D iscourse Parallel i sm, S c op e , and Ell i ps i s
Nicholas Asher
University of Texas at A ustin
D aniel H ardt
Villanova University
Joan Busquets
IRIT/ UniversitE P. Sabatier
1
Introduction
It has frequently been observed that structural ambigui ty does not multiply
in contexts i nvolving ellipsis: ! that is, if there is an ambigui ty associated with
the antecedent of an ellipsis occurrence, that ambiguity must be resolved in
the same way in both the antecedent and at the ellipsis site. The following
example ( D alrymple et aI . , 1 99 1 ) i llustrates this wit h a case of quantifier scope
ambiguity:
(1)
John gave every student a tes t , and B i l l d i d too.
The antecedent clause allows two read ings, depending upon whether a test
or every student receives wide scope. However, if a t est receives wide scope in
the antecedent , it must also receive wide scope at the ellipsis site; conversely,
if e very student receives wide scope in the antecedent, it must receive wide
scope at the ellipsis site as well.
Many accounts of ellipsis attempt t o account for t h i s observation in terms
of the ellipsis recovery mechanism. However, simi l ar effects are observed in
cases that do not i nvolve ellipsis, where the ellipsis recovery mechani sm cannot
apply, as i n the following vari ant of ( 1 ) :
(2)
John gave every student a tes t , and Bil l gave every student a project .
To exp l ain these facts, we will defi n e a general parallelism constra,int on
related sentences i n a di scourse. This makes i t possible to define an extremely
simple recovery mechanism for ellipsis - an exact identi ty condition in which
the recovered material and the antecedent are interpreted i ndependently i n
their respecti ve contexts, subject only to t h e general discou rse constraints on
paTalielism . Furthermore, this approach m akes it possible to gi ve a uniform
account for paralleli sm facts , whether or not there i s ellipsi s . In addition , our
account explains the wide scope puzzle ( S ag , 1 976 ) , illustrated by the following
example:
(3)
A nurse saw every patient . Dr. Smith d i d too.
© 1 997 b y N i c h o l as Asher, Dan i e l H ardt a n d J o a n B u squets
SALT VII, 1 9- 3 6 , Ithaca, NY: Corne l l Uni versity.
Aaron Lawson (ed),
20
ASHER, HARDT AND BUSQUETS
As observed by Sag, "a nurse" must take wide scope.
In what follows , we first consider the recovery mechanism for V P ellip­
sis. Next , we describe the basic parallelism constraints on related sentences in
discourse, using the Segmented D iscourse Representation Theory ( S D RT ) of
( Asher, 1 993 ) . We show how these constraints capture well-known fact s about
scope parallelism in ellipsis , and we show how our account captures similar
facts about parallel scope not i nvolving ellipsi s . 2 Next we show how our ap­
proach accounts for the wide scope puzzle. We then consider related work ,
and discuss certain extensions t o our approach .
2
VP Ellipsis Recovery Condition
In our view , facts about parallel i nterpretation in ellipsis contexts reflect gen­
eral constraints on related sentences in a discourse, rather than constraints on
the specific mechanism for resolving ellipsi s . This suggests t h at the ellipsis
recovery mechanism i s much simpler than is generally supposed . 'We propose
that the recovery mechan i sm is a simple identity of structure, in which the re­
covered material is interpreted i ndependently of the antecedent , subject only
to general discourse parallelism conditions that apply to all related sentences.
This i dentity condition could be defined at a variety of levels of repre­
sentation . The argument of this paper would be consistent with an i dentity
condition defined at Surface Structure ( SS ) , Logical Form ( LF ) , or at the level
of Discourse Represent ation Structure ( D RS ) . For concreteness, we describe
two possible i dentity conditions, at L F and DRS.
2. 1
LF
Recove7'Y Con dition
We assume that the L F representations are deri ved from S S representations by
means of applications of a Quantifier Raising ( QR) operation ( as defined , for
example, i n ( M ay, 1 9 77 ) ) , which optionally adj oins quantified N P 's to S nodes .
