PRESUPPOSITION & VP-ELLIPSIS* 
Johan Bos 
(bos@col i. uni-sb, de) 
Universitgt des Saarlandes, Computerlinguistik 
Postfach 1150, D-66041 Saarbrficken, Germany 
Abstract 
We discuss a treatment of VP-ellipsis resolution 
in DRT in general, and particularly cases where 
the source clause of the elliptical VP contains 
presupposition triggers. We propose to restrain 
VP-elfipsis resolution by presupposition neutrali- 
zation. We view presupposition as a kind of ana- 
phora, with the ability to accommodate an ante- 
cedent if not provided by discourse. 
1 Introduction 
In this paper we discuss the treatment of VP- 
ellipsis resolution in general, and particularly its 
interaction with presupposition. We share the opi= 
nion of those who argue that ellipsis resolution 
should take place at a semantic level \[Dalrymple 
et al., 1991; Kehler, 1993; Sere, 1993\]. We will 
provide a framework in which ellipsis resolution 
is constrained by presupposition projection, and 
furthermore, anaphora and presupposition are re- 
presented underspecified in the semantics. 
The latter postulation is necessary for a proper 
treatment of VP-ellipsis on the semantic level. 
The source clause of an elliptical VP often con- 
tains presupposition triggers, and resolution of the 
elided VP asks for presupposition projection in 
the context of the target elliptical clause. This is 
an issue which has been neglected in the literature 
hitherto. 
The other thesis we put forward in this paper is 
that VP-ellipsis resolution is constrained by pre- 
supposition. Every elided VP is evidently escorted 
by some presupposition trigger. The cases we will 
pursue through this paper is the presupposition 
*This work was partly funded by the German Ministry 
for Research and Technology (BMFT) under contract 01 
IV 101 k/1 (VERBMOBIL). 
introduced by focusing particles such as too. 
Of our interest are examples like: 
(1) John kicked his dog, and Tom did, too. 
(2) With Betty, John visited her parents, 
and with MARY, he did, too. 
Example (1) presupposes that only John owns a 
dog (in the strict reading), or presupposes that 
both John and Tom own a dog (in the sloppy rea- 
ding). Example (2) shows that this strict/sloppy 
ambiguity also occurs in cases where there is a 
non-subject parallelism. 
We use the level of discourse representation for 
VP-ellipsis resolution, in an extension of Discourse 
Representation Theory \[Kamp, 1981\]. For the re- 
construction of elided material we adopt a version 
of Asher's Concept Abstraction mechanism \[As- 
her, 1993\]. 
We furthermore integrate Van der Sandt's pre- 
supposition projection algorithm \[1992\]. Van der 
Sandt argues that presuppositions are kind of ana- 
phoric expressions which interpretation is strongly 
influenced by discourse structure. The main dif- 
ference to pronouns is that presuppositions have 
more descriptive content, which enables them to 
accommodate an antecedent, in case not provided 
by discourse. 
2 DRT-framework 
In this section I will outline a proper framework 
that integrates anaphora resolution, presupposi- 
tion projection, and ellipsis resolution. Basically, 
we will extend Kamp's Discourse Representation 
Theory slightly, by integrating the treatment of 
presupposition of Van der Sandt and reference to 
1784 
abstract entities by Asher. What is new is the 
combination of these three formalisms into one, 
leading to interesting results concerning the ana- 
lysis of VP-ellipsis. 
\])RT focuses on the semantic interpretation of dis- 
courses. A major aspect of I)RT is the use of Dis- 
course Representation Structures that hold the se- 
inantic content of sentences as a pair < U, C >, in 
which U is a set of discourse markers (referents) 
and C a set of conditions upon them. The full 
syntax of DRSs is given in Definition 1. 
Definition 1: DRS Syntax 
1. If U is a set of reference markers, C a set 
of conditions, then the pair < Uq~,C¢ > is a 
1)RS I~; 
2. If P is n-place predicate constant and tl ... 
t~ are terms, then P(tl ... tn) is a condition; 
3. If (i) and g~ are DRSs, then ~ (P, • => qJ and 
(I) V • are conditions 
4. If (I) is a I)RS, P a predicative I)RS, tl, t2 are 
terms, then ~(h,t2):(I), cP(h) and h:O are 
conditions. 
Clause (2) forms atomic conditions. Clause (3) 
states negation, universal quantification, and dis- 
junction. Clause (4) defines anaphoric, elliptical 
material, and propositions and deserves more at- 
tention because it deviates from Kamp's original 
proposal. In our framework we introduce the alfa- 
condition (~:~) which functions to indicate that 
the information in \])\]IS ~ must be anaphorically 
Linked to previously established discourse markers. 
