AN IMPLEMENTABLE SEMANTICS FOR COMPARATIVE 
CONSTRUCTIONS 1 
Manny Rayner and Amelie Banks 2 
Swedish Institute of Compu~ter Science 
Box 1263 
S-164 28 KISTA 
Sweden 
We describe a comprehensive treatment of the syntax and semantics of comparative constructions based on 
theoretical work by Pinkham, which can be implemented in a relatively straightforward fashion within a 
feature-based phrase-structure grammar. Comparatives are divided up into "clausal" and "phrasal" 
constructions; in contrast to most previous theories, however, phrasals are not regarded as reduced forms of 
clausals. We begin by defining a Montagovian semantics for phrasal comparatives that directly links 
interpretation rules to the surface syntactic structure; we 1then show how this solution can be made 
computationally more efficient by "factoring" the interpretation through an intermediate level of representa- 
tion, using a method similar to that used for dealing with scoping phenomena. Detailed examples are 
provided, showing how the method can correctly describe the semantics of a variety of superficially widely 
different comparative constructions. The ideas have all been implemented within a large-scale grammar for 
Swedish, a "toy" version of which is presented, along with examples of the output. 
1 INTRODUCTION 
1.1 OVERVIEW 
This paper is written with two different, though to some 
extent overlapping, audiences in mind. On the practical 
side, we address ourselves to the natural language interface 
constructor, who wants to expand the coverge of her system 
so as to incorporate comparative constructions; the state of 
the art has now progressed to the point where it is generally 
acknowledged that this 4s a problem that a serious system 
must attempt to deal with. In the following, we will thus 
attempt to describe our ideas in a sufficiently concrete 
fashion that they can be used as an implementation guide. 
Typical examples of comparatives according to the tradi- 
tional classification are the following: 
Clausal comparatives 
1) Mary was happier in New York than John was in 
London. 
2) John has more books than Mary has newspapers. 
3) The table is longer than it is wide. 
Comparative ellipsis 
4) John is taller than Mary. 
5) Few people run as fast as John. 
6) John bought more books than Mary. 
7) John was happier in New York than in London. 
8) Mary had more friends than John thought. 
9) John hit Mary harder than he meant to. 
10) \]More men than women bought the book. 
11) \]More people voted for the proposal than against. 
12) John likes Mary's house better than Mary John's. 
Unclear cases 
13) More than 50 people signed the petition. 
14) Mary needs a larger car than this Fiat. 
15) .John ran faster than the world record. 
16) John was born in the same city as Mary. 
17) John arrived before Mary. 
On tile theoretical side, we want to re-examine some funda- 
menta\]L questions about the nature of the comparative 
construction, and in particular about the phenomenon gen- 
erally referred to as "comparative ellipsis"; by this, we 
mean comparative constructions like those listed above in 
which the element after the comparative marker is not a 
clause, and which traditionally have been explained in 
terms of various kinds of deletion rules. Here, we will argue 
that, in most common cases, it is by no means necessary to 
postulate syntactic deletion operations. We will claim, 
rather, that it is possible (and indeed simpler) to assign a 
syntactic representation to such constructions that closely 
follows the apparent surface constituent structure. We will 
then slhow how to define semantic interpretation rules for 
such s~ructures, which at no level reconstruct a representa- 
tion ,of' a syntactic clause, but rather operate on the princi- 
ple of directly comparing constituents of similar type. To 
highli~,ht the difference between our approach and the 
86 Computational Linguistics Volume 16, Number 2, June 1990 
Mammy Rayner and Amelie Banks An lmplementable Semantics for Comparative Constructions 
traditional one, we will refer to constructions handled by 
this method as examples, not of comparative ellipsis, but 
rather of contrastive comparison. 
Our opinion is that the issues we are raising are probably 
applicable to most grammatical frameworks subsumed un- 
der the feature-based phrase structure grammar paradigm; 
this includes established formalisms like LFG, GPSG, 
HPSG, PATR-II etc., and a vast number of more or less 
obscure formalisms in use around the world. At risk of 
offending everybody and pleasing nobody, we will make no 
particular attempt to align ourselves with any one of these 
theories; in Section 1.2, we will describe in general terms 
the properties we will expect a framework to possess, if it is 
to be capable of supporting the type of operations we will 
need. Basically, we will demand distinct levels of represen- 
tation for constituent structure, function-argument struc- 
ture, and logical form, related in the normal way; we will 
also require certain constructions to be treated as syntactic 
constituents. Most of this will be quite uncontroversial. 
To clear the decks before moving into action, we now 
spend a couple of paragraphs making clear which questions 
we are not attempting to answer. We regard the lexical 
semantics of comparatives as being outside the scope of the 
paper; we are only interested in determining how the 
phrasal semantics can be derived from them. We explain 
exactly what we mean by this statement in Section 1.2. We 
will ignore complex comparative operators ("more than 
twice as much as"; "at least two inches longer than three 
times as long as"); these are well dealt with in Ballard 
(1988), and in any case do not seem to pose fundamental 
difficulties. For similar reasons, we refrain from discussing 
determiners with phrasal comparatives, like "more than 
two" or "at least half": here, the most comprehensive 
reference is perhaps Keenan and Stavi (1986). We also 
ignore certain idiosyncratic constructions ("as fast as ever"; 
"as much as usual"), which do not seem to fit any pattern 
known to us. 
In our treatment of clausal comparatives, we will present 
two slightly different variants of a solution. The first is 
simple to implement, and appears capable of giving correct 
semantics to most normal examples; however, it fails to give 
both readings for the notorious Russell example, "I thought 
your yacht was longer than it is." The second solution, on 
the other hand, is capable of dealing with this kind of 
sentence, but needs a number of additional scoping rules. 
We say more about this in Section 4. 
With regard to cross-linguistic coverage, we will restrict 
ourselves to English, Swedish, and a few other languages in 
which the comparative construction is syntactically similar 
in nature; this actually appears to include most European 
languages. Although we suspect that our results are proba- 
bly applicable to at least some languages outside this 
group, 3 we shall not make any further attempt to lend 
credibility to this claim. 
The organization of the rest of the paper is as follows. In 
Section 2 we review previous work: in particular, we point 
out what we regard as the main weaknesses of the deletion 
method, and summarize earlier attempts to describe phrasal 
comparatives by direct interpretation methods. The next 
two sections contain the main results of the paper. 
In Section 3, we examine contrastive phrasal compara- 
tives. We begin by defining a Montagovian semantics for 
these, and then show how this can be improved by 
"factoring" it through an intermediate level of representa- 
tion, in which the "contrasting" relationship between 
phrases is left undefined. We then go on to show how this 
methodology can be used to provide a readily implement- 
ablesemantics for a wide variety of contrastive construc- 
tions, which also gives a simple explanation of the ambigu- 
ity of certain comparative sentences. Section 4 then goes on 
to describe our treatment of clausal comparatives, which is 
largely adapted from the work reported in Klein (1980) 
and Pinkham (1985). 
In Section 5 we briefly discuss noncoreference of com- 
pared objects; we also look at sentences containing the 
words "before" and "after," pointing out some differences 
between these and comparative sentences. A corpus analy- 
sis, which gives some indication of the relative frequencies 
of the various constructions, is presented in Section 6. In 
Section 7 we summarize our results. 
The theoretical ideas advocated here were first developed 
and tested in practice within the framework of the SNACK- 
85 project (Rayner and Banks 1986; 1989). In Appendix 2 
we give the complete program code for a "scaled-down" 
version of the system, which handles all the constructions 
described in the main body of the paper, and in Appendix 3 
we show examples of the system's output. 
1.2 THEORETICAL ASSUMPTIONS 
1.2.1 GENERAL REMARKS ON THE THEORETICAL 
FRAMEWORK 
In this section, we attempt to summarize the theoretical 
assumptions needed to support our arguments. The main 
body of the paper is Section 3, which deals with phrasal 
comparatives: here we present our theory in two separate 
forms. 
