COMPARATIVES AND ELLIPSIS 
s. G. Puhnan 
SRI International, and University of Cambridge Computer Laboratory 
SRI International Cambridge Computer Science Research Centre 
23 Miller's Yard, Cambridge CB2 1RQ 
sgp@cam.sri.com 
ABSTRACT 
This paper analyses the syntax and seman- 
tics of English comparatives, and some types 
of ellipsis. It improves on other recent analy- 
ses in the computational linguistics literature in 
three respects: (i) it uses no tree- or logical-form 
rewriting devices in building meaning represen- 
tations (ii) this results in a fully reversible lin- 
guistic description, equally suited for analysis or 
generation (iii) the analysis extends to types of 
elliptical comparative not elsewhere treated. 
INTRODUCTION 
Many treatments of the English comparative 
construction have been advanced recently in the 
computational linguistics literature (e.g. Rayner 
and Banks, 1989; Ballard, 1988). This interest 
reflects the importance of the construction for 
many natural language applications, especially 
those concerning access to databases, where it is 
natural to require information about quantita- 
tive differences and limits which are most nat- 
urally expressed in terms of comparatives and 
superlatives. 
However, all of these analyses have their de- 
fects (as no doubt does this one). The most per- 
vasive of these defects is one of principle: they 
all place a high reliance on non-compositional 
methods (tree or formula rewriting) for assem- 
bling the logical forms Of comparatives even in 
cases that might be thought to be straightfor- 
wardly compositional. These devices mean that 
the grammatical descriptions involved lack, to 
varying extents, the important property of re- 
versibility: they can only be used to analyse, not 
to generate, expressions of comparison. This is 
a serious restriction on the practic,'d usefulness 
of such analyses. 
The analysis presented here of the syntax 
and compositional semantics of the main instances 
of the English comparative and superlative is in- 
tended to provide a fairly theory-neutral 'off the 
shelf' treatment which can be translated into 
a range of current grammatical theories. The 
main theoretical claim is that by factoring out 
the compositional properties of the construction 
from the various types of ellipsis also involved, a 
cleaner treatment can be arrived at which does 
not need any machinery specific to this construc- 
tion.. A semantics in terms of generalised quan- 
tifiers is proposed. 
SYNTAX 
Intuitively, a sentence like: 
John owns more horses than Bill owns 
seems to consist of two sentences ascribing owns 
ership of horses, together with a comparison of 
them, where some material has been omitted. 
Despite appearances, however, this pre-theoretical 
intuition is ahnost wholly wrong, both syntacti- 
cally, and, as we shall see, semantically. The 
sequence 'more horses than Bill owns' is in fact 
an NP, and a constituent of the main clause, as 
can be seen from the fact that it can appear as 
a syntactic subject, and be conjoined with other 
simple NPs: 
\[More horses tha~ Bill owns\] are sold 
every day 
John, Mary, and \[more linguists than 
they could cope with\] arrived at the 
party 
In order to accommodate example like these 
we must analyse the whole sequence as an NP, 
with some internal structure approximately as 
follows. (We use a simple unification grammar 
formalism for illustration, with some obvious no- 
tational abbreviations). 
NP\[-comp\] -> NP\[+comp,postp=P,<feats~,R>\] 
S ' \[+comp, postp=P, <feats=R>\] 
A \[+comp\] NP is one like: 
a nicer horse, a less nice horse, less 
nice a horse, several horses more 
several more horses, as many horses, 
at least 3 mot, I,,:~rses, etc. 
-2- 
We will not go into details of the internal 
structure of these NPs, other than to require 
that whether the comparative element is a de- 
terminer or an adjective, the dominating NP 
carries feature values which characterise it as a 
comparative NP, and which enforce 'agreement' 
between comparative pre- and post-particles (- 
er/than,as/as, etc.) via the variable 'P'. We as- 
sume that NPs marked as comparative in this 
way are not permitted elsewhere in the gram- 
nlar. 