It has two additional arguments, one for indica- 
ting the prhlcipal referent of the anaphoric con- 
struction, and (optional) one for stating the ante- 
cedent. So a condition c~(x,y):~ states that y is 
the antecedent for x~ under restriction of (I). 
In the case of pronouns, e0 only contains discourse 
markers and no conditions. But in the case of, for 
example, definite descriptions, (I) carries the re- 
strictions in its conditions for linking the discourse 
marker associated to the definite description to an 
earlier introduced marker. 
Referential constructions such as ellipsis and 
event-type anaphora, are not linked to discourse 
markers but, instead, refer to portions of dis- 
course, and are indicated by e: P(t), where P is 
an abstracted piece of the previous DRS. Resolu- 
tion of epsilon-conditions is done by applying the 
abstracted DRS P to its argument t. 
Alfa- and epsilon conditions do not c~rry any sub- 
ordination relations with respect to other DRSs, 
and neither do propositional conditions. They 
are, in contrast to the sub-DRSs formulated under 
clause (3), accessible for anaphoric relations and 
inherit the subordination relations of the I)RS in 
which they are situated. 
Ellipsis resolution is done by a process called C- 
Abstraction (cf. Asher 1993, p. 249). It is stated 
in a simplified form as: 
Definition 2: C-Abstraction for VP:ellipsis 
(Asher) 
1. If c:P(t) is a condition in DRS K and is de- 
rived from auxiliary do, then P may be iden- 
tiffed with Ay.K*, where K* is an alphabetic 
variant of a part of K. 
2. K* is underspecified for alfa- and epsilon- 
conditions. 
While parsing a sequence of sentences, we aS- 
sume tile following: firstly, we have got ~ pro 
per I)RS of the sentences that we have parsed so 
far, and secondly, a compositional bottom-up con- 
struction procedure that returns the DRS of the 
actual sentence, which is called the sentence-l)RS 
(henceforth s-I)RS). 
An s-DRS is in a sense underspecified, because all 
anaphoric material that it includes is still unresol-. 
ved. On the representationM level this is marked 
by leaving the optionM slot in the Mfu-condition 
for the antecedent untilled. Anaphoric material 
contains, besides the 'normal' anaphors, also all 
presuppositioual information of the sentence un- 
der consideration. Accordingly all presupposition 
inducers are marked as such in the lexicon. 
3 Presupposition Projection 
In this section we will show how presupposi- 
tion projection (aild hence, anaphora resolution) 
is treated in I)RT. The Mgorithm I present is 
in essence conform to Van der Sandt's proposal 
\[Van der Sandt, 1992\]. Van der Sandt's theory 
is principally based on two mechanisms: binding 
1185 
and accommodation. Compared to classical pre- 
supposition theories, the former corresponds by 
and large to presupposition cancellation (or bet- 
ter: neutralization), while the latter is sort of re- 
pairing the discourse in the style of Lewis \[1979\]. 
The idea of Van der Sandt's work is that "anapho- 
ric expressions are either linked to some previously 
established antecedent or, if they have enough de- 
scriptive content, accommodated at some level of 
representation" \[Van der Sandt, 1992\]. All ana- 
phoric information is resolved (under normal cir- 
cumstances), conform the following rules: 
1. Try to bind the anaphoric material to an ac- 
cessible antecedent. 
2. If (1) fails, accommodate an antecedent. 
Accommodation must take place at some accessi- 
ble level of discourse. It has been argued in the 
literature that accommodation must take place as 
global as possible. \[Helm, 1983; Van der Sandt, 
1992\]. Rather than using a non-monotone moving 
operation for accommodation we obey the follo- 
wing algorithm: 
1. 
2. 
3. 
4. Ready. 
If there is a superordinated level then (2) else 
(4). 
Copy the presupposed information to this le- 
vel, but only if this does not lead to semantic 
contradictions (unbound variables or inconsi- 
stencies) or pragmatic violations, else (4). 
Repeat step (1). 
We will not elaborate in detail on the issue which 
constrains constitute the elimination of possi- 
ble accommodation sites. The interested reader 
should consult Van der Sandt's paper (1992) for 
proposals. 
We exemplify the projection algorithm with (3) 
and (4). The former presupposes John as a (tog 
owner, the latter, in contrast, does not presuppose 
that, although it contains the same presupposition 
inducer. This is named the the projection problem. 