Version one is a Montague grammar, modified slightly to 
allow use of generalized quantifiers. This has the advantage 
of theoretical elegance, but as we shall see is computation- 
ally unattractive. We consequently recast it in a form more 
suitable for implementation purposes, which draws its inspi- 
ration from the well-known treatment of scoping phenom- 
ena originally described in Woods et al. (1972); later 
elaborations and refinements have been implemented in a 
number of systems, notably CHAT-80 (Pereira 1983), 
TEAM (Grosz et al. 1986), and CLE (Moran 1988; Alshawi 
et al. 1989). We will continue to use this framework in 
Section 4, where we consider clausal comparatives, and 
now describe it in more detail. 
Most importantly, we have three distinct levels of linguis- 
tic representation, which we refer to as syntax, quasi- 
logical form, 4 and logical form; we stress that these terms 
are merely used for convenience, and are not to be read as 
referring to any specific linguistic theory, Chomskian or 
otherwise. The levels will encode the following information: 
Computational Linguistics Volume 16, Number 2, June 1990 87 
Manny Rayner and Amelie Banks An Implementable Semantics for Comparative Constructions 
Syntax. At this level, the structure of the sentence is 
represented as a phrase structure tree, where each node is 
associated with a set of features. We will make two assump- 
tions about the feature structure. First, we distinguish a 
special feature, which encodes the quasi-logical form of a 
constituent; not all nodes need possess this feature. Second, 
there will be some mechanism that permits the definition of 
long-range dependencies, by allowing features in different 
constituents to share information. 
Quasi-logical form (QLF). This level encodes the predi- 
cate-argument structure of the phrase; the only demand we 
will make is that, like any other feature value, its value can 
be derived entirely by phrase structure rules with feature 
unification. (This is in spirit similar to a compositionality 
restriction, but is weaker.) 
Logical form (LF). At this level, the sentence is associ- 
ated with an expression in a (generally higher-order) predi- 
cate calculus; the logical form of a sentence will be deriv- 
able from its quasi-logical form by application of rewriting 
rules representing scoping and other transformations. Since 
there is little agreement concerning the representation of 
logical forms, we now say a few words about the less usual 
features of our system. 
First, we will find it convenient to treat events as objects, 
since this can often greatly simplify the semantics of adver- 
bial modification. For example, we will represent Gustav 
III ruled for 21 years as something like 
3 e. event_type(e, rule)dlagent(e, cyastav_iii)/i dtu ation(e, 21 ) 
We will also make extcnsive usc of gcneralized quantifiers 
(Barwise and Cooper 1981 ); these will play a kcy role in our 
represcntation of comparatives. We will not, however, usc 
Barwise and Cooper's notation, which involves combining a 
determiner and a set-descriptor to form a quantifier, but 
rather will take the equivalent approach of treating deter- 
miners as two-place higher-order predicates on sets. We 
will use {N l~b(N)} for the determiner "A number N such 
that qb(N)": thus we write 
no(rose, hx.send(john, x,mary)) 
for "John sent no roses to Mary," 
{N I N<SKroso,M~.send(john,x, mary)) 
for "John sent less than 5 roses to Mary," and 
INI 3 N'.N<N'&{N'\] 
(rose, Xx.rose(x)ddn(x,garden))} 
(rose,hx.send(iohn,x, mary)) 
for "John sent fewer roses to Mary than there were roses in 
the garden." Formulas like the third one above will occur 
frequently in Section 3, and we advise the reader to spend a 
minute at this point making sure that she understands the 
notation. 
1.2.2 SPECIFIC SYNTACTIC AND SEMANTIC 
ASSUMPTIONS 
The basic scheme, or some not too distant relative, is the 
one used in many large-scale implemented systems; as 
examples, we can quote TEAM (Grosz et al. 1987), PUN- 
DIT (Dahl et al. 1987), TACITUS (Hobbs et al. 1988), 
MODL (McCord 1987), CLE (Alshawi et al. 1989), and 
SNACK-85 (Rayner and Banks 1986). It also has close 
links with theoretical work in situation semantics (Pollard 
and Sag 1988; Fenstad et al. 1987). We start by enumerat- 
ing tlhe basic syntactic constituents S, NP, VP, DET, AP, 
ADVF', PP; as far as our ontological commitments go, we 
need a set of THINGS, a set of EVENTS, and a set of DEGREES. 
We will assume that DEGREES are isomorphic to some kind 
of numbers. 
An NP will consist of a DET and a CN (we borrow this 
nonstandard term for N-bar from Montague grammar). A 
DET will semantically correspond to a generalized deter- 
miner, and a CN to a subset of THINGS. An NP will thus 
become a generalized quantifier. 
A VP consists of a VERB, followed by a list of VERB- 
ARGs (or just ARGs), by which we mean its obligatory 
and optional complements. An ARG is represented at QLF 
level as a pair (arg-type, arg-value). We will need at least 
the following kinds of complements: NP, PP, S-COMP (a 
suitab\]~e S), VP-COMP (a suitable VP), APs. Semanti- 
cally, a verb will be associated with a subset of EVENTS, 
which we can think of as a type of event, state, or situation. 
The VALUE of each ARG will also be semantically repre- 
sented by a suitable object, and the ARG-TYPE will 
translate to a relation between the verb-object and the 
representation of the ARG-VALUE. We will require a 
special kind of QLF node, called an abstraction, to repre- 
sent VPs, APs, and other constituents whose denotation is a 
function from individuals to propositions; one component of 
the abstraction node will be the abstracted variable. 
A scalar adjective A translates to a two-place predicate 
A'(x, d) on OBJECTS × DEGREES, with the interpretation: the 
object x is A' to degree d. Similarly, a scalar adverb A 
translates to a two-place predicate A'(x, d) on EVENTS X 
DEGREES, with the interpretation: the event x is A' to degree 
d. We will assume that degree expressions like "more," 
"less,'" or "at least twice as much as much as" translate to 
two-place predicates on DEGREES × DEGREES. Since we are 
assuming that DEGREES are numbers, it will also make 
sense to use a generalized quantifier as the second argu- 
men't to an adjective: for example, A(x, {N IN <2}) will be 
interpreted as "x is (less than 2) A." 
We will also need to be able to form "slash categories" or 
something similar. In particular, the following will be 
required (in each example the "gap" is represented as an 
underscore): 
S/DET (e.g. "John bought _ vases") 
S/NP (e.g. "John gave _ to Mary") 
S/S-COMP (e.g. "John probably believed _ ") 
S/VP-COMP (e.g. "John presumably meant to _ ") 
A rnore exact formulation of the basic question we are 
attacking is thus: 
In terms of the above framework, state rules by which we 
can systematically calculate the denotation of a complex 
expression involving a comparative construction in terms of 
88 Computational Linguistics Volume 16, Number 2, June 1990 
Mammy Rayner and Amelie Banks An Implementable Semantics for Comparative Constructions 
the denotation of its scalar adjectives and adverbs, the 
denotations of its degree expressions, and the denotations of 
its other constituents. 
2 PREVIOUS WORK ON COMPARATIVES 
This section will summarize relevant previous work on 
comparatives; we begin by listing sources. So far, there has 
been a surprisingly small amount of work done in computa- 
tional frameworks: the only major attempts known to us 
that integrate syntactic and semantic processing are those 
reported in Ballard (1988) and Friedmann (1989). Limited 
syntactic/semantic coverage has appeared in some other 
systems (e.g. DIALOGIC \[Robinson 1982\] and CLE 
\[Alshawi et al. 1989\]), and the Linguistic String Project 
(Sager 1981) has an advanced syntactic coverage. 
On the theoretical front, we have been considerably 
influenced by Bresnan (1973), Hankamer (1973), Pinkham 
(1985), and Klein (1980), especially the last three; we were 
also surprised to discover at a late stage of our research that 
unpublished work by Heim (1985) and Krifka (1987) had 
pursued a course almost parallel to our own. We now go on 
to describe what we regard as relationships between these 
treatments and ours. 
