VP Ellipsis and Contextual Interpretation 
Daniel Hardt 
Department of Computer and Information Sciences 
University of Pennsylvania 
Philadelphia, PA 19104 USA 
(hardt @line. cis. upenn, edu) 
April 23, 1992 
Abst ract possibility of deictic VP ellipsis, inferrable antecedents, 
non-syntactically parallel antecedents, eases where the 
A computational account of VP ellipsis is described, in antecedent is formed by combining two or more salient 
which VP's are represented in the discourse model as predicates, and cases where the antecedent is sepa- 
contextually dependent semantic objects. It is argued rated from the target by one or more intervening sen- 
that this approach can handle examples that are not tences(\[27\],\[ll\]). However, existing semantic accounts 
allowed by alternative accounts. An implementation is have important empirical problenm. For example, I ar- 
defined in terms of extensions to the Incremental In- gue in \[11\] that they do not permit pronouns to "switch 
terpretation System. The treatment of VP ellipsis is reference" from antecedent to target in examples such 
analogous to that of pronominal anaphora. It is sug- as1: 
gested that the recency and salience constraints com- 
monly thought to apply to pronominal anaphora might 
apply in a similar way to VP ellipsis. 
1 Introduction 
Tim problem of verb phrase ellipsis can be divided into 
two sub-problems: 
Problem (1): how is an antecedent selected? 
Problem (2): given a particular antecedent, how is it 
to be reconstructed at the ellipsis site? 
Most work on VP ellipsis has dealt with Problem (2), 
concerning the copying or reconstruction of a partic- 
ular antecedent. A wide variety of approaches to this 
problem have been proposed, including snrface struc- 
ture accounts (\[141, \[18\]), "syntactic" LF (\[5\]), and se- 
mantic (\[251, \[28\], \[15\], \[21\], \[4\], \[23\], \[24\]). However, 
I will argue that there is a natural level of representa- 
tion that has not been pursued, which I will call the 
"properly semantic" level. I will show that this alter- 
native has significant empirical advantages over other 
approaches to Problem (2). In addition, the approach 
suggests some possible ways of addressing Problem (1), 
which concerns selecting among alternative potential 
antecedents. This problem has been largely ignored. 
There Is a variety of evidence that indicates that VP 
ellipsis is resolved at a semantic rather than syntac- 
tic level of representation. This evidence includes the 
(1) a. I told John/ that I didn't expect him i to 
fail hisl exam. 
b. I told Bill/ that I did. \[expect him/ to fail 
hisj exam\] 
Similarly, most existing accounts 2 do not permit a 
pronoun to be bound by different binders in antecedent 
and target, as in: 
(2) Every boyi in Bill's class hoped Mary would 
ask himl out, but a boyj in John's class 
actually knew that she would. \[ask himj out\] 
It is interesting to note that none of the existing se- 
mantic accounts qualify as "properly semantic" accord- 
lug to some fairly standard criteria. The modifications 
required to comply with these criteria, I will argue, are 
exactly the ones needed to solve these empirical prob- 
lems. The criteria I have in mind are tile following 
two general requirements for semantic representation, 
imposed in Montague's\[20\] "Universal Grammar": 
Condition (1): Tile logical form language must be 
"dispensable". 
I ha exeanplea of VP ellipaln, the a.ntecedent in in bold, and 
the target, or reconstructed material, is bracketed. 
2A po~ible exception is the account of Prfist et a1(\[23\], \[24\]). 
I di$ctms problenm with this account in section 4. 
ACRES DE COLING-92, NANTES, 23-28 Ao~'r 1992 3 0 3 PROC. OV COLING-92, NANTES, AUO. 23-28, 1992 
Condition (2): Semantic representations must have 
contextual parameters. 
None of the existing semantic accounts satisfies both 
of these requirements. As Partee and Bach\[21\] argue, 
the Sag/Williams account does not satisfy Condition 
(1), because it imposes an "alphabetic variance" con- 
dition, making essential reference to the syntax of log- 
ical form expressions. This condition is also imposed 
in Partee and Bach's account, and a similar condition 
arises in a very different setting in the account of Dal- 
rymple, Shieber and Pereira\[4\]. s Only Lappin's ac- 
count \[17\] explicitly removes the alphabetic variance 
condition, bringing this account in accord with Con- 
dition (1). However, semantic representations do not 
have contextual parameters in Lappin's account, or in 
any of the other accounts. 
