Unifying Parallels 
Claire Gardent 
Computational Linguistics 
University of the Saarland 
Saarbriicken, Germany 
claire0coli, uni-sb, de 
Abstract 
I show that the equational treatment of ellipsis 
proposed in (Dalrymple et al., 1991) can further 
be viewed as modeling the effect of parallelism 
on semantic interpretation. I illustrate this 
claim by showing that the account straightfor- 
wardly extends to a general treatment of sloppy 
identity on the one hand, and to deaccented foci 
on the other. I also briefly discuss the results 
obtained in a prototype implementation. 
1 Introduction 
(Dalrymple et al., 1991; Shieber et al., 1996) 
(henceforth DSP) present a treatment of VP- 
ellipsis which can be sketched as follows. An el- 
liptical construction involves two phrases (usu- 
ally clauses) which are in some sense struc- 
turally parallel. Whereas the first clause (we 
refer to it as the source) is semantically com- 
plete, the second (or target) clause is missing 
semantic material which can be recovered from 
the source. 
Formally the analysis consists of two com- 
ponents: the representation of the overall dis- 
course (i.e. source and target clauses) and an 
equation which permits recovering the missing 
semantics. 
I Representation Equation I S A R(T1, • • •, Tn) 
R(S1,..., Sn) = S I 
S is the semantic representation of the source, 
$1,..., Sn and T1,... ,Tn are the semantic rep- 
resentations of the parallel elements in the 
source and target respectively and R represents 
the relation to be recovered. The equation is 
solved using Higher-Order Unification (HOU): 
Given any solvable equation M = N, HOU 
yields a substitution of terms for free variables 
that makes M and N equal in the theory of 
a/~v-identity. 
The following example illustrates the work- 
ings of this analysis: 
(1) Jon likes Sarah and Peter does too. 
In this case the semantic representation and the 
equation associated with the overall discourse 
ar e: 
Equation R(j) = like(j,s) 
For this equation, HOU yields the substitution1: 
{R  x.like(x,s)} 
and as a result, the resolved semantics of the 
target is: 
Ax.like(x, s)(p) - like(p, s) 
The DSP approach has become very influen- 
tial in computational linguistics for two main 
reasons. First, it accounts for a wide range of 
observations concerning the interaction of VP- 
ellipsis, quantification and anaphora. Second, 
it bases semantic construction on a tool, HOU, 
which is both theoretically and computationally 
attractive. Theoretically, HOU is well-defined 
and well-understood - this permits a clear un- 
derstanding of both the limitations and the pre- 
dictions of the approach. Computationally, it 
has both a declarative and a procedural inter- 
pretation - this supports both transparency and 
implementation. 
1As (Dalrymple et al., 1991) themselves observe, 
HOU also yields other, linguistically invalid, solutions. 
For a proposal on how to solve this over-generation prob- 
lem, see (Gardent and Kohlhase, 1996b; Gardent et al., 
1999). 
49 
In this paper, I start (section 2) by clari- 
fying the relationship between DSP's proposal 
and the semantic representation of discourse 
anaphors. In section 3 and 4, I then show that 
the HOU-treatment of ellipsis naturally extends 
to provide: 
• A treatment of the interaction between par- 
allelism and focus and 
* A general account of sloppy identity 
Section 6 concludes and compares the approach 
with related work. 
2 Representing discourse anaphors 
The main tenet of the DSP approach is that 
interpreting an elliptical clause involves recov- 
ering a relation from the source clause and ap- 
plying it to the target elements. This leaves 
open the question of how this procedure relates 
to sentence level semantic construction and in 
particular to the semantic representation of VP- 
ellipsis. Consider for instance the following ex- 
ample: 
(2) Jon runs but Peter doesn't. 
Under the DSP analysis, the unresolved se- 
mantics of (2) is (3)a and equation (3)b is set 
up. HOU yields the solution given in (3)c and 
as a result, the semantics of the target clause 
Peter doesn't is (3)d. 