To implement our VPE recovery condition at L F , we propose an operation VP­
copy, which can copy a V P to an empty V P node. We i mpose n o ordering on
QR and Vp-copy 3 .
Consi der the foll owing example:
(4)
A
nurse saw every patient . A doctor did too
[[A nurse] [past [ see [every patient]l l l [[A doctor] did [] too] .
The application of VP-copy resul t s i n
[[A nurse] [past [see [every patient] l l l [ [A doctor] d i d [see [every patient]] too]
The application of QR in each clause results i ll one possi ble reading:
[ [every patient] [[A nurse] [past [see [e lllll
[[every patient] [[A doctor1 [past [see [e llll]
21
DISCOURSE PARALLELISM, SCOPE, AND ELLIPSIS
In fact , our recovery condition would permit four possible readings here.
A s we will see in section 4 , the non-parallel scopings are ruled out by the
general discourse parallelism constraint .
2. 2
DRS Recovery Condition
A similar effect can be obtained with a semantic recovery condition , in which
V P E recovery and scope determination are freely ordered. 4 We describ e a
recovery condition at the DRS level. To permit wide scope object readings
i n the DRS construction process, we permit type raising, to allow a certain
flexibility in the order i n which constituents are combined . We consider agai n
example ( 4 ) . The normal representation of the V P saw every patient would
be:5
X
Au
*
p a t i en t ( x )
L-_ _
_____--,
§
The subject a nUl·se i s represented
AP
y
nurse(y)
P(y)
Application o f t h e subject to t h e VP results in a narrow scope for the obj ect :
y
nurse(y)
x
::::}
patien t ( x )
see (y,x )
An optional type raising rule gives the fol lowing representation for t h e
X
A 7r
p a tI. e nt ( x )
*
rr
( Au
§
VP:
J
L...-______--,
Application of this VP representation to t h e subject results i n a w i de scope
reading for the object :
ASHER, HARDT AND BUSQUETS
22
y
x
patient ( x )
�
nurse(y)
see(y,x)
Thus, we simply copy the VP representation constructed during the normal
application of the DRS construction process . We allow a type raising operation
as a way of obtai ning wide scope object readings , and this type raising of VP
representations can be interleaved with the VPE recovery operation.
For the p urposes of this paper, either the LF or D RS recovery mechanism
woul d be acceptable. We now turn to the basic discourse constraint that
determines preferences among the various scopings permitted by our VPE
recovery mechanism.
3
S D RT and the Maximization Const raint
Segmented Discourse Representation Theory ( S D RT ) , ( Asher, 1 993; Lascarides
and Asher, 1 993) extends Kamp's DRT ( K am p , 1 980) by adding a m ore com­
plex account of discourse structure. The constituents of d iscourse structure
are segmented DRSs or S D RSs. These S D RSs are defined recursively out of
D RS s and discourse relations, which are taken to be binary relations between
propositions.
In resolv i ng scope ambiguity, we claim that there i s a preference to produce
the Maximal Common Theme (MCT) of related discourse constituents. This
is a modified version of the Maximization Constraint of ( A sher, 1 99 3 ) .6 We
now define M aximal Common Theme i n terms of operations for eliminating or
generali z i ng information in a DRS.
•
Operations
We define four operations to eliminate or general ize information
DRS:
I II
a
1. Delete a n atomi c condition
2. Generalize an atomic condition ( i . e . , replace a rel ation R with a
relation R' where the denotation of R is a subset of the denotation
of R'· f
3 . Systematically rename a bound discourse marker
4. Delete a discourse marker
We say that K "" K' iff K' is constructed from
cations of rules 1 - 4 .
K
by (0 or more) appli­
23
DISCOURSE PARALLELIS M , SCOPE , AND ELLIPSIS
•
•
•
Theme: if K
�
K',
then we say that K' is a theme of
K.
Maximal Common Th eme (M CT) : given two D RS ' s K , J the M C T i s the
D RS T such that K � T and J � T , and for any other T' such that K
� T' and J � T', T � T'.