We will start by looking at clausal comparatives, where 
the immediate problem is clearly to account for the appar- 
ent "missing material" in the comparative clause. An early 
and still very influential study of comparative constructions 
is that of Bresnan (1972; 1973; 1977), working within trans- 
formational grammar; the key concept is the introduction 
of the rule of Comparative Subdeletion, which will for 
example derive sentences like la) and 2a) by deleting the 
bracketed material from the base forms 1 b) and 2b). 
1 a) John bought more books than Mary bought. 
1 b) John bought more books than Mary bought \[x many 
books\]. 
2a) John bought more books than Mary bought records. 
2b) John bought more books than Mary bought \[x many\] 
records. 
Although Comparative Subdeletion explains many of the 
facts, it makes a number of erroneous predictions. A very 
long and thorough criticism was advanced in Pinkham 
(1985), where reasons are given to believe that it is prefera- 
ble to adopt an analysis that represents the "missing" 
material as (in English) null proforms; these are bound to 
the head of the comparison by a mechanism that Pinkham 
calls Quantifier Binding. Pinkham's view of the clausal 
comparative has many points in common with that pro- 
posed in Klein (1980), in the context ofa GPSG/Montague 
grammar framework, although Klein only really considers 
sentences of the type in example 2); our own treatment will 
in this respect be similar to Pinkham's and Klein's. 
Like Bresnan and Pinkham, but unlike Friedmann 
(1989), we will also regard the comparative clause as in 
general modifying the comparative head in the main clause, 
as opposed to treating the two clauses as parallel; we 
discuss further in Section 4 the reasons behind this deci- 
sion. 
Moving on to phrasal comparatives, there would appear 
to be two basic approaches. The earlier and more common 
one is to treat these as reduced forms of clausal compara- 
tives; for example, Hankamer (1971) introduces a rule of 
"C-ellipsis," which deletes material from the comparative 
clause under identity with material in the main clause. 
Thus for example, 3a) and 4a) would be regarded as 
reduced forms of 3b) and 4b), where the bracketed mate- 
rial has been deleted: 
3a) John bought more books than Mary. 
3b) John bought more books than Mary \[bought x many 
books\]. 
4a) John bought more books than Mary thought. 
4b) John bought more books than Mary thought \[that he 
bought x many books\]. 
In a computational treatment, this means that the deletion 
rule has to be "reversed," so as to reconstruct the deleted 
material from the phrasal remnant: this is the method used 
in Sager (1981) and Friedmann (1989). 
However, a number of researchers have showed that 
there are drawbacks to the "C-ellipsis" account. Although 
both Hankamer and Pinkham use C-ellipsis in their theo- 
ries, they also provide strong evidence for the existence of at 
least some comparatives that are not elliptic in nature 
(Hankamer 1973; Pinkham 1985). Three examples are 
shown in 5)-7), where Pinkham in each case argues that 
there are severe difficulties involved in deriving a sentence 
of this type from a clausal comparative; the natural choice 
in a transformational framework is to regard the italicized 
portions as base-generated phrasal. 
5) I invited more men than women. 
6) John ran faster than the world record. 
7) Mary looks taller than John when she wears high 
heels. 
Of particular interest here is Pinkham's treatment of exam- 
ples like 5), which are interpreted using a rule that she calls 
"distributive copying." 5) receives the logical form 5a), 
which after distributive copying becomes 5b). Although the 
details of the solution are not fully worked out (in particu- 
lar, the notation is never given a formal semantics), the 
intuitive idea is clearly that of duplicating a "shared" or 
"matrix" predicate, substituting in the two compared ele- 
ments in a suitable way. 
5a) I INVITED (MORE \[ql (ql men), q2 (q2 women)\]) 
5b) MORE \[ql (I INVITED ql men), q2 (I INVITED q2 
women)\] 
Similar suggestions have also been made in a rather dif- 
ferent context by Keenan and Stavi (1986; 282-284); con- 
sidering the semantics of comparative adjectival construc- 
tions like that in 8a), they argue convincingly that these are 
to be regarded as directly interpreted, rather than as re- 
duced forms of sentences like 8b) or 8c): 
Computational Linguistics Volume 16, Number 2, June 1990 89 
Mammy Ra~er and AmeHe ~nks An Implement~ble Semantics for Comparative Cons~ucfiomus 
8a) More male than female students passed the exam. 
8b) More male students than female students passed the 
exam. 
8c) More male students passed the exam than female 
students passed the exam. 
We should also mention the work of M cCord (1981; 1985; 
1987) on "focalizers"; the key notion we borrow is the use 
of rewriting rules on semantic representations, to produce a 
logical form in which contrasted items appear at the same 
level. Although McCord does not attempt, as we do, to 
justify his operations formally, the intuitions behind them 
clearly overlap to a large extent with ours. 
In our own treatment of phrasal comparatives, we take 
all these ideas to their logical conclusion: we dispense with 
the C-ellipsis rule altogether, and regard all nonclausal 
comparatives as essentially phrasal, interpreting them by a 
method analogous to Pinkham's distributive copying. The 
abstract scheme is concretely implemented in the form of 
rewriting rules, which are applied to an intermediate quasi- 
logical form. A solution along these lines, which builds on 
previously reported work (Banks 1986; Banks and Rayner 
1987; Rayner and Banks 1988), is described in Section 3. 
As we complete this article, we discover that a similar 
approach for German comparatives has independently been 
suggested by Krifka (1987); Krifka also proceeds by using 
direct interpretation rules involving contrasting of com- 
pared constituents, although the details of his analysis are 
in some respects fairly different. The following is a typical 
example: 9a) is given the semantics represented by 9b), 
where pdO(d) is to be read as "the maximum d, for which 
O(d) holds," and KOMP(x, y, f) is defined by 
KOMP(x, y, ~) ,~. <I,(x) > ~y) 
9a) Ich babe ihr bessere ZahNrtze 
I have him better dentist 
empfohlen als du. 
recommended than you-NOM. 
(I have recommended him a 
better dentist than you \[did\]). 
9b) KOMP(ich, du, hxpd\[x hat ihr d-gute Zah~irtze 
empfohlen\]). 
3 PHRASAL COMPARATIVES 
3.1 BASIC IDEAS 
As we have already indicated, our strategy for handling 
phrasal comparatives will be to provide direct interpreta- 
tion rules, rather than to assume the existence of deletion 
rules and attempt to reconstruct a clausal comparative. In 
the preceding section, we referred to a number of authors 
who have pointed out weaknesses in the C-ellipsis theory; 
using their arguments and some of our own, we now 
describe our reasons for preferring our method to the 
traditional one. 
Our fundamental argument will be Occam's razor: espe- 
cially from the implementation viewpoint, assuming that 
phrasals are derived from clausals has little real explana- 
tory power. Since the authors quoted above give good 
theoretical arguments to show that at least some phrasal 
compa:ratives are not the result of C-ellipsis, we are at any 
rate \[going to have to provide direct interpretation rules for 
these cases. If it then turns out that these rules can be 
systematically extended so as to cover the other phrasal 
comparatives as well, we can dispense with C-ellipsis alto- 
gether and arrive at a simpler system. We claim that this is 
exactly what we have done. 
It is worth looking a little more closely at the case in 
which the comparative complement is of the form than NP; 
this is certainly the one that occurs most commonly in 
practice. The first point is well known, and was first de- 
scribed in detail in Hankamer (1971): in English (and in 
fact a good many other languages), it is possible to extract 
out of contrastive NP complements, but not from clausal 
comparative complements. For example, compare 10a) 
with 10b): 
10a) ~Vho i does John run faster than tt? 
10b) *:Who i does John run faster than t,. runs? 
The relevance of this observation is obvious: if contrastive 
NP complements really are elliptic forms of clausal comple- 
ments, we would appear to need some mechanism by which 
something originally an extraction island could cease to be 
one when a reduction is performed. This would be a very 
unusual phenomenon, which it would certainly be prefera- 
ble to ~Lvoid introducing into a syntactic theory; rather than 
do this, it seems much simpler to treat the two construc- 
tions a:~ fundamentally different, as we have done. 