(3) a. pos(run(jon)) A R(neg)(peter) 
b. R(pos)(jon) = pos(run(jon)) 
c. 
d.  O x.O(run(x))(neg)(peter) 
neg(run(peter)) 
It is unclear how the semantic representa- 
tion (3)a comes about. Under a Montague-type 
approach where syntactic categories map onto 
semantic types, the semantic type of a VP- 
Ellipsis is (et), the type of properties of individ- 
uals i.e. unary relations, not binary ones. And 
under a standard treatment of subject NPs and 
auxiliaries, one would expect the representation 
of the target clause to be neg(P(peter)) not 
P(neg)(peter). There is thus a discrepancy be- 
tween the representation DSP posit for the tar- 
get, and the semantics generated by a standard, 
Montague-style semantic construction module. 
Furthermore, although DSP only apply their 
analysis to VP-ellipsis, they have in mind a 
much broader range of applications: 
\[...\] many other elliptical phenom- 
ena and related phenomena subject to 
multiple readings akin to the strict and 
sloppy readings discussed here may be 
analysed using the same techniques 
(Dalrymple et al., 1991, page 450). 
In particular, one would expect the HOU- 
analysis to support a general theory of sloppy 
identity. For instance, one would expect it to 
account for the sloppy interpretation (I'll kiss 
you if you don't want me to kiss you) of (4). 
(4) I'll \[help you\] 1 if you \[want me tol\] 2. 
I'll kiss you if you don't2. 
But for such cases, the discrepancy between 
the semantic representation generated by se- 
mantic construction and the DSP representa- 
tion of the target is even more obvious. Assum- 
ing help and kiss are the parallel elements, the 
equation generated by the DSP proposal is: 
R(h) = wt(you, h(i, you)) --+ h(i, you) 
and accordingly, the semantic representation of 
the target is -~R(k) which is in stark contrast 
with what one could reasonably expect from a 
standard semantic construction process namely: 
-~P(you) -+ k(i, you). 
What is missing is a constraint which states 
that the representation of the target must unify 
with the semantic representation generated by 
the semantic construction component. If we in- 
tegrate this constraint into the DSP account, 
we get the following representations and con- 
straints: 
(5) 
Representation S A R(T1,...,Tn) 
Equations R(S1,..., Sn) = S 
R(T1,...,Tn) = T 
where T is the semantic representation gener- 
ated for the target by the semantic construction 
module. The second equation requires that this 
representation T unifies with the representation 
of the target postulated by DSP. 
With this clarification in mind, example (2) is 
handled as follows. The semantic representation 
50 
of (2) is (6)a where the semantic representation 
of the target clause is the representation one 
would expect from a standard Montague-style 
semantic construction process. The equations 
are as given in (6)b-c where C represents the se- 
mantics shared by the parallel structures and P 
the VP-Ellipsis. HOU then yields the solution 
in (6)d: the value of C is that relation shared 
by the two structures i.e. a binary relation as 
in DSP. However the value of P (the semantic 
representation of the VPE) is a property - as 
befits a verbal phrase. 
(6) a. pos(run(jon)) A neg(P(peter)) 
b. C(pos)(jon) = pos(run(jon)) 
c. C(neg)(peter) = neg(P(peter)) 
d. {C -+ AOAx.O(run(x)),P 
)~x.run(x) } 
e. AO)~xO(run(x))(neg)(peter) 
neg(run(peter)) 
-.+ 
B 
In sum, provided one equation is added to 
the DSP system, the relation between the 
HOU-approach to VP-ellipsis and standard 
Montague-style semantic construction becomes 
transparent. Furthermore it also becomes im- 
mediately obvious that the DSP approach does 
indeed generalise to a much wider range of data 
than just VP-Ellipsis. The key point is that 
there is now not just one, but several, free vari- 
ables coming into play; and that although the 
free variable C always represents the semantics 
shared by two parallel structures, the free vari- 
able(s) occuring in the semantic representation 
of the target may represent any kind of un- 
resolved discourse anaphors - not just ellipsis. 