Thus, although there is a persistent intuition that 
VP ellipsis requires a semantic treatment, no existing 
account is "properly semantic" in the sense required 
by conditions (1) and (2). In this paper I will describe 
such an account, in which the semantic representation 
ofa VP is a three-tuple < DM~,P,DMo,t :>, consisting 
of a property P and input and output discourse models. 
A key feature of this approach is that the antecedent is 
reconstructed at the ellipsis site as a semantic object 
which includes contextual dependencies. These con- 
textual dependencies can be resolved independently in 
the antecedent and the target. This is required for 
examples such as (1) and (2). 
No reference to the syntax of logical form expres- 
sions is made in this approach, satisfying Condition 
(1). The representation of VP's as relations involving 
input and output discourse contexts satisfies Condi- 
tion (2). So this account is more "properly semantic" 
than alternative semantic accounts, whose theoretical 
status is somewhat less clear. One consequence of this 
theoretical clarity is the ease with which the approach 
can be computationally implemented. 
I will describe an implementation of this approach 
in terms of some simple extensions to the Incremental 
Interpretation System\[22\]. The fact that this system 
incorporates contextual dependencies, as required by 
Condition (2), makes it very simple to implement the 
approach. Indeed in an important sense there are no 
additional mechanisms required for VP ellipsis, over 
and above those independently required for pronominal 
and other forms of anaphora. 
I begin with a brief overview of the Incremental In- 
terpretation System. I then describe my extensions to 
aThe account of Klein \[15\], while couched in the DI~F formal- 
hum, ¢uentlally duplicates the Sag/Willian~ approach, defining 
verlinn~ of the Derived VP rule and the Pronoun Rule in DITr 
terms. Sells \[2ill also suggests storing properties in a DRT-style 
dlacour~ model, although he does not apply thls to VP elllpais. 
this system which implement the type of approach to 
VP ellipsis I am advocating, and I describe the deriva- 
tion of an example that cannot be accommodated by 
alternative accounts. Finally, 1 point out that the 
current approach suggests some promising avenues for 
progress on the neglected question concerning the se- 
lection of an antecedent VP. 
2 Background: The Incremen- 
tal Interpretation System 
A semantic representatiou in the Incremental Interpre- 
tation (henceforth II) System is called a "Conditional 
Interpretation", which is defined as an assumption- 
sense pair, A:s, where A is a set of assumptions, and 
s is the sense. The sense can be thought of as the or- 
dinary truth-conditional semantic representation. The 
assumption set consists of assumptions that have been 
introduced during the derivation, and must be dis- 
charged before the derivation is complete. The as- 
sumption set "represents constraints ou how the sense 
may be further connected to its context." \[22\] 
The process of interpretation is defined by a set of 
structural rules and a set of discharge rules. Structural 
rules build the conditional interpretation of a phrase 
compositionally, from the conditional interpretation of 
its parts. Discharge rules remove assumptions. In 
principle all rules have an input and output discourse 
model, but only the discharge rules actually interact 
with the discourse model. 
The form of a structural rule is 
P ~ A:s ff P1 ~ Al:sl and ...and Pk ~ Ak:s:¢ 
The ~ denotes the interpretation relation between 
a node of a syntactic analysis tree (produced by the 
parser) and a node of a semantic derivation tree. P 
denotes a syntactic node, where its immediate con- 
stituents are denoted by variables P1 through Pk. The 
rule schema is to be understood as stating a constraint 
that P receives the interpretation A:s if it has con- 
stituents PI through Pk, and these constituents have 
the interpretations indicated. 
The form of a discharge rule is 
P ~ A':s' if P ~ A:s 
Here, A I ~- A - {P~}, where R is the discharged 
assumption. The discharge of R, together with the 
current state of the discourse model, determines some 
modifications to s, resulting in s ~. 
The assumption storage mechanism is based on 
Cooper storage \[3\], which was applied to quantifier 
phenomena. In the II system, this mechanism is ap- 
plied to several additional phenomena. Below, I will 
ACT~ DE COLING-92, NANTES, 23-28 AoLrr 1992 3 0 4 PROC. OF COLING-92, NANTES, AUG. 23-28, 1992 
describe the rules for pronominal anaphora and for 
quantifiers. 