Maximization Constraint: i n resolving a scope ambiguity within a pair
of related discourse constituents , prefer the choice that produces the
maximal MCT.
In the next section , we see how our constraint applies to the basic parallel
scope examples.
3. 1
Parallel Scope Exa mples
Consider example ( 1 ) , repeated here:
John gave every student a test , and Bill d i d too.
(5)
We consider a parallel readi ng, in which a student t akes wide scope in both
conj uncts, and a non-parallel reading, in which a student t akes w i de scope i n
the first conj unct and narrow scope in the second .
Parallel reading:
u
u
bill ( u )
john ( u )
x
student ( x )
�
y
x
test ( y )
gi ve ( u , x , y )
student ( x )
This produces the following m aximal com mon t heme, T 1 :
u
x
st ude n t ( x )
y
test ( y )
gi ve( u , x , y )
y
�
tes t ( y )
gi ve (u,x , y )
24
ASHER, HARDT AND BUSQUETS
Non-parallel reading:
u ,y
u
john ( u )
test (y)
x
student ( x )
bill ( u )
y
x
=}
student ( x )
give ( u , x ,y )
T h i s produces t h e following maximal common theme,
=}
test ( y )
give( u , x , y )
T2:
u
x
student ( x )
=}
gi ve( u , x , y )
S i n ce TJ "-> T2 , t h e parallel reading is preferred over t h e non-parallel read­
ing. Similar reasoning will apply to the other pai r of parallel and non-parallel
readi ngs .
Consider now ( 2) , repeated here:
John gave every student a test, and B i l l gave every student a proj ect .
(6)
Parallel reading:
u
u
bill( u )
john ( u )
y
x
student ( x )
=}
test ( y )
give ( u ,x , y )
y
x
student ( x )
T h i s produces t h e following maximal common theme, T 1 :
=}
proj ect ( y )
gi ve( u ,x , y )
25
DISCOURSE PARALLELISM , SCOPE, AND ELLIPSIS
u
x
student ( x )
y
=?
give ( u , x ,y )
Non-parallel reading:
u,y
u
bi l l ( u )
john ( u )
test ( y )
x
y
x
=?
student ( x )
student ( x )
give( u,x,y)
=?
proj ect ( y )
give( u , x , y )
T h i s produces t h e following maximal common theme, T 2 :
u
x
student ( x )
Agai n , we h ave
Tl
"->
=?
gi ve ( u , x ,y)
T2 •
Our account woul d apply i n a simi lar way to the following examples , w h i ch
exhibit the same preference for parallel scopi ng:
( 7)
a. John gave every student a proj ect , and Bill gave every student an
assignment , too.
b . J ohn gave every linguistics student a project , and Bill gave every
phi losophy stu dent a test.
AS HER HARDT AND BUSQUETS
,
26
4
Wide-scope Puzzle
We now examine the wide-scope puzzle first observed by ( Sag, 1 976) , i llus­
t rated by (3), which is repeated here:
A nurse saw every patient . Dr. S m i t h d i d too.
(3)
S ag observed that , while the first sentence in i solation would have the
expected two possible readings , i n which a nurse can take either wide or n arrow
scope, ( 3 ) only permits one reading, in which a nurse must t ake wide scope.
We now show that this i s a consequence of our A1aximization Constraint.
There are two p otenti al readings for ( 3 ) :
x
x
smi t h ( x )
u
nurse ( x )
u
*
patient ( u )
see(x,u)
�
patient ( u )
�
x
smith ( x )
x
u
nurse(x)
see(x,u)
patient ( u )
:
p a t ie t ( u )
,--_______---,
�
�
The Maxim al Common Themes for these two readi ngs are :
x
u
patient ( u )
u
*
see(x,u)
p at i en t ( u )
,--_______�
Since
Tl
"-+
T2 , the wide scope for a nurse i s preferred .