In the case of the \[+comp\] S' constituent, 
there are several possibilities. Some forms of 
comparative can be regarded as straightforward 
examples of unbounded dependency construc- 
tions: 
... more horses than Bill ever dreamed 
he would own _ 
... more horses than Bill wanted ~ to 
run in the race 
These involve Wh-movement of NPs. The see- 
ond type involving a lnissing determiner depen- 
dency: 
John owns more horses than Bill owns 
_ sheep 
There were more horses in the field 
than there were _ sheep. 
Rules of the following form will generate \[+comp\] 
sentences of this type, using 'gap-threading' to 
capture the unboullded dependency: 
S' \[+comp,postp=P, <feats=R>\] -> 
COMP \[form=P\] 
S \[-comp, gapIn= \[CAT \[<f eat s=R>\] \], gapOut= \[\] \] 
(.here CAT is either NP or Det) 
As well as these 'movement' colnparatives 
are those involving ellipsis: 
John owns more horses than Bill/Bill 
does~does Bill/sheep. 
Name a linguist with more publica- 
tions than Chomsky. 
lie looks more intelligent with his glasses 
off than on. 
It is noteworthy that sentences like the sec- 
ond of these dernonstra.te that the appropriate 
level at. which ellipsis is recovered is not syn- 
tactic, but semantic: there is no syntactic con- 
stituent in the first portion of the sentence that 
could form an appropriate antecedent. We there- 
fore do not attempt to provide a syntactic mech- 
anism for these cases, but rather regard them as 
containing another instantiation of an S' \[7+compJ 
introdnced by a rule: 
S'\[+comp\] -> COMP S\[+ellipsis, -comp\] 
An elliptical sentence is not a constituent re- 
quired solely for comparatives, but is needed to 
account for sentence fragments of various kinds: 
John, Which house?, Inside, On the 
table, Difficult to do, 
John doesn't, He might not want to, 
etc. 
All of these, as well as more complex se- 
quences of fragments (e.g. 'IBM, tomorrow' in 
response to 'Where and when are you going?') 
need to be accommodated in a grammar. 
Very many cases of this type of ellipsis can 
be analysed by allowing an elliptical S to consist 
of one or more phrases (NP, PP, AdjP, AdvP) 
or their corresponding lexical categories. Most 
other commonly occurring patterns can be catered 
for by allowing verbs which subcategorise for a 
non-finite VP (modals, auxiliary 'do', 'to') to ap- 
pear without one, and by adding a special lexical 
entry for a main verb 'do' which allows it to con- 
stitute a complete VP. Depending, of course, on 
other details of the grammar in question the lat- 
ter two moves will allow all of the following to 
be analysed: 
Will John?, John won't, He may do, 
tie may not want to, Is he going to? 
etc. 
With this treatment of ellipsis, our syntax will 
be able to analyse all the examples of compara- 
tives above, and many more. It will also, how- 
ever, accept examples like: 
John owns more horses than inside. 
Bill is happier than John won't. 
for there is no syntactic connection between 
tile main clause and the elliptical sentence. We 
assume that some of these examples may actu- 
ally be interpretable given the right context: at 
any rate, it is not the business of syntax to stig- 
matise them as unacceptable. 
Comparatives with adjectives and adverbial 
phrases, are, mulalis mulandis, exactly analo- 
gous to those with NPs, and we omit discussion 
of them here. 
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SEMANTICS 
In tile interests of fanailiarity the analysis will 
be presented as far as possible in an 'intension- 
less Montague' framework: a typed higher order 
logic. 
Firstly, we need tile notion of a generalised 
quantifier. It is well known that most, if not 
all, complex natural language quantifiers call be 
expressed as relations between sets. Specifically 
(Barwise and Cooper, 1981) a quantifier with a 
restriction R and a body B can be expressed as 
a relation on the sizes of the set satisfying R, 
and the set which represents the intersection of 
the sets satisfying R and B. A quantifier like 'all' 
can be represented using the relation =, and so a 
sentence like 'all men are mortal', in a convenient 
notation, will translate as: 
quant(~nna.n=m,)~x.man(x),)tx.mortal(x)) 
(In logical forms, lower case variables will be of 
type e, and upper case variables will be of type 
e--~t unless indicated otherwise. All functions 
are 'curried': thus Sxy.P is equivalent to SxAy.P. 