Another fairly clear-cut piece of evidence can be found in 
Swedish, where a different possessive pronoun is used de- 
pending on whether the comparative is clausal or phrasal, 
as in 1 la) and 1 lb). Here, the point is that sin refers back 
to the ~ubject of the clause, while hans refers to a nonsub- 
ject NP in the same clause, or an NP in a different clause. 
Once :again, this would be strange if the comparative 
complement in 11 a) were a clausal remnant. 
l la) Sven kSpte tier bScker ~in sin far. 
Sven bought more books than his father. 
1 lb) Sven kSpte tier b~Scker ~in hans far gjorde. 
Sven bought more books than his father did. 
However, in practice the biggest problem seems to be that it 
is not easy to provide a satisfactory definition of the C- 
ellipsis deletion operation; to be more exact, we need to 
define the inverse of this operation, so as to reconstruct the 
comparative clause from the reduced form. A relatively 
simp\]\[e example is 12a), which we quoted in Rayner and 
Banks (1988); the sentence is also discussed at length by 
Friedmann. Here, a naive definition of "deletion of identi- 
cal material" will result in reconstructing 12b); what we 
want is. rather 12c), which requires an NP to be regarded as 
"identicar' to a pronoun bound by it. 
90 Computational ~ng~sfics Volume 16, Num~r 2, June 1~0 
Manny Rayner and AmeHe Banks An lmplementable Semantics for Comparative Constructions 
12a) Every tourist spent more in London than in New 
York. 
12b) Every tourist spent more in London than every tourist 
spent in New York. 
12c) Every tourist spent more in London than he spent in 
New York. 
Friedmann's solution to the problem begins by reconstruct- 
ing a form like 12b), and then makes use of rewriting rules 
that "merge" the two occurrences of every tourist into a 
single quantifier that has wide scope over the whole sentence; 
the final result is essentially 12c). This idea is, however, 
open to several criticisms. To begin with, it has little 
linguistic motivation; more important, it is difficult to see 
how to extend it to handle harder cases without adding 
more ad hoc rules. For example, getting the normal 
("sloppy") reading of 13a) by Friedmann-like analysis 
seems to involve transforming it to something like 13b), 
which rather begs the question of how to account for the 
different possessive pronouns in the two clauses. On a 
direct-interpretation account, however, the intended read- 
ing for sentences like 13a) can be derived in a natural way; 
we describe how this can be done in Section 3.4.6. 
13a) Few men are as loyal to their country as George (is). 
13b) Few are as loyal to their country as George is loyal to 
his country. 
The remainder of Section 3 will give a detailed description 
of our version of the direct-interpretation method. We start 
in Section 3.2 by showing how to construct a Montagovian 
semantics for a fragment containing phrasal constructions; 
the basic trick is to have a phrase structure rule that 
combines a syntactic structure with a pronoun-like "slot," a 
"filler" for the "slot," and an element of the same semantic 
type as the "filler," against which it is contrasted. This rule 
can then be linked in the normal way with a corresponding 
semantic rule, which defines the semantics of the composite 
structure in terms of the semantics of its constituents. 
However, this has the same drawbacks as the original 
Montague treatment of scoping phenomena, namely that 
we are introducing phrase structure rules that lack syntac- 
tic motivation. Consequently, we introduce in Section 3.3 a 
computational version of the theory; here we perform inter- 
pretation in two stages, with the intermediate QLF level of 
structure interposed between phrase structure and logical 
form. At QLF level, comparative phrases are linked to the 
associated graded element, but not to the element they are 
compared against. A subsequent transformation of the 
QLF structure introduces links between compared ele- 
ments, resulting in a form that can be converted into an LF. 
At the penultimate stage, we will have a higher-order 
four-place predicate, which takes the following arguments: 
the two contrasted elements, the way in which they are 
compared, and a parameterized "matrix" formula contain- 
ing two "slots," one for the degree, and one for the con- 
trasted element. 
In Section 3.4 we give examples showing how our frame- 
work can be used to define the semantics of a variety of 
phrasal comparative complements, and also touch briefly 
on the question of ambiguity in phrasal comparative eono 
structions. Finally, in Section 3.5 we say a few words about 
how the theoretical ideas presented above can be realized 
concretely within a unification-based grammar. 
3.2 MONTAGOVIAN SEMANTICS FOR PHRASAL 
COMPARATIVES 
We now proceed to show how the intuitive picture sketched 
out in Section 3.1 can be expressed formally in terms of 
Montague grammar; the technical idea is essentially in- 
spired by the PTQ treatment of scoping phenomena 5 (Mon- 
tague 1972; Dowty et al. 1982, pp. 203-215). There are 
three slightly different variants of the method, one for 
constituents of type t (clauses), and two for constituents of 
type (e, t ) (VPs, APs). Since we are treating adverbials as 
properties of verb-objects, ADVPs will also fall into this 
second group. 
For each variant, we have a rule-schema, parameterized 
by the syntactic type of the comparative complement; we 
call this constituent COMPLEMENT, and we also assume the 
existence of a "proform" that can stand for constituents of 
type COMPLEMENT. An example of such a proform will be 
written as c-proform i for some suitable i. We will also need 
a set of proforms to stand for determiners; we will write 
these as q-proform i. Finally, we will assume a syntactic 
class COMP-OPERATOR, which will include expressions 
like more, less, at least twice as much, and so on. The 
denotation of an expression in COMP-OPERATOR will 
be a constant two-place relation between degrees. 
We then add syntactic rules, to say that a constituent of 
type COMPLEMENT can be realized as c-proformi, and that 
its denotation is a variable e i of the appropriate type; 
similarly, a determiner can be realized as q-proformi, and 
its denotation will be a variable qi of the type associated 
with degree expressions. Since the semantic rules are all 
defined relative to a variable-substitution g, it naturally 
follows that the truth conditions for a phrase containing 
any of these proforms depends on the values assigned by g 
to the associated variables. 
We are now in a position to define the syntactic rule- 
schema for composition of phrasal comparatives. We first 
take the simpler case, where the phrase is of clausal type; 
the input to the rule will be the following: 
1) A phrase • of type S, containing occurrences of 
c-proform i and q-proform i for some i and j. 
2) Two phrases A ! and A 2 of type COMPLEMENT. 
3) A phrase ~ of type COMP-OPERATOR. 
and produces as output the phrase Comp(~, Al, A2, ,It) 
constructed by doing the following: 
a) Replace c-proform i in • by the phrase A 1. 
b) Replace q-proform| in ~ with the comparative operator 
xI,. 
c) Concatenate than or as (depending on '~') + A 2 to the 
end. 
d) Perform necessary morphological operations (e.g. change 
more big to bigger, less many to fewer, etc.) 
Computational Linguistics Volume 16, Number 2, June 1990 91 
Manny Rayner and Amelie Banks An lmplementable Semantics for Comparative Constructions 
We let ~' be the denotation ofO, ~' the denotation of~, etc. 
Since 4, contains instances of the pronouns e-proform i and 
q-proforml, 4,' will contain corresponding free variables el 
and q|. It will thus make sense to abstract over these: for 
convenience's sake, we will refer to Xei~,qjO' as ~". The 
associated semantic rule will then define the denotation of 
Comp(O, A l, A2, q) to be the value of the expression 
O"(AI', {N I ¢"(A2', {N' I ~"(N, N')})}) (*) 
This formula is both central to the paper, and sufficiently 
obscure as to require some further explanation. To under- 
stand what it means in intuitive terms, we focus first on 4>". 
This can be viewed in the usual way as a predicate with two 
argument slots: the first filled by an object denoting a 
phrase of type COMPLEMENT, and the second by an object 
denoting a degree. 