*
�
�
DISCOURSE PARALLELISM , SCOPE, AND ELLIPSIS
5
5. 1
Related Work
Related A pproaches
There are many ellipsis accounts (eg, ( Sag, 1 976; Williams, 1 977; D alrymple
et aI . , 1 99 1 ; Fiengo and May, 1 994 ) ) that capture certain scope parallelism
effects that occur in ellipsis contexts. However, as we h ave argued above,
t hese accounts do not apply to similar effects where ellipsis does not occur.
Also, none of these approaches successfully account for the wide scope puzzle.
There are also discourse accounts, such as that of ( Prust et al , 1 987) , which
are similar i n spirit to ours . But i t is not clear how an approach like Prust 's
would apply to the data examined i n this paper. In particular, i t does not
apply to the wide scope puzzle.
However, the approach of ( Fox, 1 995) , does provides an account of the
wide-scope puzzle and other data we have consi dered above, and we now turn
to an examination of this approach . In this account , a general parallelism
constraint ( Root h , 1 992; Fiengo and May, 1 994 ) 8 ) together with an economy
constraint on Scope Shift i ng Operations captures scope effects, i ncluding the
wide-scope puzzle.
Consider example (3) again :
(3)
A nurse saw every patient . D r . Smith d i d too.
Fox presents the following ellipsis scope generalization ( ES G ) :
the relati ve scope of two quantifiers . . . may differ from t h e sur­
face c-command relation only if the parallel difference w i l l h ave
semantic effects in the elided VP.
By the ES G , every patient cannot QR over a nurse because it wou ld not
have a semantic effect for every patient to Q R over Dr Smith. In Fox's theory,
ESG is a consequence of p arallelism plus "economy" , which prohibits an ap­
plication of QR ( and related operations) if it does not h ave a semantic effect .
There are two fundamental differences between Fox 's approach and ours, the
first theoretical , and the second empirical .
We consider first the theoreti cal difference. I n our approach , the wide-scope
puzzle is captured by the parallelism theory - we don 't need to appeal to econ­
omy as well . The fact that we are applying parallelism to D R S ' s ensures that
n o quantifier can outscope a name, because i n D RT discourse referents and
conditions introduced by n ames must occur i n the top level D RS ( see ( K amp
and Reyle, 1 99 3 ) for detai ls ) . 9 For Fox , the i nabi l i ty of a quantifier to outscope
a n ame in subj ect position is a consequence of economy, which doesn 't permit
an operation to apply unless it has a semantic effect . The D RT processing
constraint on n ames might be construed as a principle of economy in some
sense, since i t eliminates certain spurious ambiguities. But the economy prin­
ciple employed by Fox i s quite different from this. We draw attention to two
crucial differences . First, Fox 's constraint i n corporates a version of the " H ave
27
ASHER , HARDT AND BUSQUETS
28
an Effect on Output Condition" constraint into the derivation system , which
introduces major conceptual and computational compli cations (see (Johnson
and Lappin, 1 997) for discussion) . Second , Fox's approach complicates the
syntax/semantics i nterface, since i t requires i nformation about possible read­
i ngs i n determining the applicability of a syntacti c operation . The D RT rule
for representing names does not i nvolve any of these complications.
We now turn to empirical differences. In our approach , the w ide-scope
puzzle reflects a parallelism in representation between names and wide scope
existential quantifi ers. For Fox , the effect is much more general and leads to
empirical differences . In the following examples , Fox predicts a required wide
scope subject reading, while our approach permits both readings:
(8)
A nurse saw every patient . Every doctor did too.
(9)
Every student read a book and Harry d i d too.
We would argue that the wide-scope effect i s not present here; the n arrow
scope object reading is permitted . This is parti cularly clear i n ( 9 ) , where we
find that the reading in which a book takes wide scope over e very student is
perfectly acceptable.
Conversely, our approach enforces the wide-scope subject preference i n the
following example, while Fox does not :
( 1 0)
Dr. Smith saw every patient . A nurse did too.
Here, every patient can take wide scope over a nurse. (p. 334, ex 79) . Our
approach applies symmetrically, treating this example j ust like ( 3 ) .