2.1 Rules for Pronominal Anaphora 
The treatment of pronominal anaphora in the Itsystem 
is similar to the approach in Discourse Representation 
Theory(\[13\], \[12\]): indefinite NP's introduce new ele- 
ments in the discourse model. Pronouns and definite 
descriptions find their referent among elements in the 
discourse model. 
Four types of referential NP's are defined: pronouns, 
definite descriptions, indefinites, and names. They are 
represented as follows: 
bind(x,pronoun,number/gender): x 
bind(x,def,sor t): x 
bind(x,indef,sort): x 
bind(x,name,N): x 
In each case, the sense is represented by a parame- 
ter z, and a binding assumption expresses constraints 
on the way x will be replaced by an entity in the dis- 
course model. This is achieved by discharging the bind 
assumption. The discharge rules are: 
A, bind(x,pronoun,number/gender): S =:, A: Six/el 
A, bind(x,def, sort):S =~ A: Six/el 
A, bind(x,indef,sort):S =*- A: Six/el 
A, bind(x,name,N): S :=~ A: Six/el 
In the ease of pronouns and definite descriptions, 
the element e must be a salient element in the input 
discourse model, satisfying the constraints expressed 
in the binding assumption. An indefinite assumption 
causes a new element e to be added to the output dis. 
course model. In each case, e is substituted for each 
occurrence of x in the sense S. At least for pronouns, 
there is a second possibility: instead of selecting e 
from the discourse model, some other, undischarged 
parameter can be selected. This allows a pronoun to 
be bound by a quantifier, as described below. 
2.2 Rules for Quantifiers 
The treatment of qunntifiers in the II system essen- 
tially duplicates that of Cooper\[3\]. A quantified NP 
is represented by storing a quantifier assumption, to- 
gether with a parameter representing the sense. At 
some later stage in the derivation, the quantifier as- 
sumption is discharged, determining the scope of the 
quantifier. There are two general rules for quantifiers, 
governing the introduction and discharge of quantifier 
assumptions. A quantified NP is represented as: 
bind(x,q,n): x 
where x is a parameter, q is the quantifier, and n is 
the common noun. For example, "every jet" is repre- 
sented 
bind(x,every,jet): x 
Simplifying slightly, the discharge of quantifier as- 
sumptions cml be represented as follows: 
bind(x,q,s): Pt =*" (q s x) p 
As an example, 
bind(x,everyjet): fly(x) =~ (every jet x) fly(x) 
As mentioned above, when a pronoun assumption is 
discharged, its parameter is replaced either by an entity 
in the discourse model, or by some, yet undischarged 
parameter. A pronoun becomes "bound" by a quan- 
tifier if the quantifier parameter replaces the pronoun 
parameter in this way. 
3 The Account of VP Ellipsis 
1 now describe a semantic account of VP ellipsis in 
terms of some simple extensions to the II system. The 
approach parallels the above approach to pronominal 
anaphora. I will define a rule to add VP-meanings 
in the discourse model, and a rule for recovering those 
VP-meanings to resolve an elliptical VP. Thus full VP's 
are analogous to indefinite NP's, in that they both 
typically introduce semantic objects into the discourse 
model, and elliptical VP's are analogous to pronouns, 
in that their interpretation requires the selection of an 
appropriate object from the discourse model. The dis- 
course model will have two sets: SE, the set of salient 
entities, and SP, tile set of salient predicates. 
To add VP-meoafings to the discourse model, I allow 
all lexical verbs to introduce all assumption which adds 
the VP-meaning to the discourse model. I call this 
binding assumption type "pred". It is discharged as 
follows: 
A, bind(pred):S :=~ A: S 
where 
DMou, (SP) = DMi. (SP) U {A:S) 
That is, tile discharge results in the semantic rep- 
resentation of the VP (i.e.,the ~.ssumption-sense pair 
A:S) being added to the SP set of the output discourse 
model. 
l add the requirement that all arguments except the 
subject must be filled hefore the assumption is dis- 
charged. That is, the discharge of this a~sumption is 
permitted only if tile sense is of the form 
ACRES DE COLING-92, NANTES, 23-28 AOI~T 1992 3 0 5 PROC. O1; COL1NG-92, NANTES, AUO. 23-28, 1992 
P(SUB~I, at ..... an) 
where SUBJ represents an unfilled subject argument 
position, with the remaining arguments al through a. 
filled. 