Read expressions like 'quant(Q,R,B)' as 'the re- 
lation Q holds between the size of the set de- 
noted by R, and the size of the set denoted by 
Sx.lLx&Bx'. This latter is tile intersection set. 
The important thing to note at this point is 
that the relation Q can be arbitrarily complex, 
as it needs to be in order to accommodate de- 
terminers like 'at least 4 but not more than 7'. 
The second important thing to notice is that for 
many quantifiers, we are only interested in the 
size of the intersection set, and thus tile first 
lambda variable in Q will be vacuous. Thus 
'some' can be expressed as the relation ')mm.m 
_ 1', as in 'some men snore': 
quant(,~nnl.m > 1, )~x.man(x)/~x.snore(x)) 
In tile case of the movement types of compara- 
tive we can give the semantics in a wholly com- 
positional way by building up generalised quan- 
tilters which contain tile comparison. Informally, 
the gist of the analysis is that in a sentence like 
'Jolm owns more horses than Bill owns', there 
is a generalised quantifier characterising the set 
of horses that John owns as being greater than 
the set of horses that Bill owns. hfformally, we 
can think of the complenaent of a comparative 
NP as a complex determiner: 
John owns \[more than Bill owns\] horses 
(Ill this respect, as in the use of generalised 
quantifiers, this analysis yields logical forms some- 
what similar to those of Rayner and Banks, 1989). 
rio build these quantifiers we assume that the 
various relations signalled by the comparative 
construction are part of the quantifier. Thus the 
final analysis of the example sentence is: 
quant($nm.more(rn, 
Sx.horse(x)& own(Bill,x)), 
)~y.horse(y),)~z.own(John,z)) 
'More' (or 'less' or 'as') is the relation used to 
build the quantifier. To avoid notational clutter 
we call assume that 'more' is 'overloaded', and 
can take as its arguments either a number, or 
an expression of type e---,t, in which case it is 
interpreted as taking the cardinality of the set 
denoted by that expression. 'More' in fact takes 
a third argument, which is another quantifier 
relation. Thus the meaning of a sentence like 
'john owns at least 3 more horses than Bill owns' 
would get a logical form like 
quant(Anm.more(m,Aab.b_> 3, 
Ax.horse(x)&own(Bill,x)), 
Ay.horse(y),Xz.own(john,z)) 
The way to read this is 'the relation of being 
more (by a number greater than or equal to 3) 
than the size of the set of horses owned by Bill, 
hol:ds of the set of horses owned by John'. Where 
this extra argument to 'more' is not explicit, we 
assume it defaults to 'greater than 0'. Itowever, 
we;shall ignore this refinement in the illustra- 
tioias that follow). 
~Note that this quantifier is only interested in 
the intersection set: this is always true of com- 
parative quantifiers. 
:We now give the meanings of each constituent 
involved in a couple of examples, along with the 
relevant rules, in skeletal form. We indicate the 
trail of gap threading using the 'slash' notation. 
For the purposes of this illustration we use the 
analysis of the semantics of unbounded depen- 
dencies from Gazdar, Klein, Pullum and Sag 
(1985): a constituent C containing a gap of cat- 
egory X is of type X---,C. So given a tree of the 
form \[A \[B C\]\] which might normally \],ave as 
the interpretation of A as B applied to C, the 
interpretation of a tree \[A/X \[B C/X\]\] would be 
',~X.B(C(X))'. Since gaps themselves are anal- 
ysed as identity fimctions this will have the right 
type. 
