of each other, and that factor lines that split coordinate structures be drawn so as to split all conjuncts of that structure. By this proposal, (3) will be written as follows:

(5) COMP [[John saw who]s and] [ilhit who]s s

It will be factored for the application of Wh Movement as in (6):

(6) COMP [[John saw who]s and] [[Bill hit who]s s

1 2 3 4

Application of Wh Movement will place a single copy of who in COMP and will delete factor 3, giving (7):

(7) COMP [John saw ]s ] I ~~~~and

who [Bill hit 4]s s

1.2. To make possible derivations like the one just described, we must define "well formed labeled bracketing" so as to allow (5), and "factor" so as to allow (6).

To this end, I propose that to the standard definition of "'well formed labeled bracketing"' be added:

(8) Definition The structure2

[X],C 1

and [Xn]Cn IC

is a well formed labeled bracketing if Xl, . . ,XXn are.

We will say that a string containing structures defined by (8) is in "ATB format". To the usual definition of factor,3 I propose the following addition:

(9) If F is a factor and C a coordinate structure containing conjuncts C, ...Cn then for F to be a well-formed factor the following must hold: if for any i, [c, E F and ]c, E F, then for all i, it must be the case that [c, E F and ]c, E F.

This definition of factor says essentially that if one conjunct is split by a factor line, all must be split, and further, that if the conjuncts are split, then the left conjunct brackets must all belong to the same factor.

This definition of factor is quite particular. We will examine predictions made by

' See Peters and Ritchie (1973). 2 Subscripts here and elsewhere are merely for reference in the text. 3 See Peters and Ritchie (1973). Peters and Ritchie define factor as any substring of a well-formed

labeled bracketing that does not begin with a right bracket or end with a left bracket.



ACROSS-THE-BOARD RULE APPLICATION

this definition in the next section. First, we will show that the factorization in (6) is valid by this definition:

(10) COMP [[John saw who]s and [[Bill hit who]s s

1 2 3 1

Factor 2 satisfies (9) because it contains all left conjunct brackets, and no right conjunct brackets. Factors 1, 3, and 4 trivially satisfy (9), since they contain no left conjunct brackets.

We will say that a factor like 3 consists of "simultaneous factors", since it contains a part of each conjunct. Factors that do not contain parts of conjuncts, such as 1 and 4, we will call "simple". When a factor contains a whole coordinate structure, as factor 1 below, we will again call it "simple".

(1 1) [[John]NP and] left L[Bill]Np ]NP

1 2

2. Predictions from the Definition of Factor

Although we have not yet defined the deletion or movement of a factor that consists of a set of simultaneous factors (we will do this in section 3), a great deal is predicted by the definition of factor alone. We will now examine these predictions.

For each type of prediction, a schematic diagram will be given. All examples will be in ATB format. X, Y, Z, and W will stand for material not affected by the transformation; a will stand for material affected. An asterisk will stand before diagrams representing ungrammatical cases. Factors will be divided by vertical lines.

2.1. (12) [Xa]C and] [Y a]c c

This is the example (10) just discussed. The mirror image case (13) is also good, as (14) shows:

(13) [a X]c and]

(14) COMP [[who opened the door]s] , COMP [bP opened the door]s and1 [who left]s is who [[4 left]s is

2.2. (15) *[[X a]c| and] [ee [o a Y]C2 it

Here, conjuncts are split, but the left conjunct brackets belong to different factors,



34 EDWIN WILLIAMS

and this is not allowed by (9). An example is (16):

(16) COMP [Bill saw [who]s M and] > L | ~~[who likes Mary]s Js

*COMP[ [Bill saw | ]s l

and] WAO 14 like Mary]s (*I know a man who Bill saw and likes Mary.)

2.3. (17) [X a Y]Cand]

Example:

(18) COMP [John likes who]s and L[we hope [who will win]s ]s Js

(I know the man who John likes and we hope will win.)

Example (18) is an important case: on the basis of 2.1 and 2.2, one might say that ATB rule application requires various sorts of "parallelism" between the two conjuncts. This is true, but we are claiming that the relevant parallelism is that given by our definition of factor and nothing further.

Several kinds of "parallelism" are not observed in this example, and yet it is grammatical. To name a few: the conjuncts are split into different numbers of factors- a subject is removed from the second conjunct, but an object from the first; the removal site is final in one conjunct, but nonfinal in the other; the removal site in the second conjunct is contained in one more cyclic category than the removal site in the first conjunct; and the right conjunct brackets do not belong to the same factor.4

On the other hand, both conjuncts are split in (18) and the left conjunct brackets belong to the same factor, so (18) meets the definition of factor.