We now work "from the inside out." We thus begin with 
the subformula {N'\[#'(N,N')}; remember that this is a 
generalized determiner (see Section 1.2). For example, if 
has the value more, it will be the determiner 
{N'I more(N,N') }, or to express this in more usual terms (less 
than N). Working outward to the next level, the subformula 
O"(A2', {N'\[~"(N,N')}) is that formed by substituting the 
complement denotation A z' in the first argument place of 4," 
and the determiner denotation {N'\[#'(N,N')} in the second. 
It is consequently a condition on N, which means that 
{N I ¢"(A~', {N'\[ ~'(N,N')}) } is also a generalized determiner. 
The final formula is now constructed by once again substi- 
tuting suitable values into the argument slots for $", these 
now being A l' and {N \[ ~"(A2',{N' \[ g/(N,N') }) }. 
To summarize: what we have described here is a rule- 
schema that allows us to construct what could be called a 
comparative S, which contrasts two constituents of type 
COMPLEMENT. 
A small extension now gives us corresponding schemas 
for comparative constituents of type (e, t) (this includes 
VPs, APs, and relative clauses); it seems that there are 
actually two slightly different versions. The most obvious 
case is the one in which contrasting takes place, as previ- 
ously, between the comparative complement and some 
other constituent of similar type. Here, we can use the 
syntactic conditions for the rule above in unchanged form; 
since the type of ~' is (e, t) rather than t, the semantic part 
of the rule has to be rewritten slightly, as the old definition 
would no longer make the condition on N a truth-value. We 
solve this problem by substituting in a value x in ~" 
(reducing it to a truth-value), and later abstract x away 
again at the outermost level. The denotation of 
Comp(~, Al, Az, ~) will then be 
hx.O"(A{,{N I O"(A2',IN' I ~"(N, N')}, x)}, x) (**) 
An important special case, which we will make use of in 
Sections 3.4.4 and 3.4.6, occurs when the comparative 
complement is an NP, and the "contrast" is between it and 
the entity referred to by the abstracted variable in 4>. 
Sentences 14)-16) illustrate this. In each, we claim that 
contrasting is occurring within the italicized portion. 
14) A man taller than John was chosen for the team. 
15) Most people don't expect to live as long as John (did). 
16) People who travel to London as often as John usually 
have season tickets. 
One way to deal with these constructions would be to make 
them all equivalent with the case represented by 16): for 
relative clauses, it is reasonable to maintain that contrast- 
ing is between the complement, and a "gap" linked to the 
relative pronoun. On this account, 14) and 15) are regarded 
as derived from something like 14a) and 15a). 
14a) A man (who is) taller than John was chosen for the 
'team. 
15a) Most people don't expect (that they will) live as long 
as John. 
Although this approach is certainly also feasible, it seems 
technically simpler to dispense with the null pronouns and 
instead use the following semantic analogue of the idea, 
essentially a type-raising trick. We let 4> be a constituent of 
type < e, t), containing an occurrence of q-proforml, • a 
COMP-OPERATOR, and A z an NP; we define 
Compl (~, A z, ~) to be the phrase formed by substituting 
for q-proformi, and concatenating than/as A 2 to the end, 
and now want to define its denotation. We let e i be a 
parameter ranging over NP denotations, x be a parameter 
ranging over individuals, and A1' be the function XQ.Q(x); if 
we now define ~" to be the formula hcihqi • e i (~'), the 
denotation of Compl(O, A z, ~) is given by yet another 
variant on our basic formula, namely 
Xx.O"(A{,{N I O"(A2',IN' I ~I,'(N, N')})}) (***) 
Readers who wish to see examples of derivations using the 
three :interpretation schemas defined above may now want 
to turn to Section 3.4; when they have returned, we will 
proceed to describe how our theoretical picture can be 
converted into one that is more readily implementable. 
3.3 A COMPUTATIONAL VERSION 
The analysis we have just presented gives a simple and 
compact formalization of our theory of phrasal compara- 
tives, but it is still not easily implementable as it stands. 
The reasons for this are exactly the same as those applying 
to the original PTQ treatment of scoping phenomena; 
essentially, the rules have insufficient syntactic motivation. 
However, the solution (as far as scoping goes) is by now 
standard, and has been successfully implemented in a 
number of well-known systems (e.g., Pereira 1983; Lesmo 
1985; Grosz et al. 1986; Alshawi et al. 1989); the methodol- 
ogy can originally be traced back to Woods (1978). 6 The 
trick is to split interpretation into two stages, the first 
linked to the syntax and the second to the semantics; 
mediating between these, we have an intermediate level of 
representation, the quasi-logical form. This is produced 
compositionally from the syntax, and then subjected to 
rewriting rules before being converted into the final logical 
form. Normally, these rewriting rules formalize scoping 
transformations; here, we will also use them to describe the 
interpretation of nonclausal comparison. In Section 1.1, we 
92 Computational Linguistics Volume 16, Number 2, June 1990 
Mammy Rayner and Amelie Banks An Implementable Semantics for Comparative Constructions 
summarized briefly the basic properties we demanded of 
the QLF level of formalism. We now describe those fea- 
tures that are specially concerned with comparative con- 
structions. 
We start by defining the various kinds of nodes we will 
need in the QLF. These will be the following. 
Node name Represents 
c-complement Comparative complement. 
c-operator Comparative operator. 
c-degree Comparative degree; includes the com- 
parative complement and compara- 
tive operator as subnodes. 
q Placeholder; the q-proform of the Mon- 
tagovian analysis. 
c Placeholdcr; the c-proform of the Mon- 
tagovian analysis. 
comparison Corresponds to Comp(&, A l, A 2, ~I,) and 
Compl(~, A z, ~) of the Montagovian 
analysis. The part of the tree under 
the node corresponds to cI,. The sub- 
nodes are: the "contrasted material" 
(An), the comparative complement 
(A2), the comparative operator (~'), 
and pointers to the relevant q and c 
nodes (qi, ci) 
The fundamental idea should be fairly easy to grasp, if the 
reader has understood the previous section; the QLF is 
successively transformed through a number of stages, until 
it is in a form consonant with the Montagovian analysis of 
Section 3.2. We go through the stages in turn, illustrating 
each of them schematically; in Sections 3.4.1 and 3.4.2, we 
give examples of their application. 
(Stage 0) In the original QLF, the comparative comple- 
ment and comparative operator turn up as c-complement 
and c-operator nodes, modifying the c-degree node repre- 
senting the comparative degree; the c-complement is not yet 
associated with the constituent it is contrasted against (see 
Figure 1). 
(Stage 1) Rewriting rules replace the c-degree with a q 
placeholder, and save the c-complement, c-operator, and 
associated q in a separate location; we call this the "compar- 
ative store," by analogy with Cooper's "quantifier store" 
(Figure 2; Cooper 1983; Engdahl 1985). 
(Stage 2) The contents of the "store" are moved upwards 
in the tree; at each higher node N, attempt to do one of i), 
ii) or iii). (The second and third alternatives are special 
cases) (Figure 3). 
I c-degree I 
\[ c-operator I I c-complement \[ 
Figure I Original QLF 
I H I I 
comparative 
store 
c-complement \] 
c-operator \[ 
Figure 2An item is placed in the "store" 
i) Find a suitable constituent below N to contrast the 
c-complement against. If such a constituent is found, 
replace it by a c placeholder, and insert a comparison 
node in the tree above N. The comparison node is 
constructed from the following components: the c-com- 
plement, the contrasted constituent, the c-operator, 
and the q and c placeholders. 
ii) (This is to deal with the third schema from Section 3.2) 
If N is an abstraction node (representing a constituent 
of type (e, t)), insert a c node above N, a comparison 
I  - om 'emeot I 
H comparison 
I 
contra$t 
c-complement 
\[ c-operator I 
\[ Habstracti°n H c°mparis°n ~abstracti°n ~ 
~1 I ~ x ~ 
Figure 3 (a) A node has been located, which can 
serve as a contrast to the comparative 
complement. (b) The contrast node is replaced 
with a c placeholder, and a comparison node is 
inserted. (c) Special case for third schema in 3.2. 