-4- 
/ 
NP 
I 
John 
S 
\ 
VP 
/ \ 
V NP 
I / \ 
omas NP S ' 
/ \ / 
Det Nbar Comp 
/ f f 
more horses than 
\ 
s/sP 
/ \ 
HP VP/NP 
I I \ 
Bill V NP/NP 
I J 
owns e 
The relevant rules and sense entries in schematic 
form are: 
S --* NP VP : NP(VP) 
VP -. V NP : V(NP) 
NP -* NP\[+comp\] S' :NP(S) 
S' --* Comp S/NP : Ax.S(AP.P(x)) 
S' -¢ Comp S/Det : Ax.S(APQ.P(x) Ir Q(x)) 
S/Gap --~ NP VP/Gap : AG.NP(VP(G)) 
VP/Gap --~ V NP/Gap : AG.V(NP(G)) 
NP/NP -~ e : AN.N 
NP/Det -~ Nbar : AD.D(Nbar) 
NP --~ bill : AP.P(bill) 
NP -~ Det Nbar : Det(Nbar) 
Det --~ more : 
APQIt.quant (Anm.more(m, 
Ax.Px & Qx),Ay.Py, Az.Rz) 
Nbar --~ horses : Ax.horse(x) 
V --* owns : ANx.N(Ay.owns(x,y)) 
'Gap' abbreviates either NP\[-comp\] or Det, 
and G is a variable of the appropriate type for 
that constituent. N is an NP type variable; D a 
Det type variable, as are their primed versions. 
Notice that comparative determiners and their 
NPs are of higher type than non-comparative 
NPs, at least for those analyses which analyse 
relative clauses as modifiers of Nbar rather than 
NP. Constituent meanings are assembled by the 
rules above as follows: 
\[NP+cemp more horses\]: 
AQR.quant (Anm.more(m, 
Ax.horse(x)&: Q(x)), 
Ay.horse (y),Az.it(x)) 
\[VP/NP owns ,\]: 
AG.\[ANx.N (Ay.owns (x,y))\] (\[AN'.N'\] G) 
= AG.Ax.G (Ay.owns(x~y)) 
\[S/NP Bill owns el: 
AG'.\[AP.P (bill)/(\[AG.Ax.G (Ay.owns(x,y))\] G') 
= AG'.G'(Ay.owns (bill,y)) 
IS' than Bill owns el: 
= Ax.\[AG'.G'(Ay.owns (bill,y)/(AP.P (x)) 
= Ax.owns(bill,x) 
\[NP \[more horses\]\[S' than Bill owns el: 
AR.quant(Anm.more(m, 
Ax.horse(x) Y., own(bill,x)), 
Ay.horse(y),Az.R(z)) 
The remainder of the sentence is straightforward. 
The second example for illustration is: 
John owns more horses than Bill owns. sheep. 
For the subdeletion cases, a fully compositional 
treatment demands a separate sense entry for 
'more', since the Nbar of the NP in which 'more' 
appears does not occur inside the comparative 
quantifier: 
APQR.quant (Anm.more(m, Ax.Qx), 
Ay.Py, Az.Rz) 
We do not have to multiply syntactic ambigui- 
ties: the appropriate sense entry can be selected 
by passing down into the NP a syntactic fea- 
ture value indicating whether tile following S' 
contains an NP or a Det gap. Constituents are 
assembled as follows: remember that D has the 
type of ordinary determiners: (e--+t)--,((e---+t)---~t). 