5. 2
Problematic Examples
Several researchers have called into question the reality of the "wide- scope
puzzle" . (Johnson and Lappin , 1 997) present the folllowing apparently prob­
lemati c examples:
(11)
At lea. s t one Labour M P attended most committee meetings, an d
Bill did too .
( 1 2)
At least one natural number other than one divides i nto every prime
number, and one does too.
( 13)
At least two cabinet members bear responsi bi lity for each govern­
ment department, and the Prime Minister does too.
( J ohnson and Lappi n , 1 99 7 ) observe that the subject N P ' s i n these sen­
tences can take narrow scope, despite the occurrence of a n ame in p arallel
position in the second sentence l O . While these are delicate j udgements, we
concur that the wide- scope effect does not appear to be present in these cases .
DISCOURSE PARALLELISM , SCOPE , AND ELLIPSIS
Our account imposes a preference ordering on possible D RS representa­
tions . If the preferred representation conflicts with general knowledge or ex­
pectations , it may b e rej ected in favor of some other representation . This
provides a reasonable explanation for ( 1 2 ) , since the wide scope reading con­
flicts with general knowledge about numbers. However, i t i s not clear to us
that the wide scope readi ngs for examples ( 1 1 ) and ( 1 3 ) , conflict with general
knowledge ( at least for American English speakers) . Consequent ly, we will
explore the possi bility that a structural effect accounts for the absence of the
wide scope reading i n these cases .
We will examine the following variant of example ( 1 3) : 1 1
( 1 4)
At least two cabinet members bear responsibility for each govern­
ment department , and Prime Minister Major does too.
The N P at least two cabin e t m embers introduces a plural discourse referent.
The most natural reading i s a distri butive one - each of the cabinet members
mentioned bears responsibility for each departmen t , rather than the respon­
sibility being a collecti ve one. Thus, fol lowing ( Kamp and Reyle, 1 993 , page
327 ) , we i ntroduce a duplex condition, or quantificational structure, represent­
ing the distribution.
Thus we have the following representations for the two readi ngs of ( 1 4 ) :
Reading
1:
x
card ( X ) 2: 2, cabi net-members( X )
u
department ( u )
=?
responsible-for ( x , u )
p
mr-rnajor(p)
u
department { u )
res poTisi ble-for( p , u )
29
30
ASHER. HARDT AND BUSQUETS
Reading
2:
x
p
mr-maj or ( p )
u
department ( u )
=>
responsi ble-for( p , u )
On ei ther reading, t h e two sentences do n o t share t h e same nesting struc­
ture. Thus, no Maximal Common Theme can be constructed, and our ap­
proach does not impose a scope preference. For ( 1 2 ) and ( 1 1 ) , we would give
similar representations, based on the idea t hat any N P of the form at least
N can be represented as a plural discourse referent with a quantificational
structure representing a distributive reading. 1 2
While the j udgements are delicate, we find that the wide-scope effect reap­
pears in example ( 1 3 ) if the determiner "at least two" is replaced by a simple
i ndefinite "a" , and we find a similar effect with ( 1 1 ) . However, a replacement
i n example ( 1 2 ) , does not reinstate the wide-scope effect s . This supports our
view that ( 1 1 ) and ( 1 3 ) exhibit a structural effect , while ( 1 2) must be explained
i n terms of knowledge about numbers .
6
Ext ending the Approach
In this section , we discuss some extensions to the approach , both to "loosen"
the constrai nts on parallelism in certai n ways, and t o capture similar effects
i n embedded contexts.
DISCOURSE PARALLELISM, SCOPE, AND ELLIPSIS
6. 1
Loosening th e Parallelism Constraint
In the account described so far, scope parallelism effects are captured i n exam­
ples where the related D RS ' s have the same nesting structure, and i dentical
parallel quantifiers. In this section , we suggest some ways in which we envision
"loosening" our account to capture some parallelism effects with n on-i dentical
quantifiers and differences in nesting structure.