Computational Linguistics Volume 16, Number 2, June 1990 93 
Manny Rayner and Amelie Banks An Implementable Semantics for Comparative Constructions 
node above the c, and a further abstraction node above 
that. The comparison node is constructed from the 
c-complement, c-operator, c and q; the "contrast" com- 
ponent is that corresponding to a pronoun with associ- 
ated variable x, where x is the abstracted variable in 
the new abstraction node. 
iii) (See Section 3.4.3) If N is a constituent of type t or 
(e, t), and e-complement is an S-OPERATOR, insert 
an s-operator node above N, and a comparison node 
above that; the body of the s-operator node will be a c 
placeholder. The comparison node has the same struc- 
ture as that in case i), except that the "contrasted 
material" slot contains the special value it-is-true-that. 
(Stage 3) The tree is now in a form where the Montagovian 
analysis can be used directly; one of the formulas (*), (**), 
or (***) is applied to yield the logical form, the choice 
depending on which alternative was chosen in the preced- 
ing step. In the final stage, the portion of the QLF under the 
comparison node is duplicated twice, and the q and c 
placeholders instantiated in each copy in an appropriate 
manner (see Figure 4). 
3.4. APPLICATIONS OF THE THEORY 
3.4.1 NP- AND PP-COMPARATIVES 
Phrasal comparative constructions in which the compara- 
tive clause is an NP or PP appear to have fundamentally 
the same structure, and we shall consequently consider 
them under one heading. We will present a typical exam- 
ple, first using the Montagovian framework, and then 
reworking it in the computational one. 
The following table represents a semantic derivation for 
the sentence each woman received more roses from toronto 
than from london; we will analyze this as being composed of 
the subject each woman, and the comparative VP received 
more roses from toronto than from london. We will use an 
instance of the second schema from 3.2, with COMPLEMENT 
equal to PP, and accordingly write c-proform i as from- 
there I. Received will be treated as a verb taking three argu- 
ments, with received'(x, y, z) interpreted as "x received y 
from z." For example, {16}(hr.rose'(r)& ted'(r), ~ r.received' 
(amelie', r, toronto')) will correspond to amelie received 16 
red roses from toronto, and (no'(rose', ~r.received'(amelie', 
r, graham')) will correspond to amelie received no roses from 
graham. 7 (see Table 1). 
H e°mpari'°n H s'°perat°r H I ,tistr',ethat ? 
I c-complement 
c-operator 
W 
Figure 4 Special case for 3.4.3. 
Table 1. Montagovian Analysis of Contrasted PPs 
1. each woman 
2. from toronto 
3. from london 
4. q-l)roform I roses 
5. received 
6. from-there~ 
7. received from-therei 
8. received q-proform I 
roses from-there 1. 
9. more 
10. rec.eived more roses 
from toronto than from 
london 
11. each woman received 
more roses from toronto 
than from london 
XP.each'(woman',P) 
hP.P(toronto') 
hP.P(london') 
hP.ql(rose',P) 
Xx~y~,z.received'(x,y,z) 
11 
Xx~y.ll (hz.received'(x,y,z)) 
;~x.ql(rose',hy.1 l(hz.received' (x,y,z))) 
;~x~y.more'(x,y) 
Xx.{N I {N' I more'(N,N')} 
(rose'Ay.received'(x,y,london')) } 
(rose',;~y.received'(x,y,toronto')) 
each'(woman'Ax.{N I 
{N' I more'(N,N')}(rose', 
hy.received'(x,y,london') ) } 
(rose',Xy.received'(x,y, 
toronto'))) 
*Remember that since q~ is a variable ranging over determiner 
denotations it takes two arguments, which should both be of the 
type (e,l~). Similarly, 1~ (an NP denotation) takes a single 
argument of the same type. 
Figure 5 presents in outline the analysis of the same 
sentence: in the computational framework of Section 3.3, 
and should be compared with Figs. 1-4. 
3.4.2 CN COMPARATIVES 
Comparative constructions of the type illustrated in 17a) 
have been the object of considerable controversy. The 
orthodoJ~ position was that they were "parallel" construc- 
tions: 17a) would thus be a reduced form of 17b). 
17a) More women than men read "Playgirl." 
17b) More women read "Playgirl" than men read 
"Playgirl." 
Pinkham, as we have already mentioned, gives good rea- 
sons for supposing that this is not the ease, and that the 
construction is in base generated phrasal (pp. 121-123). 
We now show how her analysis can be recast in our 
framework: once again, we present our derivation first in 
terms of Montague grammar and then in the computa- 
tional version. 
In Montague grammar, we instantiate the first schema 
from Section 3.2, this time with COMPLEMENT equal to CN; 
in the interests of readability we write c-proform t as of-that- 
kind i. The derivation appears in Table 2. 
The corresponding treatment in the computational frame- 
work is another direct application of the method from 
Section 13.3, and appears in Figure 6. 
3.4.3 "S-OPERATOR" AND "V-P-OPERATOR" 
COMPARATIVES 
Our next type of construction is illustrated in 18a), 18b) 
and 18c). 
18a) Mary had more friends than John had expected. 
94 Computational Linguistics Volume 16, Number 2, June 1990 
Mmnmy Rayner and Amelie Bank~ An Implementable Semantics for Comparative Constructions 
Tree-rewriting analysla of PP con~asting 
I "each woman" ~from Toronto" ~ 
Original QLF 
I I 
comp . vo I store L~ 
comparative I"f~L°~, °n" l ~' l 
store 
A suitable contrast is found for the comparative complement. 
"from Toronto" 
"from London" 
Figure 5 Tree-rewriting analysis of PP-cxmtrasting 
18b) Most people ate more biscuits than Mary said. 
18e) John's yacht was longer than I thought. 
To handle examples like these within our framework, we 
need a syntactic representation that does not involve ellip- 
sis. Our solution is to introduce a syntactic constituent that 
we call an S-OPERATOR: by this, we mean a constituent 
of the form S/S-COMP, that is to say, a clause with a 
Table 2. Montagovian Analysis of CN Comparative 
1. woman 
2. mall 
3. "Playgirl" 
4. read "Playgirl" 
5. q-proform~ of-that- 
kind1 
6. q-proforml of-that- 
kind ! read "Playgiri" 
7. more women than men 
read "Playgirl" 
woman' 
man' 
~,Q.Q(playgirl') 
kx.read(x,playgirl') 
~,Q.q~(I~,Q) 
ql(llAx.read(x,playgirl')) 
{NI {N' I more'(N,N')} 
(man'Ax.read(x,playgirl'))} 
(woman',Xx.read 
(x,playgirl')) 
\[(reads(x,y) is to be understood as "x habitually reads y")\] 
Tree-rewriting analysis of CN contrasting 
Original QLF 
comp tivol 17n 
store 
The comparative complement and operator have been placed in the "store" 
comparatiVestore I~ "Playgirr' 
A suitable contrast is found for the comparative complement. 
I "women" 
"ll~n" 
Figure 6 Tree re-writing analysis of 
CN-~ntrasting 
missing sentential complement. The italicized portions of 
the sentences above are accordingly deemed to be S- 
OPERATORs, and the contrast is with an implicit trivial 
S-OPERATOR that we can write as (it is true that). Note 
that there is an unbounded dependency here between the S 
and its missing constituent; we say a little more about this 
in Section 3.5. 
An example in the Montagovian framework is shown 
below; we use the second schema from Section 3.2, with 
COMPLEMENT instantiated to S-OPERATOR, and write 
c-proform i as attitude l. There are in fact two tricky techni- 
cal points here, which we are forced by space limitations to 
gloss over. 
First, we are assuming that it is possible when introduc- 
ing complex categories of the form A/B to derive the 
associated semantic rule from those for the component 
categories A and B. Since it is at any rate fairly obvious in 
the present case that this is feasible (that is, that we can 
justify the semantic value of the phrase mary said), we shall 
Computational Linguistics Volume 16, Number 2, June 1990 95 
Manny Rayner and Amelie Banks An Implementable Semantics for Comparative Constructions 
not discuss the matter further. Second, we allow applica- 
tion of the denotation of an S-OPERATOR to the denota- 
tion of a VP, which formally is of the wrong type. Here, our 
reasoning is that since an S-OPERATOR denotes a func- 
tion a from propositions to propositions, it will naturally 
induce a function a': Xx.P(x)---~ Xx.a(P(x)) from VP- 
denotations to VP-denotations; we will identify a and a' 
(see Table 3). 