2.4. (19) *[ [a]c, ad1 [[[a]c X]Ca2 c

In this case, a whole conjunct is affected on top, but only part of the bottom conjunct is affected. The factorization in (19) is ruled out by (9) because the bottom

'This example is important for another reason: examples like (1) could be derived by an application of Right Node Raising (RNR) before Wh Movement without the ATB principle:

(i) COMP [[John saw who]s and [Bill hit who]s]s I RNR

COMP [[[John saw]s and [Bill hit]s]s who]s | Wh Movement

COMP [[[John saw]s and [Bill hit]s]s]s

who But (18) cannot be derived in this way since it would require RNRing who out of the subject position of

a tensed S, and RNR cannot perform this kind of operation. Thus this kind of derivation cannot be considered an alternative to ATB rule application.




conjunct is split, but the top one is not. ([cl and ]c belong to the same factor, but [c2 and ]c2 belong to different factors.)

This case can be illustrated by the rule of Wh Movement if the structural description of that rule gives an internal analysis to the moved constituent:5

(20) SD: COMP X [Y wh-word Z]x W

It is the factorization internal to the moved constituent that is responsible for the ungrammaticality of the following example:

(21) COMP you saw [|rwho]NP and] I[[whose]NP friends]NP J NP

1 2 3 4 (22) *John, who and whose friends you saw, is a fool.

It is factor 3 that is ill-formed in (21)-it contains both the left and right conjunct brackets of the top conjunct, but only the left conjunct bracket of the bottom conjunct.

The ungrammatical who and whose friends should be contrasted with the grammatical to whom and to whose friends:

(23) [[to whom]pp and1 [to whose friendsJpp pp X wh-word Y

Example (23) satisfies the definition of factor, so the following example is grammatical:

(24) John, to whom and to whose friends that letter was addressed, is a fool.

2.5. (25) [acI and]

The factorization shown here is permitted, since no conjuncts are split, though of course we do not find constituents of the form "/ and 0" where both conjuncts have been deleted or moved, and the and left behind; that is, we do not find such sentences as (26):

(26) *John was seen [ and] by Pete.

But (26) follows from the principle of recoverability of deletion to be defined in section 3, which would require that the deep structure of (26) be (27), which is itself ill- formed.

(27) *Pete saw John and John.

Hence, it is not necessary to change our definition of factor to exclude the factorization

5 For example, the version of Wh Movement given in Bresnan (1976). If one's rule of Wh Movement is simply "Move WH" then the following discussion applies to whatever rule there is, and there must be one, that factors the term moved by Wh Movement into "X wh-word Y".



36 EDWIN WILLIAMS

shown in (25); (26) will be excluded by a principle independent of the rules for factorization.

In fact, factorizations of the form (25) are needed anyway, for sentences like (28), whose deep structure must be factorized as in (29) for the application of Wh Movement:

(28) When and where did you see her? (29) COMP you saw her [[when] and1

[[where] J COMP X [wh-word YRx

2.6. An unrestricted rule of Conjunction Reduction, such as the one given in Chomsky (1957), is capable of deriving the ungrammatical sentences we have discussed in this section. For example, such a rule could derive the relative clause in (22) from (30):

(30) [s[s who you saw] and [whose friends you saw]flg

Such cases, for which the ATB principle makes the correct predictions, suggest that the unrestricted Conjunction Reduction be replaced by the ATB principle and a highly restricted rule of Conjunction Reduction. Such a highly restricted rule will be given in section 4.

3. Recoverability and "is a"

In this section, I will extend the definitions of Recoverability of Deletions (ROD) and the "is a" relation to cover cases of ATB rule application. It will be seen that the Coordinate Structure Constraint (CSC) follows from these extensions.

(31) Recoverability of Deletions (ROD) If T is a term moved or deleted by a transformation, and T consists of simultaneous factors F1 . . . F, then it must be the case that F1 = . . . = Fn.

(31) says that if a set of simultaneous factors is deleted, they must be identical. For example, ROD prevents Wh Movement from applying to the following structure,

(32) COMP [[Bill saw who]s and [[Pete ate what]s s

1 2 3 4

because the two factors composing factor 3 are not identical (with respect to (31), T =

factor 3, F1 = who]s, F2 = what]s).

(33) "is a" If F is a factor consisting of simultaneous factors F1 . . . Fn, then F "is a" X if F, "is a" X and ....... and Fn "is a" X.

For example, in (32), factor 3 "is a" WH term, because who]s "is a" WH term and what]s "is a" WH term.

Now consider a typical example explained by the CSC:




(34) *Who did John see and Bill hit Mary.