The assumption for recovering a VP-meaning is in- 
troduced by a lexical auxiliary verb; this assumption 
is termed "epred', for elliptical predicate. 
The discharge rule is: 
bind(epred): AUX ::~ A:S 
where A : S is some element of the SP set in DMIn. 
That is, upon discharge of the epred assumption, an 
auxiliary verb is replaced by some VP-meaning in the 
input discourse model. 
The crucial point in these rules is that the antecedent 
VP is represented as an assumption-sense pair, since 
it is the assumptions that represent dependencies on 
context. For example, the representation of the VP 
"help him" might be 
bind(x,pronoun,male): help(SUBJ,x). 
This expresses the constraint that the object po- 
sition must be filled by some entity in the discourse 
model according to constraints of pronominal refer- 
ence. Two copies of this VP, as antecedent and target 
in VP ellipsis, could allow the pronoun to refer to dif- 
ferent entities, depending on the state of the current 
discourse model. 
:(e,.yx boy)(~mk.oot(V,m~)) 
/ 
:(oXhb 
4 An Example ~,e(e~,~, 
I describe the derivation of example (2), which is re- 
peated here. bh~exkit~)~b / 
(2) Every boy~ in Bill's class hoped Mary would / 
ask hhnl out, but a boyj in John's class / 
actually knew that she would. \[ask himj out\] 
The derivation is displayed in Figure 14 , in the form 
of a simplified derivation tree. The derivation tree is 
defined as follows: each node contains a conditional in- 
terpretation, a current discourse model, and a deriva- 
tion rule R, such that the node is consistent with the b~(Hklji~bo~:z 
application of 1~ to the node's daughters. For brevity, 
the discourse models are not displayed, and only cer- 
tain rules are labeled. A~'s~,s 
The antecedent VP "ask him out" is represented as 
bind(pred), 
bind(y, pronoun,male): ask-out(SUBJ,x). 
4Note: it is a~umed that the auxiliary verb contributea tense 
and polarity. This contribution is ignored in the derivation for 
the ~e of ~implicity. 
I~d(Ixo,y,m ale) mk.~(SU BJ,y) 
~d(,cro,y~lo) u~.~ut(SUBJ,H 
z boy) Om o~z~k.o~(Mary~z)) 
~(pro,y,m~e):k~,~.~(l~q,y)) 
bfn ~'o,y,mlel:~.~(tJ~,y) 
I~ne(w,pro,fiNk~)~ \[ 
new 
b0m 
0M 
Figure 1: Derivation of Example (2) 
AVrES o13 COLING-92, NANTES, 23-28 ^olYr 1992 3 0 6 Paoc. OF COLING-92, NANTES, AUO. 23-28, 1992 
The discharge of the pred assumption results in 
bind(y, pronotm,maln): ask-out(SUBJ,x) 
being added to the discourse model. Later, the binding 
assumption for the pronoun is discharged, allowing it 
to be bound by the quantifier every boy. 5 In the in- 
terpretation of the elliptical VP, the auxiliary "would" 
is represented 
bind(epred):would 
The discharge of the epred assumption results in the 
selection of a VP-meaning from the current discourse 
model: in this case, 
blnd(y, pronoun,mule):ask-out (SUB3,x) 
is selected. Later, the binding assumption for the pro- 
noun is discharged, allowing the pronoun to be bound 
to '% boy". 
This example receives a straightforward derivation 
in the system I am proposing. In other accounts, it 
appears that examples of this sort cannot be acconl- 
modated. It is clear, for example, that the example 
violates the alphabetic variance condition imposed in 
the Sag/Williams approach. This condition requires 
that the antecedent mid target VP's be identical up 
to renaming of bound variables. In the example, the 
antecedent VP contains a free variable (him/) which 
becomes him./ in the target, violating the alphabetic 
variance condition. Partee and Bach\[21\] adopt essen- 
tially the same alphabetic variance condition, as does 
Klein\[15\], so that their accounts also rule out the exam- 
ple. Lappin's\[17\] acemmt explicitly rejects the alpha- 
betic variance condition, replacing it with the following 
condition: 
For any two occurrences c~ and fl of an 
open VP intension ¢xl, tr can serve as the 
antecedent of/~ iff both occurrences of xl can 
be naturally interpreted as having the same 
intended range of possible values. 