Consider the following example for instance: 
(7) Jon 1 took his1 wife to the station. No, 
BILL took his wife to the station. 
There is no ellipsis in the target, yet the 
discourse is ambiguous between a strict and a 
sloppy interpretation 2 and one would expect the 
HOU-analysis to extend to such cases. Which 
indeed is the case. The analysis goes as follows. 
~I assume that in the target took his wife to the station 
is deaccented. In such cases, it is clear that the ambiguity 
of his is restricted by parallelism i.e. is a sloppy/strict 
ambiguity rather than just an ambiguity in the choice of 
antecedent. 
As for ellipsis, anaphors in the source are 
resolved, whereas discourse anaphors in the 
target are represented using free variables 
(alternatively, we could resolve them first and 
let HOU filter unsuitable resolutions out). 
Specifically, the target pronoun his is repre- 
sented by the free variable X and therefore we 
have the following representation and equations: 
Representation tk(j, wife_of(j), s) 
Ark(b, wife_of(X), s) 
Equations C(j) = tk(j, wife_of(j), s) 
C(b) = tk(b, wife_of(X), s) 
HOU yields inter alia two solutions for these 
equations, the first yielding a strict and the sec- 
ond, a sloppy reading: 
{C <-- Az.tk(z, wife_of(j), s), X +- j} 
{C +-- Az.tk(z, wife_of(z), s), X +- b} 
Thus the HOU-approach captures cases of 
sloppy identity which do not involve ellipsis. 
More generally, the HOU-approach can be 
viewed as modeling the effect of parallelism on 
interpretation. In what follows, I substantiate 
this claim by considering two such cases: first, 
the interaction of parallelism and sloppy iden- 
tity and second, the interaction of parallelism 
and focus. 
3 Parallelism and Focus 
Since (Jackendoff, 1972), it is widely agreed that 
focus can affect the truth-conditions of a sen- 
tence 3. The following examples illustrate this, 
where upper-letters indicate prosodic promi- 
nence and thereby focus. 
(8) a. Jon only introduced MARY to Sue. 
b. Jon only introduced Mary to SUE. 
Whereas (8a) says that the only person intro- 
duced by Jon to Sue is Mary, (8b) states that 
the only person Jon introduced Mary to, is Sue. 
To capture this effect of focus on semantics, 
a focus value 4 is used which in essence, is the 
3The term focus has been put to many different uses. 
Here I follow (Jackendoff, 1972) and use it to refer to 
the semantics of that part of the sentence which is (or 
contains an element that is) prosodically prominent. 
aThis focus value is defined and termed differently 
by different authors: Jackendoff (Jackendoff, 1972) calls 
it the presuppositional set, Rooth (Rooth, 1992b) the 
Alternative Set and Krifka (Krifka, 1992) the Ground. 
51 
set of semantic objects obtained by making an 
appropriate substitution in the focus position. 
For instance, in (Gaxdent and Kohlhase, 1996a), 
the focus value of (8a) is defined with the help 
of the equation: 
I Focus Value Equation I Sere = X(F) I 
where Sern is the semantic of the sentence 
without the focus operator (e.g. intro(j,m,s) for 
(8)), F represents the focus and X helps deter- 
mine the value of the focus variable (written X) 
as follows: 
Definition 3.1 (Focus value) 
Let X = Ax.¢ be the value defined by the focus 
value equation and T be the type of x, then the 
Focus value derivable from X, written X, is {¢ J 
x wife}. 
Given (8a), the focus value equation is thus 
(9a) with solution (9b); the focus value derived 
from it is (9c) and the semantics of (8a) is (9d) 
which given (9c) is equivalent to (9e). 
(9) a. intro(j,m,s) = X(m) 
b. {X +-- Ax.intro(j,x,s)} 
c. --X = {intro(j, x, s) I x E wife} 
d. VP\[P E -X A P -+ P = intro(j,m,s)\] 
e. VP\[P E {intro(j, x, s) I x E wife} A 
P ~ P = intro(j,m,s)\] 
In English: the only proposition of the form 
John introduced x to Sue that is true is the 
proposition John introduced Mary to Sue. 