The deep structure of (34) in ATB format is (35):

(35) COMP [[John saw who]s and] [[Bill hit Mary]s is

There is no way to factor (35) to meet the "is a" relations required by Wh Movement. For example, if it is factored as in (36a), factor 3 does not satisfy "is a WH term" (because the bottom factor of 3 does not). If it is factored as in (36b), factor 3 again does not satisfy "is a WH term", since the bottom factor of 3, the identity element, does not satisfy "is a WH term".

(36) a. COMP [[John saw who]s and [[Bill hit Mary]s s

1 2 3 4

b. COMP [John saw who]s and [[Bill hit Mary]s Is

1 2 3 4

Hence (34) cannot be generated, independent of the Coordinate Structure Con- straint. In general, the extensions of ROD and "is a" given in (31) and (33) make the CSC entirely superfluous.

(31) and (33) permit all of the good derivations we discussed in section 2. For ROD permits the derivation of (37), even though when - where.

(37) When and where did he see her?

To see why, consider the deep structure of (37) in ATB format and factored for Wh Movement:

(38) COMP he saw her [[when] and]

1 2 3 4

If 3 were the moved term, ROD would be violated, since it contains two nonidentical simultaneous factors. But the moved term is 3-4, and 3-4 is not composed of simultaneous factors (that is, it is simple), since 3-4 contains the entire coordinate structure.

4. Coordination We will now turn our attention to rules that concern coordination directly.

4.1. To begin with, I propose that there are base rules of the form (39) for every category of the base.

(39) X -- X and X



38 EDWIN WILLIAMS

Even with such base rules, there is need for a rule of Conjunction Reduction,6 because there are surface coordinated strings that are not constituents. For example, in (40) the books to Mary and the records to Sue are not constituents.

(40) John gave the books to Mary and the records to Sue.

To generate such examples, we need a rule that will delete John gave from the second conjunct of the deep structure:

(41) John gave the books to Mary and John gave the records to Sue.

We might formulate the rule as follows:7

(42) [X Y]s and [X Y']s => [X Y]s and [4 Y']s

But this rule can perform illicit derivations. Consider the following examples:

(43) John has more cows than Bill has dogs and John has more cows than Pete wants to have

*John has more cows than Bill has dogs and/or Pete wants to have.

To bar such derivations, we must prevent CR from eating into Ss. To do this, we will prevent CR from applying to strings factorized in the following way:

(44) . .. [s . .. I* .. *]s * *

This implies that the domain of CR will always be conjoined Ss, not conjoined Ss. Hence this constraint will block the derivation of (1) from (2).

There are grammatical sentences akin to (43), with deletions in two coordinated Ss in a than clause:

(45) John has more cows than Bill has dogs or Pete has horses. (46) John has more cows than Bill has or Pete wants to have.

However, these can be derived by an ATB application of Comparative Deletion8 to

6In addition, rules for Right Node Raising and Gapping will be needed, but these rules will be ignored here.

'This rule, unlike the rule of Conjunction Reduction in Chomsky (1957), does not create new derived coordinated phrases. We have formulated this rule as a deletion rule; it could as easily be a rule of interpretation.

8 See Bresnan (1976) for the formulation of Comparative Deletion implicit in this discussion.




deep structures with conjoined Ss in the than clause:

(47) John has more cows than [[Bill has QP dogs]s or1 [[Pete has QP horses]s is

(48) John has more cows than [[Bill has NP]s 1 [[Pete wants to have NP]s orjs

Thus such examples provide no evidence for an unrestricted rule of CR. In addition, ROD prevents any ATB application of Comparative Deletion that would derive the ungrammatical (43):

(49) (= 43) John has I more cows than [[Bill has QP dogs]s 1 L[Pete wants to have NP]s orIs

Since NP : QP, ROD blocks this derivation. (In addition, it is impossible to uniquely factorize the matrix so as to provide an antecedent for both the deleted NP and QP.) Thus we have evidence for restricting CR by (44), and for claiming that (45) and (46) are uniquely derived by ATB applications of Comparative Deletion to deep structures with conjoined Ss in the than clause.

4.2. Now we will show that CR can be greatly simplified if it applies to Ss in ATB format and, finally, that it must apply to structures in ATB format.

4.2x1. If CR applies to structures in ATB format, we may write it thus:

(50) CR SD: [s X Y]s and SC: X2 ... X, k, where X is composed of simultaneous factors

X1 ... Xn.

For example, if CR applies to (51), we derive (52):

(51) [[John saw Bill] and [John saw Mary]

X Y and (52) [[John saw Bill]s and

[ saw Mary]s X Y and

where the X2 position is occupied by 4.

4.2.2. It is possible to show that CR must apply to Ss in ATB format. The deletion of the X2 ... Xn, simultaneous factors is subject to ROD, which says here that X1 = ...