It is interesting to see that Krifka independently arrives 
at exactly the same conclusion; he writes our "it is true 
that" as the operator FAKT, and for example analyses 
19a) below as 19b): 
19a) Anna ist reicher als Otto glaubt. 
Anna is richer than Otto thinks. 
19b) KOMP(FAKT,Otto glaubt,Xd.\[Anna ist d-reich\] 
Analogously with the "S-OPERATOR" introduced above, 
we can also define a "VP-OPERATOR" to be a constituent 
of the syntactic category S/VP, i.e. something that can 
combine with a VP complement to yield an S; note that this 
includes subject NPs. We can then give a similar account 
for sentences like those illustrated in 20a) to c): 
20a) Mary opened more bottles than John told her to. 
20b) Mary scored more points than I normally can. 
20c) Mary needs to get a better result than she's so far 
managed. 
We sketch a Montagovian derivation for the first of these: 
here we use the first schema from 3.2, this time with 
COMPLEMENT instantiated to VP-OPERATOR. Note that 
we give mary wide scope over the whole sentence, so as to 
get the pronoun bindings right (see Table 4). 
Readers who wish to understand the implementation 
details for the computational version are referred to the 
relevant program code in Appendix 2. Parse-tree and logi- 
cal forms are given in example sentence 8 in Appendix 3. 
3.4.4 CONTRASTING INSIDE ADJECTIVAL AND 
ADVERBIAL PHRASES 
So far, all the examples of contrastive comparatives that we 
have shown have involved using one of our two schema to 
Table 3. Montagovian Analysis of "S-OPERATOR" 
Comparative 
1. most people 
2. mary said 
3. (it is true that) 
4. ate 
5. ate so-many I biscuits 
6. attitude~ ate so-many~ 
biscuits 
7. (it is true that) ate more 
biscuits than Mary said 
8. most people ate more 
biscuits than Mary said 
XQ.most'(person',Q) 
XQ.said'(mary',Q) 
XQ.Q 
XxXy.ate'(x,y) 
hx.(ql (biscuit',Xy.ate'(x,y))) 
a~ (Xx.(q~ (biscuit',Xy.ate'(x,y)))) 
Xx.{N I said'(mary',{N' I more' 
(N,N')}(biscuit',Xy.ate'(x,y))} 
(biscuit',Xy.ate'(x,y))) 
most'(person',Xx.{said'(mary', 
{N' I more'(N,N')} 
(biscuit',Xy.ate'(x,y)) } 
(biscuit',Xy.ate'(x,y)))) 
Table 4. Montagovian Analysis of "VP-OPERATOR" 
Comparative 
1. nmry XQ.Q(mary') 
2. h e~ XQ.Q(x~) 
3. john told he I to kQ.told'(john',xl,Q(x0) 
4. opened so-many I bottles kx.(q~(bottle',Xy.opened'(x,y))) 
5. vp-ap I opened so-many I cl(Xx.(ql(bottle',Xy.opened'(x,y)))) 
bottles 
6. he I opened more bottles {N I told'(john',xl,{N' I more'(N,N')} 
than john told he~ to (bottle',ky.opened'(Xl,y))))} 
(bottle',ky.opened'(x~,y)) 
7. mary opened more hot- {N I told'(john',mary',{N' I more' 
ties than john told her to (N,N')}(bottle',Xy.opened' 
(mary,y))))} 
(bottle',Xy.opened' 
(mary,y)) 
construct a phrase that is either an S or a VP. In this 
sectior:, we will consider sentences where the contrasting 
operation is used internally within adverbial and adjectival 
phrases: Pinkham quotes constructions of this kind as some 
of the clearest instances of phrasal comparatives. We start 
in 21)--23) by giving some typical examples; 21) and 22) 
are taken from Pinkham (1985). 
21) A man taller than John was chosen for the team. 
22) He ran faster than the world record. 
23) John needs a spanner bigger than the No. 4. 
In each of these sentences, contrasting appears to occur 
within the italicized phrase; in 21), John need not have 
been chosen for the team, in 22) the world record certainly 
cannol run, and in 23) John presumably does not need the 
No. ,4. We would, however, derive all these conclusions if 
contrasting were at VP or clausal level, since we would then 
copy t\]:e verb. 
In accordance with Pinkham's suggestions, our approach 
will rather be to use a direct interpretation method based 
on predicate copying; we will in fact use the third schema 
from Section 3.2, defined by formula (***). This applies in 
a straightforward fashion to adjectival constructions like 
those i.n 21) and 23). Pinkham notes that a similar treat- 
ment is also possible for sentences like 22) if we take fast to 
be a predicate applying to the "running" event, although 
we imagine that some people may find this move unattrac- 
tive. 
In 'Fable 5, we present a sketch of a Montagovian 
analysis for 21). Note that "Q tall" will be represented as 
Xx.tall(x, Q), where Q is a generalized determiner, and that 
formula (***) is used when deriving 5 from 3 and 4. 
3.4.5 CONTRASTED PREPOSITIONS 
The types of contrastive comparatives described in Sections 
3.4.1 1:o 3.4.4 appear to account for the vast majority of 
those that occur in practice) There are also a few rare 
cases, one of which we here touch on briefly. As a final 
example, we consider the case of contrasted prepositions, as 
shown in 24) below. 9 
24) There are more points for the proposal than against. 
96 Computational Linguistics Volume 16, Number 2, June 1990 
Manny Rayner and Amelie Banks An lmplementable Semantics for Comparative Constructions 
Table 5. Montagovian Analysis of Contrasting in AP 
2. player 
3. john 
4. q-proform I tall 
5. taller than john 
1. was chosen for the team was-chosen' 
player' 
XQ.Q(john') 
hx.tall'(x,ql) 
hx.tall'(x,{D I tall'( john, 
{D' I more'(D,D')})}) 
6. player taller than john hx.player'(x)&tall'(x,{D I tall' 
( john,{O' l more'(D,D')})}) 
7. a player taller than john XQ.a'(hx.player'(x)&tall'(x,{D I tall' 
( john,{D' I more'(D,D')})}),Q) 
8. a player taller than john a'(Xx.playcr'(x)&tall'(x,{D I tall' 
was chosen for the team ( john,{D' I more'(D,D')})}), 
was-chosen') 
These can be treated in a completely straightforward man- 
ner in the computational version from Section 3.3; the key 
step will be the replacement of the ARG-TYPE field of a 
suitable NP denotation with a C-placeholder. A Montagov- 
ian treatment of the construction is of course somewhat 
problematic with the framework we have so far adopted, 
since there is no sensible way to quantify over ARG-TYPE 
of anything similar; some people may see in this fact an 
argument against Montagovian formalisms. (Parse-tree 
and logical form in example sentence 12 in Appendix 3). 
3.4.6 AMBIGUITIES IN CONTRASTIVE 
CONSTRUCTIONS 
It is well known that phrasal comparative constructions can 
easily give rise to ambiguities: sentences 25)-27) illustrate 
three typical possibilities. Here, we will discuss how our 
system fares when attempting to explain these. 
25) Nobody talked more to John about Carol than Mary. 
26) Few men give their wives more presents than George 
(does). 
27) John intends to buy more books than Mary. 
We claim that most speakers find all these sentences ambig- 
uous, the first in three ways, and the others in two. The 
simplest case is 25), where we can paraphrase the various 
readings as 25a-c): 
25a) Nobody talked more to John about Carol than Mary 
did. 
(Mary talks a lot to John about Carol.) 
25b) Nobody talked more to John than to Mary about 
Carol. 
(John is less popular than Mary when people want to 
hold conversations about Carol.) 