\[NP/Det e sheep\]: AD.D(As.sheep(s)) 
\[VP/Det owns • sheep\]: 
AD'.\[ANx.N(Ay.owns(x,y))\] (\[AD.D(As.sheep(s))\]D') 
= AD'.Ax.\[D' (As.sheep(s))/(Ay.owns(x,y) ) 
\[S/Det Bill owns e sheep\]: 
AD'.(\[D'(As.sheep(s))\] (Ay.own~ (bill,y))) 
\[S' than Bill owns e sheep\]-" 
Ax.\[ AD'.(\[D' (As.sheep(s))/(Ay.owns (bill,y)) )\] 
(APQ.P(x) ~" Q(x)) 
= Ax.sheep(x) & owns{bill,x) 
\[NP+eomp more horses\]: 
AQR.quant (Anm.more(m, Ax.Qx), 
Ay.horse(y),Az.R(z)) 
\[NP more horses 
than Bill owns e sheep\]: 
AQIt.\[quant(Anm.more (m, Ax.Qx), 
Ay.horse(y),Az.tt(z))\] 
(Ax.sheep(x) & owns(bill,x)) 
= AR.quant(Anm.more(m, 
Ax.sheep(x) ~ owns(bill,x)), 
Ay.horse(y),Az.It(z)) 
The final logical form for the whole sentence is: 
quant(Anm.more(m, 
Ax.sheep(x) & owns(bill,x)), 
Ay.horse (y) ,Az.own (john,z)) 
-5- 
ELLIPSIS 
In order to explain our treatment of ellipsis, 
we need more about the actual logical forms pro- 
duced compositionally for sentences. These are 
the 'quasi logical forms' (QLF) of Alshawi and 
van Eijck (1989), differing from 'resolved logi- 
cal forms' (RLF) in several respects: they con- 
tain 'a_terms' representing the memlings of pro- 
nouns and other contextually dependent NPs; 
'a.fornm' (anaphoric formula) representing the 
meanings of sentences containing contextually 
determined predicates (possessives, compound 
nominals, 'have' 'do' etc); and 'q_terms' rep- 
resenting the meaning of other quantified NPs 
before the later explicit quantifier scoping phase 
(see Moran 1988). QLFs are fleshed out to RLFs 
via a process of contextually guided inference 
(Alshawi, 1990). Since ellipsis is clearly a con- 
textually deternfined aspect of interpretation we 
extend the 'a_form' construct to provide a QLF 
for elliptical sentences, and treat the process of 
interpretation as akin to reference resolution for 
pronouns. 
Take a sequence like (A) 'Who came.'?' (S) 
'John'. We represent the meaning of the 'miss- 
ing' constituent by an 'a_form' binding a vari- 
able of the appropriate type to combine with the 
meaning of the 'present' constituents to form an 
expression of the appropriate type for the S' con- 
stituent containing the ellipsis. Thus the mean- 
ing of the two utterances will be represented as: 
past(come(who)) 
a_form(P,P(john)) 
One can think of 'a_form' as asserting that there 
is such a P: resolution finds *that P. For consis- 
tency with the Montague notation we are using 
we will indicate an 'a_form' variable as a free 
variable: 'P (john)'. 
for P. In this example the only possibility is that 
P = Ax.past(come(x)). Thus the meaning of the 
elliptical sentence after resolution is: 
\[Ax.past (come(x))\] (john) 
= past(come(john)) 
The theoretical advantages of higher-order 
unification in the interpretation of ellipsis are 
amply documented in Dalrymple, Shieber, and 
Pereira (forthcoming). More details of our own 
treatment are in Alshawi et hi. (forthcoming). 