The following example invol ves different quantifiers in parallel p ositions:
(15)
John gave every student a test. Bill gave most students a project .
In our view , the relati ve scope between a test and e very student will be the
same as the relative scope between a project and most students. To capt ure
this, we envision add i ng an operation like the following:
Replace a quanti fier Q with a quantifier Q' where either both Q
and Q' are monotone increasing in their second arguments or both
Q and Q' are non-monotone increasing i n their second arguments
This makes i t possible to replace ever'y with most i n the above example.
The following example i l lustrates a difference i n nesting structure:
( 16)
A nurse saw every patient, b u t D r . Smith didn 't.
The negation i n the second clause introduces an additional level of nest­
ing, making i t impossi ble to enforce paral lel scoping effects. To capt.ure this,
we propose to ignore negation for the purpose of determining M C T . More
generally, we will explore an extension of our approach i n which we allow de­
termi n ation of M C T t.o proceed with respect to Modified Embedding Trees
( A sher, 1 993) , i n which some levels of embedding can b e "collapsed" .
6. 2
Embedded Reading;;
In al l the examples we h ave considered , the t wo related discourse consti t uents
are at the top level of the D RS . The situation becomes more complicated if
the related constit uents are embedded . Consider the following example:
( 1 7)
If the sorority has a party, a m an will kiss every girl at the party
and B i ll will too.
We believe the same effect occurs here - because of the parallelism of Bill and
a man, there is a strong preference for a man to take wide scope w it h respect
to every girl.
A s currently formu l ated , our approach would not capt ure the scope par­
allelism effects in embedded contexts. However, a simple modification of the
approach will accomodate t h i s . The related DRS's w i l l contain a list of all ac­
cessible discourse markers . For a DRS occurring on the top- level , that is j ust
31
ASHE � , HARDT A N D BUSQUETS
32
t hose discourse markers introduced i n that DRS. However, i n an embedded
D R S , this will expand the list of discourse markers P Consider our represen­
t ation of ( 1 7 ) :
Parallel Reading:
s,b
bill (b) ,sorority( s )
f-
__________
_
v
man ( v )
party( s )
( =) �
I � . I }�
g; , ( V )
k'
==
Here, w e h ave two related D RS boxes constituting t h e consequent o f the
conditional , representing, respectively, A man will kiss every girl and Bill will
kiss every girl. Although the discourse marker b fOf Bill is i ntroduced at the
top level , i n terms of a U f parallelism determination i t also appears on the
d iscourse marker list of the embedded DRS's. Thus we represent t h e related
constituents as follows:
s,b,v
s,b,v
man ( v )
I� I
g; , ( y )
y
girl (y)
_
kiss(v,y)
--'
� , ----'---'-"--'-
kiss ( b , y )
T h e following represents t h e "rCT constfucted for t.hese t. w o const i tuent.s1 4 :
Parallel Reading ivleT:
s,v
DISCOURSE PARALLELISM, SCOPE, AND ELLIPSIS
Consider now the non-parallel reading, where a man takes n arrow scope
with respect to every girl:
Non-Parallel Reading:
s,b
�-------------------,
bill ( b ) ,sorority( s)
v
man ( v ) ,kiss( v ,y)
Non-parallel Reading
s
H
��
kiss(b,y)
!'vI eT:
kiss( v,y)
In this case, the discourse marker v ( representing the "kisser" ) d oes not
appear at the top level , as i t does in t h e M C T for the parallel reading. Since
the Parallel MCT '"'-* the Non- Parallel M C T , the preference is account.ed for .
7
vVe
C onclusions
have defined a general mechanism for imposing a preference for para.\­
lel structure in related di scourse constituents, using the S D R'T framework.
We have shown that this captures parallel scope effects both i n elli psis an d
non-ellipsis contexts. In addition , because of the D RT t.reatment of names ,
our pa.rallelism mechanism also captures puz;ding effects involving wide scope
readi ngs.