Now consider the following example: 
(10) a. Jon only likes MARY 
b. No, PETER only likes Mary. 
In a deaccenting context, the focus might be 
part of the deaccented material and therefore 
not prosodically prominent. Thus in (10)b, the 
semantic focus Mary is deaccented because of 
the partial repetition of the previous utterance. 
Because they all use focus to determine the fo- 
cus value and thereby the semantics of sentences 
such as (8a), focus deaccenting is a challenge 
for most theories of focus. So for instance, in 
the HOU-analysis of both (Pulman, 1997) and 
(Gaxdent and Kohlhase, 1996a), the right-hand 
side of the focus equation for (10b) becomes 
FV(F) where neither FV (the focus value) nor 
F (the focus) are known. As a result, the equa- 
tion is untyped and cannot be solved by Huet's 
algorithm (Huet, 1976). 
The solution is simple: if there is no focus, 
there is no focus equation. After all, it is the 
presence of a focus which triggers the formation 
of a focus value. 
But how do we determine the interpretation 
of (10b)? Without focus equation, the focus 
value remains unspecified and the representa- 
tion of (10b) is: 
VP\[P E FV A P -+ P = like(p,m)\] 
which is underspecified with respect to FV. 
(Rooth, 1992a) convincingly argues that 
deaccenting and VP-ellipsis are constrained 
by the same semantic redundancy constraint 
(and that VP-ellipsis is additionally subject 
to a syntactic constraint on the reconstructed 
VP). Moreover, (Gaxdent, 1999) shows that the 
equational constraints defined in (5) adequately 
chaxacterise the redundancy constraint which 
holds for both VPE and deaccenting. Now 
example (10b) clearly is a case of deaccenting: 
because it repeats the VP of (10a), the VP only 
likes mary in (10b) is deaccented. Hence the 
redundancy constraint holding for both VPE 
and deaccenting and encoded in (5) applies5: 
C(j) = VP\[P G {likeO, x)} A P 
--+ P = like(j,m)\] 
C(p) = VP\[P E FV A P -+ P = like(p,m)\] 
These equations axe solved by the following 
substitution: 
{C +-- 
FV +- 
Az.VP\[P E {like(z,x)} A P 
--+ P = like(z,m)\], 
{ like (p,x)} } 
so that the interpretation of (10b) is correctly 
fixed to: 
VP\[P E {like(p,x)} A P --+ P = like(p,m)\] 
Thus, the HOU approach to deaccenting 
makes appropriate predictions about the inter- 
pretation of "second occurrence expressions" 
5For lack of space, I shorten {like(j,x) I x G wife} to 
{ like(j,x)} 
52 
(SOE) 6 such as (10b). It predicts that for these 
cases, the focus value of the source is inherited 
by the target through unification. Intuitively, a 
sort of "parallelism constraint" is at work which 
equates the interpretation of the repeated ma- 
terial in an SOE with that of its source coun- 
terpart. 
Such an approach is in line with (Krifka, 
1992) which argues that the repeated material 
in an SOE is an anaphor resolving to its source 
counterpart. It is also partially in line with 
Rooth's account in that it similarly posits an 
initially underspecified semantics for the target; 
It is more specific than Rooth's however, as it 
lifts this underspecification by unification. The 
difference is best illustrated by an example: 
(11) ?? Jon only likes SARAH. No, PETER 
only likes Mary. 