This analysis of inter-sentential ellipsis gen- 
eralises cleanly to intra~sentential ellipsis, in par- 
ticular the comparative cases discussed above: 
the only difference is that location of the 'con- 
text' is not trivial, since the ellipsis is, as it were, 
contained in the logical form that yields the con- 
text. As an example, the NP in 'Name a linguist 
with \[more publications than John\]' will have a 
structure: 
\[NP \[NP more publications\] \[S' than 
\[S-I-elliptical \[NP John\]\]\]\] 
The meaning of the elliptical S will be as above, 
but the appropriate version of the semantics for 
the S' rule will (as was the case with the analy- 
sis of the movement comparatives given earlier) 
have to arrange things so that the type of the 
whole elliptical S' expression is e---*t. Thus the 
variable representing the ellipsis will be of type 
e---*(e---~t), assuming that 'john' in this context 
is of type e. Omitting some of the details, the 
meaning of the entire NP will then be: 
AR.quant(Anm.more(m, 
Ax.publications(x) ~" \[P(john)\](x)), 
Ay.publicatlons(y), Az.R(z)) 
where the meaning of the elliptical S' \[P(john)\] 
figures in the second term of the comparison af- 
The ellipsis resolution method uses a tech- ter beta~reduction. Tile meaning for the whole 
nique which is formally a restricted type of higher- sentence, again taking some short cuts will he: 
order unification (Ituet 1975). Ellipsis resolution 
proceeds ill three steps. Firstly, we have to find 
a 'context', which in the case of intersentential 
ellipsis is the logical form of the preceding utter- 
ance. Next, one or more 'parallel' elements are 
found in this context. In the example above, it 
would be 'who'. This step is somewhat analo- 
gous to the establishing of prououn antecedents, 
and may be similarly sensitive to properties like 
agreement, focus, sortal restrictions, etc. When 
the parallel element(s) have been found, the next 
step abstracts over the position(s) of the ele- 
ment(s), and suggests the result as a candidate 
name(hearer,linguist) & 
quant(Anm.more(m, 
Ax.publications(x) ~ \[P(john)\](x)), 
Ay.publlcations(y), Az.have(linguist,z)) 
We now have to find a suitable context for el- 
lipsis resolution. The only candidate expression 
with an element parallel to 'john' is 'Az.have(linguist,z)'. 
Abstracting over the parallel element gives us 
'Alz.have(l,z)', which is an appropriate candidate 
for P. After substituting and reducing the final 
meaning of the whole sentence will be: 
-6- 
name(hearer,linguist) £z 
quant (Anm.more(m, 
Ax.publications(x) ~ have(john,x)), 
Ay.publications(y), Az.have(llnguist~z)) 
In reality, of course, the details are more com- 
plex than this, but this semi-formal reconstruc- 
tion should convey the basic principles. Now 
we have succeeded in analysing all the types of 
comparative so far discussed using either purely 
IMPLEMENTATION STATUS 
Morphology, syntax and compositional seman- 
tics for NP, AdjP and AdvP comparatives of 
both movement and ellipsis types have been fully 
implemented, as well as some other common types 
of comparative not mentioned here (e.g. Nbar 
comparatives like 'more men than women'). El- 
lipsis resolution has been implemented for the 
inter-sentential cases, but not, at the time of 
writing, for the intra-sentential cases. However, compositional means, or a non-compositional de- 
. r . ......... we foresee no problem here, as this is an exten- vlceIor contextuallnterpretatlon ofelhps~s whose . ~ . .... 
• . . stun o~ existing mecnamsms. mmn properties, however, are mohvated on grounds 
other than its use for comparatives. Further- 
more, once we have this type of ellipsis mecha- 
nism in place, it is a simple matter to extend it 
to account for comparatives in which the whole 
comparison is missing: 
John has 2 more horses. 
There are at least as many sheep. 
ACKNOWLEDGEMENTS 
This work was supported by the CLARE con- 
sortium: BT, BP, the Information Engineering 
Directorate of the DTI, RSRE Malvern, and SRI 
International. I thank Hiyan Alshawi for his 
many substantial contributions to the analyses 
described here, and Jan van Eijck and Manny 
As Rayner and Banks somewhat ruefully note, Rayner for comments on an earlier draft. 
these are in many texts by far the most corn- 
monly encountered form of comparative, although 
their analysis, in common with others, fails to 
handle them. 
Syntactically, what we do is to give the vari- 
ous comparative morphemes an analysis in which 
they are marked as \[-comparative\]. Thus a phrase 
like 'at least as many sheep' will be analysed as 
either a + or - comparative NP. In the first case, 
tile syntax will only permit it to occur with an 
explicit complement, as detailed above, and in 
the second case the syntax will prevent an ex- 
plicit complement occurring. Semantically, how- 
ever, the second contains an elliptical compari- 
son. Thus the meaning of 'more' in this type of 
comparative will be: 
AP Q.quant (Anm.more(m, 
2x. P(x) & R(x)), 
~y.P(y),2z.(Q(z)) 
where R represents the meaning of the missing 
constituent• In a context where 'John has more 
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