40 EDWIN WILLIAMS

= X,. However, in cases of conjunction embedded in conjunction, each of X1... X" is itself composed of simultaneous factors, and ROD must be satisfied by identity of these sets of simultaneous factors. Consider (53):

(53) s

/ o~~~~r

and and

S2 S4 S6 S8

John gave the John gave the John gave the John gave the book to Mary record to Sue book to Sue record to Mary

CR can apply on S, and S3, giving (54), where material is deleted from S4 and S8.

(54) John gave the book to Mary and the record to Sue or John gave the book to Sue and the record to Mary.

But further reduction is possible: John gave in S6 can be deleted:

(55) John gave the book to Mary and the record to Sue, or the book to Sue and the record to Mary.

The important question is, what is the antecedent for the deletion of material in S6? One might first suppose that it is material in S2 or S4; however, if the corresponding material in S2 is different from the corresponding material in S4, then no deletion is possible in

(56) * [[John gave the book to Mary]s2 and1 [[he handed the record to Sue]s4 1slor

the book to Sue]s6 and 1 the record to Mary]s8 iS3

This example shows that the proper generalization is that material in S6 can be deleted only when it is identical to corresponding material in S2 and S4. This generalization follows from the ATB theory of rule application. To see why, consider




(53) in ATB format, factored for application of CR on the matrix level:

(57) [[John gave the book to Mary]s2 and1 L[ b the record to Sue]S4 S or

[ [John gave the book to Sue]s56 and L [? k the record to Mary]s8 iS3

X1

X= Y

X2

In this diagram, reduction has already taken place on the S1 and S3 cycles, giving Os in S4 and S8. The X factor consists of two simultaneous factors, X1 and X2, which themselves are sets of simultaneous factors:

(58) X = [[John gave

= [John gave 2 [ 0 0

Since X1 = X2, X2 can be deleted by CR, giving (59):

(59) [John gave the book to Mary] and1 k the record to Sue] - SI or

[ 4+ P the book to Sue] and the record to Mary] _ S3

Now consider a pair of possible underlying structures for the ungrammatical (56):

(60) [ [John gave the book to Mary]S2 and [ [John handed the record to Sue]s4 isi or

ohn gave the record to Sue]s6 a. [ + ?' and b. [John handed the book to Mary]s8 J S3

x Y

Here, X2 has two possibilities:

(61) X [[Johngave L[John handed

=2 a. [[John gave

b. [John gave [[John handed

We will consider the two cases (a) and (b) for (60) and (61) in turn. If X2 is (61a), no reduction can take place because X1 i X2. If X2 is (61b), then X1 = X2, but X2 cannot be deleted, because X2 itself is



42 EDWIN WILLIAMS

composed of distinct simultaneous factors, and ROD prevents the deletion of distinct simultaneous factors.9

5. Linearization

Obviously sentences are not spoken in "ATB format"-that is, with conjuncts uttered simultaneously. Thus, there must be a rule that linearizes coordinate structures in surface structure. Such a rule might be as shown in (62):

(62) [X 1 .and --[X, (and) . .. and X.]

Xn

6. Summary

I have made the following proposals: that deep structures be generated in ATB format, as defined by (8); that transformations apply to structures factored according to (9); that transformations are governed by the extensions of the definitions of "is a" and ROD given in (31) and (33); that there is a universal rule of Conjunction Reduction, as given in (50); that this rule is constrained by (44); and that there is a universal rule (62) that linearizes coordinate structures in surface structure.

These proposals describe the data better than the unrestricted versions of CR and the Coordinate Structure Constraint and therefore are intended to replace them.

The proposals made here are more complex, in an intuitive sense, than the unrestricted CR and CSC. But since both sets of proposals are intended to be completely universal, considerations of explanatory adequacy cannot be invoked to choose between the two; being universal, they are equally explanatory, by definition.

References

Bresnan, J. (1976) "On the Form and Functioning of Transformations," Linguistic Inquiry 7, 3-40.

Chomsky, N. (1957) Syntactic Structures, Mouton, The Hague. Peters, S., and R. Ritchie (1973) "On the Generative Power of Transformational Grammars,"

Information Sciences 6, 49-83.

9 One might object here-why doesn't ROD prevent the deletion of X2 in (57), since X2 is composed of simultaneous factors, X21 and X22, which are not*symbol-for-symbol identical:

(i) X21 = [John gave X2, = I 0 0

This is a valid objection, since we have not defined the "Equality" referred to by ROD. Clearly we must define it in such a way that X = Y if X controls Y via a rule of deletion or interpretation. In example (57), X2 controls X22 via CR; but in (61b) this is not the case.




Ross, J. (1967) Constraints on Variables in Syntax, Indiana University Linguistics Club, Bloomington.

Department of Linguistics South College University of Massachusetts at Amherst Amherst, Massachusetts 01003



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Across-the-Board Rule Application