Provided only likes Mary is deaccented, this 
discourse is ill-formed (unless the second 
speaker knows Sarah and Mary to denote the 
same individual). Under the HOU-analysis 
this falls out of the fact that the redundancy 
constraint cannot be satisfied as there is no 
unifying substitution for the following equa- 
tions: 
C(j) = VP\[P E {like(j,x)} A P 
--+ P = like(j,s)\] 
C(p) = VP\[P • FV A P --+ P = like(p,m)\] 
In constrast, Rooth's approach does not cap- 
ture the ill-formedness of (11) as it places no 
constraint on the interpretation of PETER only 
likes Mary other than that given by the compo- 
sitional semantics of the sentence namely: 
VP\[P E FV A P --+ P = like(p,m)\] 
where FV represents the quantification domain 
of only and is pragmatically determined. With- 
out going into the details of Rooth's treatment 
of focus, let it suffice to say, that the first 
clause does actually provide the appropriate an- 
tecedent for this pragmatic anaphor so that de- 
spite its ill-formedness, (11) is assigned a full- 
fledged interpretation. 
~The terminology is borrowed from (Krifka, 1995) 
and refers to expressions which partially or totally re- 
peat a previous expression. 
Nonetheless there are cases where pragmatic 
liberalism is necessary. Thus consider Rooth's 
notorious example: 
(12) People who GROW rice usually only 
EAT rice 
This is understood to mean that people 
who grow rice usually eat nothing else than 
rice. But as the focus (RICE) and focus value 
(Ax.eat(pwgr, x)) that need to be inherited by 
the target VP only EAT rice are simply not 
available from the previous context, the redun- 
dancy constraint on deaccenting fails to predict 
this and hence, fails to further specify the un- 
derspecified meaning of (12). A related case in 
point is: 
(13) We are supposed to TAKE maths and 
semantics, but I only LIKE semantics. 
Again the focus on LIKE is a contrastive fo- 
cus which does not contribute information on 
the quantification domain of only. In other 
words, although the intended meaning of the 
but-clause is o/ all the subjects that I like, 
the only subject I like is semantics, the given 
prosodic focus on LIKE fails to establish the 
appropriate set of alternatives namely: all the 
subjects that I like. Such cases clearly involve 
inference, possibly a reasoning along the follow- 
ing lines: the but conjunction indicates an ex- 
pectation denial. The expectation is that if x 
takes maths and semantics then x likes maths 
and semantics. This expectation is thus made 
salient by the discourse context and provides in 
fact the set of alternatives necessary to interpret 
only namely the set {like(i, sem), like(i, maths)}. 
To be more specific, consider the representation 
of I only like semantics: 
VP\[P E FV A P --+ P = like(i, sem)\] 
By resolving FV to the set of propositions 
{like(i, sem),like(i, maths)}, we get the appro- 
priate meaning namely: 
VP\[P E {like(i, sem), like(i, maths)} A P 
--+ P = like(i, sem)\] 
Following (Rooth, 1992b), I assume that in 
such cases, the quantification domain of both 
usually and only are pragmatically determined. 
53 
The redundancy constraint on deaccenting still 
holds but it plays no role in determining these 
particular quantification domains. 
4 Sloppy identity 
As we saw in section 2, an important property of 
DSP's analysis is that it predicts sloppy/strict 
ambiguity for VP-Ellipsis whereby the multiple 
solutions generated by HOU capture the multi- 
ple readings allowed by natural language. As 
(Hobbs and Kehler, 1997; Hardt, 1996) have 
shown however, sloppy identity is not necessar- 
ily linked to VP-ellipsis. Essentially, it can oc- 
cur whenever, in a parallel configuration, the 
antecedent of an anaphor/ellipsis itself contains 
an anaphor/ellipsis whose antecedent is a par- 
allel element. Here are some examples. 
(14) 
(15) 
(16) 
Jon 1 /took his1 wife to the station\] 2. 
No, BILL/took his wife to the station\]2. 
(Bill took Bill's wife to the station) 
Jon 1 spent /hisl paycheck\] 2 but Peter 
saved it2. (Peter saved Peter's pay- 
check) 
I'll /help you\] 1 if you /want me to1\] 2. 