The example clearly violates this condition: since 
him/ ranges over members of Bill's class, and him`/ 
picks out a member of John's class, they do not have 
"the same intended range of possible values". 
Next, I consider the higher order matching approach 
of Dalrymple, Shieber and Pereira\[4\] (DSP). In this 
approach, a matching operation is performed to solve 
an equation, in which a second order variable repre- 
sents the elliptical VP. To set up the equation, it is 
SThe quantifier "every boy in Bill's class" is represented in 
the derivation as "every boy", for the sake of brevity. Similarly for "a boy in John's class". 
necessary to determine the antecedent clanse and the 
"parallel elements", and DSP provide no method Ibr 
making this determination. "l~\]pieally, with VP ellip- 
sis, there are two adjacent clauses, in which tile sec- 
ond clause contains an elliptical VP. Then the first 
clause is the antecedent clause and the two subjects 
are the parallel elements. Applying this to the current 
example, we have "Mary would ask hiual out" as the 
antecedent clause, and "Mary" mad "she" as parallel 
elements. The equation to solve is 
P(Mary) = ask-out(Mary,him/) 
In this case, the desired solution, 
Az.ask-out(x,himj) 
is not a possible solution to this equation, according to 
tile matching operation used by DSP. This is the most 
straightforward method of determining parallelism to 
set up the equation, and it does not permit the deriva- 
tion of the desired reading, tlowever, it may be that 
all extended notion of parallelism might solve the prob- 
lem. While this has not been investigated by DSP, such 
an approach has been advocated in another recent ac- 
count, that proposed by Priist et a1(\[23\],\[24\]). It ap- 
pears that this account can accommodate the example, 
based on Priist et al's requirement that if a pronoun p 
is bound to Q in the antecedent, the corresponding pro- 
noun p' must be bound to a "structurally parallel" Q~ 
in the target, where this is intended as matching syn- 
tactic and semantic structure. However, example (3) 
indicates that the two quantifiers need not be in struc- 
turally parallel positions. Indeed, example (5) shows 
that there is no requirement for a corresponding quan- 
tifier at all. 
(3) Almost every boyl in the class hope Mary 
will ask hlmi out, but I know there are a 
few boys i who hope that she won't. \[ask 
him`/ out\] 
(4) Every boyi in Mrs. Smith's class hoped she 
would pass himl. In John's`/ case, 1 think 
she will. \[pass him`/\] 
Examples (1) - (4) illustrate the flexibility required 
in interpreting pronouns within the antecedent and tar- 
get VP's. I have shown how the proposed approach 
permits this flexibility. None of the alternative ac- 
counts discussed can accommodate these examples. 
5 Constraints on Selecting an 
Antecedent 
I have argued that tile current approach has significant 
advantages over other approaches to problem (2), con- 
cerning tile level of representation at which VP ellipsis 
ACRES DE COL\]NG-92, NANTf.S, 23-28 AOl~r 1992 3 0 7 PROC. OF COLING-92, NANTES, AUO. 23-28, 1992 
is resolved. In addition, this approach suggests some 
poesible ways of v~ldreasing problem (1), concerning 
the selection among alternative potential antecedents. 
Since the approach parallels the treatment of pronomi- 
nal anaphora, storing semantic representations of both 
VP's and NP's in the discourse model, a natural hy- 
pothesis is that similar constraints govern the selection 
of an antecedent in both the pronominal and the VP 
ellipsis cases. 
The problem of selecting among alternative VP an- 
tecedents has been virtually ignored in the literature. 6 
The corresponding problem in pronominal anaphora 
has received a significant amount of attention. The 
Centering model (\[6\],\[7\],\[1\]) of pronominal anaphora is 
a leading example, applying a variety of constraints 
dealing with such factors as recency, salience, and 
attention. In addition, it is generally agreed that 
there are syntactic configurational constraints govern- 
ing pronominal anaphora of the sort described in the 
"Binding Theory" of GB\[2\]. 