(3) John beats his dog. 
(4) If John has a dog, he beats his dog. 
The result of the compositional semantic construc- 
tion process for (4), given that presuppositions are 
marked in the lexicon as anaphorical, is the follo- 
wing s-DRS: 
X2 o/x ) l johXlxl, \] 
dog(x2 ) 
of(x~,x~) 
:ee 
.(x~):~ 
dog(x4) 
~(x,): of(x,,xs) 
beat(xa ,x4) 
This s-DRS is merged with the DRS of the pre- 
vious discourse, which is in this case an empty 
one. The next step is to examine the newly acqui- 
red conditions and see if there are any anaphoric 
DRSs among them. 
In the first place we find the condition for the pro- 
per name John, which is treated as a presupposi- 
tion. We cannot bind this expression to a referent, 
since there is none available, so we accommodate 
the information in the principle DRS) Accommo- 
dation is simply fulfilled by copying an alphabetic 
variant of the anaphoric DRS to the main DRS. 
Linking is possible for the personal pronoun x3 to 
the (closest) referent of John. 
The other anaphoric DRS in the conseqnent of 
tile implication paraplirases his dog has an em- 
bedded anaphoric DRS, which has to be resolved 
first. In this case the referent x5 can be linked 
to xl. Finally we can resolve x4 to x2 because 
their corresponding conditions do not conflict and 
yield: 
X6 
john(x6) 
--- X1 ~(Xl ~X6): =~ 
dog(x2) I I ot(x~,xl) / 
<xJ,xl):V  _ 
c~tx4'x~)' I of(×4,xs) 
beat(xs,x4) 
This DRS is fully specified and paraphrases the 
meaning of (4) correctly: There is a male person 
called John, and if John owns a dog, he beats it. 
For (3), our algorithm would accommodate the 
information that John owns a dog. 
XNote that proper names, treated as presuppositions, 
arc always accommodated to the top level DRS this way, 
or linked to previously established markers. 
1186 
4 VP-ellipsis Resolution by 
Presupposition Projection 
We will explain our analysis of VP-ellipsis by ex- 
ample (5). R.ecM1 that (5)is ambiguous in whe- 
ther 'Ibrn is beating John's dog (the strict in- 
terpretation) or Tom is beating TonPs dog (the 
sloppy reading). 
(5) John kicked Ms {log. 'Ibm did, too. 
Our analysis heavily relies on the interpretation of 
focusing particles. No existing approach to VP- 
ellipsis does so, Mthough absence of presuppo- 
sition introducers makes interpretation of elided 
VPs impossible (6). The set of presupposition 
triggers I am referriug to includes particles like 
too, also, so, either, discourse connectives before; 
after, and, but and other presupposition inducers 
such as certain focusing constructions. 
(6) ? John kicked his dog. Tom did. 
We will emi}hasize on the interpretation of focll- 
sing particles, especially, the adverb too. Dis- 
course particles function to enhance the cohere.nee 
of discourse. They do not add anything to the 
meaning of the propositi{}us they modify, but rat- 
her judge whether at propositions tits within the 
previous {:ontext or not;. This feature characte- 
rizes them as eliminators of possible readings in 
a given context. It makes it impossible to un- 
derstand (5) as 3ohn kicked Bill's dog, and '/bin 
kicked 51bra's dog, for example. 
The particle too typically is sensitive to fi)cused 
objects. It, words, too(qS), ¢ a propositk, n, pre 
supposes '~/), with gJ a proposition derived froln 
¢ with the focused items in ¢ replaced by their 
alternatives. We follow Rooth \[Rooth, 1985\] in 
taking the fm, ction of focus to be evoking alter- 
native sets. Focus determines in that respect an 
additional semzmtic wflue H 1. Ordinary semantic 
values ~.\]o are not affected by focus. 
(7) \[ qbmfa kicked his1 dog\] j = the set of pro 
positions of the forln "x kicked x's dog" 
(8) ~ 'Ibm/,1 kicked his2 dog~ / = the set of pro- 
positions of the form "x kicked his~ dog" 
(9) \[ !l'om/, 1 kicked his1 dog~ ° = the proposition 
"John1 kicked his1 dog" 
Note that pronouns with focused antecedents (7) 
get a referential interpretation, and pronouns with 
an unfocused antecedent get a bound interpreta- 
tion. The semantics of too, stated in terms of 
Rooth's alternative semantics is consequently: 
(lO) too({I}): \[{iq°(D I7~~ (k~-I~\]\] ') 
The merge operation (D takes two DRSs and re- 
turns a new one. The merging of I)RSs consists 
in simply taking the union of the sets of discourse 
markers and the sets of conditions separately. 