I'll kiss you if you don't2. (I'll kiss you 
if you don't want me to kiss you) 
Because the HOU-analysis reconstructs the 
semantics common to source and target rather 
than (solely) the semantics of VP-ellipses, it can 
capture the full range of sloppy/strict ambigu- 
ity illustrated above (and as (Gardent, 1997) 
shows some of the additional examples listed in 
(Hobbs and Kehler, 1997)). Consider for in- 
stance example (16). The ellipsis in the target 
has an antecedent want me to which itself con- 
tains a VPE whose antecedent (help you) has a 
parallel counterpart in the target. As a result, 
the target ellipsis has a sloppy interpretation as 
well as a strict one: it can either denote the 
same property as its antecedent VP want me to 
help you, or its sloppy copy namely want me to 
kiss you. 
The point to note is that in this case, sloppy 
interpretation results from a parallelism be- 
tween VPs not as is more usual, from a par- 
allelism between NPs. This poses no particular 
problem for the HOU-analysis. As usual, the 
parallel elements (help and kiss) determine the 
equational constraints so that we have the fol- 
lowing equalitiesZ: 
C(h) = wt(you, h(i, you)) -+ h(i, you) 
C(k) = P(you) --+ k(i, you) 
Resolution of the first equation yields 
AR.wt(you, R(i, you)) --+ R(i, you) as a 
possible value for C and consequently, the 
value for C(k) is: 
C(k) = wt(you, k(i, you)) -+ k(i,  ou) 
Therefore a possible substitution for P is: 
{P +-- x.wt(x,k(i,x))} 
and the VPE occurring in the target can indeed 
be assigned the sloppy interpretation x want me 
to kiss x. 
Now consider example (15). The pronoun 
it occurring in the second clause has a sloppy 
interpretation in that it can be interpreted as 
meaning Peter's paycheck, rather than Jon's 
paycheck. In the literature such pronouns are 
known as paycheck pronouns and are treated as 
introducing a definite whose restriction is prag- 
matically given (cf. e.g. (Cooper, 1979)). We 
can capture this intuition by assigning paycheck 
pronouns the following representation: 
Pro ~-~ )~Q.3x\[P(x) A Vy\[P(y) 
y = x\] A Q(x)\] 
with P E Wj~(e_+t ) • That is, paycheck pronouns 
are treated as definites whose restriction (P) is 
a variable of type (e --+ t). Under this assump- 
tion, (15) is assigned the following equationsS: 
C(j, sp) = 31x~)c_of(x, j) A sp(j, x)\] 
C(p, sa) = 31x\[P(x) A sa(p, x)\] 
Resolving the first equation yields 
;~y.)~O.3xx~)c_of(x, y) A O(y, x)\] 
as a value for C, and therefore we have that: 
C(p, sa) = 31xbc_of(x,p ) A sa(p, x)\] 
{P +-- )~y.pc_of(y, p)} 
That is, the target clause is correctly assigned 
the sloppy interpretation: Peter saved Peter's 
paycheck. 
7For simplicity, I've ommitted polarity information. 
sI abbreviate )~Q.3x\[P(x)AVy\[P(y) -+ y = x\] A Q(x)\] 
to)~Q.Blx\[P(x) A Q(x)\]. 
54 
Thus the HOU-treatment of parallelism can 
account for both paycheck pronouns and exam- 
ples such as (16). Though lack of space prevents 
showing how the other cases of sloppy identity 
are handled, the general point should be clear: 
because the HOU-approach associates sloppy 
identity with parallelism rather than with VP- 
ellipsis, it can capture a fairly wide range of 
data providing some reasonable assumptions are 
made about the representations of ellipses and 
anaphors. 
5 Implementation 
It is known that for the typed lambda-calculus, 
HOU is only semi-decidable so that the unifi- 
cation algorithm need not terminate for unsolv- 
able problems. Fortunately, the class of equa- 
tions that is needed for semantic construction 
is a very restricted class for which much bet- 
ter results hold. In particular, the fact that 
free variables only occur on the left hand side 
of our equations reduces the problem of find- 
ing solutions to higher-order matching, a prob- 
lem which is decidable for the subclass of third- 
order formulae (Dowek, 1992). 