For each of these types of constraints, there are in- 
teresting parallels with the case of VP ellipsis. 
Syntactlc/configuratlonah It appears that VP 
ellipsis obeys the "precede and command" constraint, 
as pointed out by Jackendo~8\], ruling out examples 
such 8.8 
(5) * Charlie will, if his mother-in-law doesn't 
leave town. 
Recency: Just as in the pronominal case, the vast 
majority of cases involves an antecedent in the current 
or immediately preceding utterance. In a survey of VP 
ellipsis in the Brown Corpus\[10\], I found this to be true 
about 95% of the time. 
Salience: VP's in less salient positions seem to be 
less available as antecedents for VP ellipsis. For exam- 
pie, Halliday and Hasan\[9\] give the following example: 
(6) A: The policeman paid no attention to the 
girl who was driving the car. 
(7) *B: Was she really? 
Presumably the unavailability of the VP "driving the 
car" is related to the fact that it appears in a restrictive 
relative clause and is thus not particularly salient. 
Attentionah There is evidence that a "center 
shift", i.e., shifting attention from one entity to an- 
other, might be correlated with the availability of VP 
antecedents. This is suggested by experimental work 
of Malt\[19\], who describes experiments that show, in 
her terms, that "changing the focus" in an intervening 
eA note by Klein ~d Stmlnton-EUiJ \[16l, points out the im- portance of problem (l), 
sentence tends to make a previous VP antecedent in- 
accessible. Thus the first example (taken from Malt's 
experiment) was understood more readily than the sec- 
ond: 
(8) a. "I liked the Monet exhibit," Heather re- 
marked. 
b. "It was really very nice". 
c. "I did too," Richard replied. 
(9) a. "I liked the Monet exhibit," Heather re- 
marked. 
b. "Renoir is my favorite, though." 
c. * "I did too," Richard replied. 
There is reason to believe, then, that constraints re- 
lating to factors such as recency, syntactic configura- 
tion, salience, and attention, might apply to VP ellipsis 
and pronominal nnaphora in a similar way. A simpli- 
fied version of these constraints is implemented in the 
pronoun case of the Incremental Interpretation Sys- 
tem, and it would a simple matter to allow the same 
constraints to apply to VP antecedents. 
6 Conclusions 
While it has been argued by many that VP ellipsis is 
a semantic phenomenon, there is no existing account 
that satisfies some standard requirements on seman- 
tic representation, relating to the "dispensability" of 
the meaning-representation language, and the incor- 
poration of contextual dependencies in semantic rep- 
resentations. In addition, existing semantic accounts 
have important empirical problems, not allowing pro- 
nouns to switch reference from antecedent to target 
with sufficient flexibility. The modifications necessary 
to comply with the standard requirements on seman- 
tic representation are exactly the ones needed to solve 
these empirical problems. I have described such a se- 
mantic account, showing that it handles the examples 
that are ruled out by alternative semantic accounts. 
The approach is easily implemented eomputationally, 
by some simple extensions to the Incremental Interpre- 
tation System. In addition, there is evidence indicating 
that the selection of a VP antecedent might be subject 
to the same sort of constraints that govern pronominal 
anaphora. 
7 Acknowledgements 
Thanks to Mary Dalrymple, Shalom Lappin, Aravind 
Joshi, Christine Nakatani, Dick Oehrle, Mats Rooth, 
Stuart Shieber, Mark Steedman, and Bonnie Webber 
AcrEs DE COLING-92, NAgrl~, 23-28 Ao~'r 1992 3 0 8 PROC. OF COLING-92, NANTES, AU6.23-28, 1992 
for helpful discussion and suggestions. This work was \[14\] 
supported by the following grants: ARO DAAL 03- 
89-C-0031, DARPA N00014-90-J-1863, NSF IRl 90- 
16592, and Ben Franklin 91S.3078C-1. \[15\] 
AcrEs DE COL1NG-92, NAm'ES, 23-28 Aot~rr 1992 3 0 9 PROC. OF COL1NG-92, NANTES, AUG. 23-28, 1992 

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