The alfa-condition in (10) introduces the presup- 
position of too. In order to preserve {:oordinafion 
be.tweeu this presupposition and the asserLion, it 
is necessary 1;o perform ellipsis and anaphora re- 
solutiou befi}re the interpretation of proposition 
modilying particles (;an take place. 
We will work out an example in detail to make 
clear how resolution is restrained by presupposi- 
tion. l)iscourse markers of type x, are used to 
range over individuals, markers of type Pl range 
over propositions. Consider (5), paraphrased in 
the following DRS: 
(11) 
. pl p2 
x1 
Pl : 
john(x1 ) 
kicked(x1 ,x2 ) 
By C-At}str;~ction (Def. 2) we derive the following 
predicative I)RS for kicked his dog', wt, ich will be 
~pplied to the argument of tile epsilon-condition 
in (11), x4. 
(t2) Ay. 
X5 
. , do~(x~) I ~{x~)' 
I" ~ ' of(x~,x0) / 
kicked (y xs ) 
1187 
Note that (12) is underspecified for anaphoric re- 
lations. It will become part of a context distinct 
from its original one, and therefore other discourse 
markers may play the role of antecedents. The dis- 
course marker x6, standing for his, can be either 
linked to the marker corresponding to Tom, or to 
the marker corresponding to John. In the former 
case we get a referential reading in the presuppo- 
sition because the antecedent is in focus position, 
in the latter case we get a bound reading. Howe- 
ver, these possible readings 2 are checked for being 
allowed by the presupposition introduced by too. 
Applying (10) to the resolved propositional DRS 
P2 with the referential reading gives us the pre- 
supposition in (13) which allows the sloppy inter- 
pretation of Tom does, too: 
(13) p2: 
X4 
tom(x4) 
dog(x~)X~ 
~(x~,x~): of(x~,x0) 
L_ kicked(xJ. ,xs) 
pa 
X9 X7 
jolm(x9 ) 
C Ip3,pl): - dog(xT) v~: of(x~,x~) 
~(~,~):\[~\] 
kicked(x9 ,xT) 
The presupposition Pa can be linked to Pl in (11) 
and is therefore not rejected. The resolved DRS 
with the bound reading in the presupposition gi- 
ves us the strict interpretation of the elided VP. 
The presupposition stemming from too for this 
case is (14) and can also be linked to Pl. 
(14) a:(p3,pl): 
p3 
jo?,:<:;) / aog(x~) 
P3: / of(x~,xs) 
\[. kicked(x~ ,xT) 
Given DRS (11), no other presuppositions can be 
satisfied and therefore these two readings are ex- 
haustive. Because linking of presuppositions has 
2Which number would be larger, if there were more sui- 
table antecedents for x6, more possible antecedents VPs, 
or more alternatives for the focused object Tom. tlowevcr, 
none of these readings would fulfil the requirement to be 
an anaphoric presupposition! 
in our framework a higher priority than accom- 
modation, readings like '/bm kicked x's donkey, 
where x does not equal John or Tom, are not al- 
lowed. 
Finally, note that, for the definite description his 
dog, in the second case presupposition neutraliza- 
tion by anaphoric binding took place, while in the 
first case the presupposition was accommodated 
(by "assertion"). 
5 Comparison to other Approa- 
ches 
I classify previous approaches to VP-ellipsis reso- 
lution as 1) approaches that take the antecedent 
VP as ambiguous, 2) approaches that pursue a 
copying-and-renaming mechanism, and 3) approa- 
ches that rely on discourse relations. None of the 
approaches to be mentioned use presupposition as 
means to restrain VP-ellipsis resolution. 
Source-clause Ambiguity Approaches 
The first class of approaches to VP-ellipsis is cha- 
racterized by claiming that the semantics of the 
elided VP is identical to another VP salient in dis- 
course. They treat the source clause as ambiguous 
in cases where there is both a strict and sloppy in- 
terpretation possible. For illustration, our exam- 
ple (5) would allow only one of the two possible 
properties for the antecedent VP, respectively the 
referential and the bound interpretation. 