These theoretical considerations have been 
put into practice in the research proto- 
type CHoLI, a system which permits testing 
the HOU-approach to semantic construction. 
Briefly, the system can: parse a sequence of sen- 
tences and return its semantic representation, 
interactively build the relevant equations (par- 
allel elements are entered by the user and the 
corresponding equations are computed by the 
system) and solve them by means of HOU. 
The test-suite includes approximately one 
hundred examples and covers the following phe- 
nomena: 
• VP-ellipsis and its interaction with 
anaphora, proper nouns (e.g., Mary, 
Paul) and control verbs (i.e., verbs such 
as try whose subject "control" i.e., is 
co-referential with some other element in 
the verb complement). 
• Deaccenting and its interaction with 
anaphora, VP-ellipsis, context and 
sloppy/strict ambiguity. 
• Focus with varying and ambiguous foci. It 
is currently being extended to sentences 
with multiple foci and the interaction with 
deaccenting. 
As mentioned in section 2 the HOU-approach 
sometimes over-generates and yields solutions 
which are linguistically invalid. However as 
(Gardent et al., 1999) shows, this shortcoming 
can be remedied using Higher-Order Colored 
Unification (HOCU) rather than straight HOU. 
In CHOLI both an HOU and an HOCU algo- 
rithm can be used and all examples have been 
tested with and without colors. In all cases, col- 
ors cuts down the number of generated readings 
to exactly these readings which are linguistically 
acceptable. 
6 Conclusion 
It should by now be clear that the DSP- 
treatment of ellipsis is better seen as a treat- 
ment of the effect of semantic parallelism: the 
equations constrain the interpretation of paral- 
lel structures and as a side effect, a number of 
linguistic phenomena are predicted e.g. VPE- 
resolution, sloppy/strict ambiguity and focus 
value inheritance in the case of SOEs. 
There are a number of proposals (Hobbs and 
Kehler, 1997; Priist et al., 1994; Asher, 1993; 
Asher et al., 1997) adopting a similar approach 
to parallelism and semantics of which the most 
worked out is undoubtly (Hobbs and Kehler, 
1997). (Hobbs and Kehler, 1997) presents a 
general theory of parallelism and shows that it 
provides both a fine-grained analysis of the in- 
teraction between VP-ellipsis and pronominal 
anaphora and a general account of sloppy iden- 
tity. The approach is couched in the "interpre- 
tation as abduction framework" and consists in 
proving by abduction that two properties (i.e. 
sentence or clause meaning) are similar. Be- 
cause it interleaves a co-recursion on semantic 
structures with full inferencing (to prove sim- 
ilarity between semantic entities), Hobbs and 
Kehler's approach is more powerful than the 
HOU-approach which is based on a strictly 
syntactic operation (no semantic reasoning oc- 
curs). Furthermore, because it can represent 
coreferences explicitely, it achieves a better ac- 
count of the interaction between VP-ellipsis 
and anaphora (in particular, it accounts for the 
infamous "missing reading puzzles" of ellipsis 
(Fiengo and May, 1994)). 
On the other hand, the equational approach 
55 
provided by the HOU-treatment of parallelism 
naturally supports the interaction of distinct 
phenomena. We have seen that it correctly cap- 
tures the interaction of parallelism and focus. 
Further afield, (Niehren et al., 1997) shows that 
context unification supports a purely equational 
treatment of the interaction between ellipsis and 
quantification whereas (Shieber et al., 1996) 
presents a very extensive HOU-based treatment 
of the interaction between scope and ellipsis. 
Acknowledgments 
I wish to thank the ACL anonymous refer- 
tees for some valuable comments; and Stephan 
Thater, Ralf Debusman and Karsten Konrad for 
their implementation of CHoLI. The research 
presented in this paper was funded by the DFG 
in SFB-378, Project C2 (LISA). 

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