33
ASHER , HARDT AND BUSQUETS
34
Endnotes
0 * The second author would like to acknowledge support by a National Science
Foundation C A REER grant , IRI-95022.57.
l This observation figures prominently i n most of the ellipsis l iterature, going
back at least to ( Sag, 1 976) , and ( Williams, 1 977) .
2 ( Tancredi , 1 992) also observes that similar interpretive effects arise whether
or not elli psis is present , and attempts to define a. mechanism general enough
to account for this. However, Tancredi does not examine i ssues of scope par­
allelism, but rather looks at the strict /sloppy alternation.
3 ( K i t agawa, 1 99 1 ) describes a V P copy operation which can precede i n dexation ,
although he does not discuss scope determinat ion . Also, ( Fox, 1 995) observes
that QR and the VP-copy operation could be freely ordered at L F .
4 0ne example o f such a n account i s that i n ( Lappi n , 1 984) . In that accoun t ,
a Cooper storage mechanism i s used to obtain wide-scope readings. Thus,
the recovered material for VP ellipsis i s a pair consisting of VP m atrix and
quantifier store. A quantifier can thus be discharged from store either before
or after being recovered at the ellipsis site.
5 We represent DRS's using the lambda operator together with the ordin ary
"box" notation of D RT . This makes it possible to describe a straightforward
compositional DRS construction algorithm. See ( Musken s , 1 996) or ( A sher,
1 993) for discussion.
6 ( Prust et al , 1 987) define a mechanism for computing the most specific com­
mon denominator ( M S C D ) of related discourse utterances . This i s in much
the same spirit as our Maximal Common Theme. However, Prust et al do not
attempt to account for the sort of phenomena discussed in this paper.
71n fact , this operation i s not needed to capture the facts considered in this
paper. \Ve leave as a topic of fut u re research the question of whether a gener­
alization operation is relevant to determination of parallelism effects.
8 ( Rooth, 1 992) and ( Tancredi , 1 992) define constraints to the effect that two
related clauses are identi cal modulo the focused elements. This i s used as a
constraint on possible readi ngs i n V P E .
9 ( M uskens, 1 996) has obj ected that t h e D RT cOllstmction rule for Ilames m akes
a composi tional approach d i ffi cu l t . While t h i s i s true for the approach of
(Kamp and Reyle, 1 99:3 ) , we feel there are a variety of ways to address this
issue, such as an approach Il sing underspecified conditions like that of ( Reyle,
1 993) . Indeed , our argument concerni ng the wide-scope puzzle could be viewed
as providing additional support for the D RT const ruction rule for names .
35
DISCOURSE PARALLELISM, SCOPE, AND ELLIPSIS
I O ( Fox , 1 995) argues that ( 1 1 ) permits ambiguity because of an existential quan­
t i fication over an event variable. However, this explanation will not apply to
( 1 2) and ( 1 3 ) , where there i s no event variable. See ( Johnson and L ap p i n ,
1997) for further discussi on .
l l vVe replace the definite description th e Prime Min ister with a name, Prim e
Minister Major, si nce, in our approach, a definite description may appear
either with wide or narrow scope, although in this example the narrow scop e
reading would be equivalent to the wide scope reading.
1 2 This is consistent with the view i n ( Szabolsci , 1 997) that quanitifiers i nvolving
a modified numeral are distinct from ordinary indefinites. We also represent
at least one as a duplex struct ure in our analysis of ( 1 1 ) . a t least o n e appears
to have two readings , a quantificational one ( Hans Kamp , p . c . ) , and a specific
indefinite reading that appears to arise only when a singular pronoun has an
N P containing at least o n e as an antecedent . The latter reading i s not relevant
to our examples .
13The reader is invited to verify that this modification of D RSs does not alter
any of the earlier predictions we have made.
1 4 A s the reader can verify, t h i s was constructed by applying the following oper­
ations: (to the first consti tuent ) delete m a n (v) , dele t e disco urs e marker b ; ( t o
t h e second consti t uent) dele t e discourse m a rker v , rename b as v.
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