(15) a) Ax. kicked(x,dog_of(x)) 
b) Ax. kicked(x,dog_of(john)) 
Resolution is simply done by choosing one of the 
possible sources given in (15) and apply it to 
the subject of the elliptical VP. This analysis is 
proposed in \[Sag, 1976\], \[Williams, 1977\], \[Klein, 
1987\], \[Roberts, 1987\] and \[Gawron and Peters, 
1990\] and are also termed "identity-of-relations" 
approaches in the literature. 
The most serious problem that these approaches 
face is "the postulation of wild ambiguity in the 
source clause, one derivation for each possible case 
of subsequent ellipsis." \[Dalrymple et al., 1991\]. 
Furthermore, it turns out to be impossible to hold 
1188 
on to this analysis for cases like (16): 
(16) With Betty, John visited her parents, 
and with MARY, he did, too. 
Example (16) also shows the strict/sloppy ambi- 
guity. Our analysis predicts this, since the focused 
object is Mary, and the presupposition stemming 
from too is either with x, John did visit x's pa- 
rents (sloppy reading) or with x, John did visit 
Betty's parents (strict reading). 
Copying-and-Renaming Approaches 
On the other hand, there are the 'sloppy-identity', 
qmn-identity', or ~flexible-copying' approaches to 
the problem of ellipsis, which abandon the as- 
sumption that the source clause is ambiguous. 
Instances of these analyses are the higher order 
unification and equationM analysis \[DMrymple et 
al., 1991\], role-based copying methods \[Kehler, 
1993\], and few posited in Discourse Representa- 
tion Theory \[B~uerle, 1988\]; \[Sem, 1993\]; and 
Kainp (Personal communication of Kamp to Gaw- 
ron & Peters \[Gawron and Peters, 1990\]). 
Their shortcomings are, generally stated, first that 
they are forced to put additional, intricate cons- 
traints on resolution to omit overgeneration of rea- 
dings. Second, these approaches do not include a 
detection of parMlelism. They take the identifi- 
cation of parallel objects for granted, or assume 
that the subjects of the source and target clauses 
are parallel (which is not necessarily the case, see 
e.g. (16)). A proper treatment of ellipsis requires 
the integration of parallelism detection between 
the source and target clause. 
Our approach can also be classified as a copying- 
and-renaming approach, with the difference that 
it uses presupposition neutralization as a na- 
turn constraint rather than using "artificial" 
constraints to restrict resolution. Copying-and- 
renaming analyses generally have better predic- 
tions than source-clause-ambiguity approaches. 
The following example, for instance, is judged to 
have five readings: 
(17) John revised his paper before the teacher 
did, and Bill did, too. 
Our analysis generates (assuming that before in- 
troduces a similar presupposition as too), when 
the embedded elided VP is strictly interpreted, 
two readings (the corresponding presuppositions 
are x revised x's paper before t revised t's pa- 
per, and x revised j's paper before the t revised 
t's paper) and three readings when the embedded 
elided VP is sloppily interpreted (here the corre- 
sponding presuppositions are: x revised x's paper 
before t revised x's paper, x revised j's paper be- 
fore t revised j's paper, and x revised x's paper 
before t revised j's paper). These are exactly the 
same readings as \[l)alrylnple et al., 1991\], \[Kehler, 
1993\] and \[Sem, 1993\] get in their analysis. 
Analyses using Discourse Relations 
A quite distinct class of approaches to VP-ellipsis 
are those that use discourse structure to restrain 
resolution lasher, 1993; Gardent, 1993; Priist and 
Scha, 1990\]. These merely built on fi'ameworks 
stemming from AI of whom the most famous one 
is Grosz & Sidner's Discourse Structure Theory 
\[Grosz and Sidner, 1986\]. In order to identify the 
underlying segments of discourse and their relati- 
ons that hold between them, interpretation of clue 
words (finguistic expressions that indicate boun- 
daries between discourse segments) and the pur- 
pose of the speaker is taken into account. Also, 
one inight need knowledge of the world in the ana- 
lysis of segmentation. 
A general problem that these approaches face 
is that they heavily rely on discourse relations. 
There definition is "notoriously elusive" \[Gardent, 
1993\], and an exhaustive classification is still sub- 
ject to future research. Although cue phrases play 
an important role ill signalling topic changes in 
discourse, in general another mechanism might be 
needed to find connections which are not clearly 
stated. The use of speaker's intentions might be 
necessary but in general there is no finite set of 
possible intentions available \[Grosz and Sidner, 
1986\]. Another problem is the difficulty of finding 
a general way to incorporate world knowledge in 
a working system. 
It is unclear in how far one needs discourse in- 
formation for ellipsis resolution. An interesting 
future research topic is how far presupposition, 
as proposed in this paper, can support this task. 
Take for example: 
(18) If John beat his donkey, Bill will too, 
but if he doesn't, Bill won't either. 
1189 
Although source-clause-ambiguity approaches 
predict the right two readings for (18), it is un- 
clear how copying~and-renaming analyses would 
eliminate any mixed strict/sloppy readings wit- 
hout using discourse relations like contrast and 
parallelism. 
6 Conclusion 
We proposed to perform VP-elllpsis resolution on 
a semantic representation level, in a DRT-style 
framework. We did so by incorporating a Van der 
Sandtian approach to presupposition projection. 
This gave us means to treat interactions of VP- 
ellipsis with presupposition, in such a way that 
we do not need any intrinsic rules that traditio- 
nal copying strategies use for VP-ellipsis resolu- 
tion. In this respect, emphasis was laid upon the 
presupposition introduced by the particle too, alt- 
hough the analysis of other discourse particles is 
not expected to be much different. 
References 
lAsher, 1993\] Nicholas Asher. Reference to Ab- 
stract Objects in Discourse. Kluwer Academic 
Publishers, Dordrecht, 1993. 
\[B~uerle, 1988\] Rainer B~uerle. Ereignisse und 
Repri~sentationen. Technical Report LILOG- 
REPORT 43, IBM Deutschland GmbIt, 1988. 
\[Dalrymple et al., 1991\] Mary Dalrymple, Stu- 
art M. Shieber, and Fernando C.N. Pereira. El- 
lipsis and Higher-Order Unification. Linguistics 
and Philosophy, 14:399-452, 1991. 
\[Gardent, 1993\] Claire Gardent. A unification- 
based approach to multiple VP Ellipsis resolu- 
tion. In ACL Proceedings. Sixth European Con- 
ference, 1993. 
\[Gawron and Peters, 1990\] Mark Gawron and 
Stanley Peters. Anaphora and Quantification in 
Situation Semantics. CSLI/University of Chi- 
cago Press, Stanford, 1990. 
\[Grosz and Sidner, 1986\] Barbara J. Grosz and 
L. Sidner, Candace. Attention, Intentions, and 
the Structure of Discourse. Computational Lin- 
guistics, 12:175-204, 1986. 
\[Heim, 1983\] Irene Heim. On the Projection Pro- 
blem for Presuppositions. In Proceedings of the 
West Coast Conference on l~brmal Linguistics, 
1983. 
\[Kamp, 1981\] Hans Kamp. A Theory of Truth 
and Semantic Representation. Formal Methods 
in the Study of Language, 1, 1981. 
\[Kehler, 1993\] Andrew Kehler. A Discourse Co- 
pying Algorithm for Ellipsis and Anaphora Re- 
solution. In ACL Proceedings. Sixth European 
Conference, 1993. 
\[Klein, 1987\] Ewan Klein. VP Ellipsis in DR 
Theory. Studies in Discourse Representation 
Theory and the Theory of Generalised Quanti- 
tiers, 1987. 
\[Lewis, 1979\] David Lewis. Scorekeeping in a lan- 
guage game. Semantics from a different Point 
of View, 1979. 
\[Priist and Seha, 1990\] Hub Priist and Remko 
Scha. A Discourse Perspective on Verb Phrase 
Anaphora. In l'roceedings of the Seventh Am- 
sterdam Colloquium, 1990. 
\[Roberts, 1987\] Craige Roberts. Modal Subor- 
dination, Anaphora and Distributivity. PhD 
thesis, University of Massachusetts, Amherst, 
1987. 
\[Rooth, 1985\] Mats Rooth. Association with Fo- 
cus. PhD thesis, University of Massachusetts, 
Amherst, 1985. 
\[Sag, 1976\] Ivan Sag. Deletion and Logical/~brm. 
PhD thesis, MIT, 1976. 
\[Sem, 1993\] tIelle Frisak. Sem. A proposal for 
ellipsis in DRT. Technical Report 2, Reports 
in Language, Logic, Information. University of 
Oslo, 1993. 
\[Van der Sandt, 1992\] Rob A. Van der Sandt. 
Presupposition Projection as Anaphora Reso- 
lution. Journal of Semantics, 9:333-377, 1992. 
\[Williams, 1977\] Edwin Williams. Discourse and 
Logical Form. Linguistic Inquiry, 8(1), 1977. 
1190 