25c) Nobody talked more to John about Carol than they 
did about Mary. 
(Everyone prefers discussing Carol to discussing 
Mary when they talk with John.) 
In terms of the discussion from Section 3.4.1, ambiguity 
arises naturally as a result of the uncertainty concerning 
the identity of the element that "Mary" is intended to be 
compared with. By successively choosing the NPs 
"Nobody," "John," or "Carol," the reader can easily sat- 
isfy herself that each of the readings above can be derived. 
Sentence 26) also appears to be fairly clear: here, the 
distinction is essentially between the "strict" and "sloppy" 
readings, which can be represented as 26a) and 26b). 
26a) Few men give their wives more presents than George 
gives them. 
26b) Few men give their wives more presents than George 
gives his own wife. 
On a Montagovian account, we will get 26a) if the pronoun 
their is still unbound in the denotation of the VP give their 
wives q-proform I presents; if, on the other hand, it is bound 
to the variable representing the subject, we will get 26b). 
The hardest case definitely seems to be sentence 27). 
Here we have at least two readings, which we represent as 
27a) and 27b): 
27a) John intends to buy more books than Mary will buy. 
(John's plan is that, no matter how many books 
Mary has, he will buy more.) 
27b) John intends to buy more books than Mary intends to 
buy. 
(John and Mary both plan to buy specific numbers of 
books, that number being in John's case greater.) 
We can obtain the first of these using formula (***) from 
Section 3.2, as can be seen from the schematic derivation in 
Table 6. 
Unfortunately, there is no very satisfactory way to derive 
the wide scope reading 27b). The problem is that the 
comparative degree will end up in our account with lower 
scope than the modal operatorwants, irrespective of the 
level at which we carry out the contrasting operation; to 
derive 27b), however, it needs to have scope over the whole 
clause. Although one can define an ad hoc rule that raises 
the scope of the comparative quantifier, this goes very 
much against the spirit of our treatment; a slightly more 
attractive possibility may be to introduce alternative "wide- 
scope" versions of formulas (*), (**) and (***) from 3.2. 
For example, (*) would become 
3 N,N'.4¢'(A~,{N}) & ~" (A2',{N'}) & ~'(N,N') 
The problem is of course to find conditions defining when 
the wide-scope formulas are applicable. One idea might be 
Table 6. "Narrow Scope" Interpretation of Sentence 27 
1. buy q-proform I books 
2. buy more books than 
mary 
3. wants to buy more 
books than mary 
4. john wants to buy more 
books than mary 
~x.ql (book',~y.buy'(x,y)) 
?,x.{N I {N' I more(N,N')} 
(book'),y.buy'(mary,y))} 
(book',Xy.buy'(x,y)) 
~,x.want'(x,{N I {N' I more 
(N,N')}(book',Xy.buy'(mary,y))} 
(book'),y.buy'(x,y))) 
want'(john; 
{N \[ {N' \[ more(N,N')} 
(book', Xy.buy'(mary,y))} 
(book', hy.buy'(x,y))) 
Computational Linguistics Volume 16, Number 2, June 1990 97 
Mammy Rayner and AmeHe Banks An Implementable Semantics for Comparative Constructions 
to allow their use when the comparative occurs in an 
embedded S or VP (as it does here), but the whole topic 
clearly needs more study. 
3.5 IMPLEMENTATION ISSUF~ 
We first discuss the syntactic level; the main implementa- 
tion problems here are caused by various kinds of long- 
range dependencies. Apart from normal "WH-movement" 
dependencies in questions and relative clauses, we have the 
following: 
1. Dependency between comparative head and compara- 
tive complement. Normally, the head is separated from 
its associated complement in surface syntax, even though 
it conceptually forms a constituent with it. 
2. Dependencies associated with missing complements in 
S- and VP-operators, which can be arbitrarily deeply 
nested. These appear to be very similar to WH- 
movement dependencies. 
3. "Verb anaphora" dependencies: as is well known, cer- 
tain verbs (in English do, be, can, etc.) can act anaphor- 
ically for verb phrases. We treat a comparative comple- 
ment consisting of an NP together with one of these 
verbs as essentially equivalent with the NP on its own, 
except that it is forced to contrast against an NP which 
is a subject in a clause whose main verb is a suitable 
antecedent. The verbal antecedent relationship also ap- 
pears to lead to an unbounded dependency. 
4. "Quantifier binding" in clausal comparatives; we dis- 
cuss this in Section 4.1. 
All these forms of long-range dependency are handled by 
application of"threading" (Pereira 1983; Kartunnen 1986). 
Properly speaking, each distinct type of dependency ought 
to be associated with a distinct feature, which will be 
present in relevant constituents; by unifying features in 
different constituents against each other, information is 
propagated through the tree. In the XG-grammar in Appen- 
dix 2, we have cheated a little, by using the "extraposition 
list" feature to handle all of 1, 2, and 4 above. Although this 
can potentially lead to problems when dependencies "cross," 
we felt that the gain in simplicity made this compromise 
worthwhile. It is a simple matter to reorganize the gram- 
mar using different features. 
The semantic part of the grammar follows very closely 
the discussion in Section 3.3. The syntax-tree is first trans- 
formed into QLF form by the predicate syn to qlt/2; the 
QLF is then searched to find potential comparisons. That 
is, it first tries to extract a c-complement and store it, then 
tries to find a suitable contrast and finally constructs the 
comparison node and inserts it. 
4. CLAUSAL COMPARATIVES 
We borrow most of the basic principles in our treatment of 
clausal comparatives from Pinkham. Firstly, just as with 
phrasals, we assume that the comparative clause is nor- 
mally a modifier to a degree expression in the main clause; 
this assumption is also shared by Bresnan, though not by 
Friedrnann, who places the two clauses at the same level. 
Secondly, we assume that the "missing material" in the 
comparative clause is a null degree expression; this may 
possibly occur together with a null copy of the material 
modified by the head degree, which can be an adjective 
(example 29), an adverb (30), or a CN (31, 32). If the head 
degree is modifying an adjective in nonpredicate position, 
then it is obligatory to copy the CN (32). This idea is more 
or less borrowed from the discussion in Pinkham (pp. 
33-40). Adapting Pinkham's notation slightly, we write a 
null degree as Q, a null adjective or adverb as PRO^, and a 
null CN as PROcN. 
Our third principle is that the denotation of the COMP- 
OPERATOR is realized as a relation between the head 
degree and the Q, and appears conjoined with the compara- 
tive clause; this means that the Q originally will have wide 
scope over the clause it occurs in. Examples 28)-32) illus- 
trate our analysis: in each, the first item is the sentence, the 
second a schematic representation of the QLF, and the 
third a schematic representation of the logical form. In the 
QLF,. we enclose the comparative degree expression in 
parentheses. 
28) -lIohn bought more books than Mary bought records. 
28a) John bought (more than Mary bought Q records) 
books. 
28b) John bought {NIMary bought {N'} records & more 
(N,N')} books. 
29) .Irohn was happier in London than he was in New York. 
29a) John was (more than he was Q PRO A in New York) 
happy in London. 
29b) John was {Dlhe was {D'} happy in New York & 
more(D,D')} happy in London. 
30) John runs faster than Mary swims. 
30a) John runs (more than Mary swims Q PROA) fast. 
30b) John runs IDI Mary swims {D'} fast & more (D,D')} 
fast. 
31) John bought more books than Mary could carry. 
31a) John bought (more than Mary could carry Q PROcN ) 
books. 
31b) John bought {NlMary bought {N'} books & 
more(N,N')} books. 
32) John bought a more expensive vase than Mary bought. 
32a) John bought a (more expensive than Mary bought Q 
PRO A PROcN) vase. 
32b) John bought a {D I Mary bought a {D'} expensive vase 
& more(D,D')} expensive vase. 
It is fairly straightforward to implement a scheme of this 
kind in a framework that can handle long-range dependen- 
cies; in Section 4.1, we describe in more detail how this can 
be done. Before doing so, however, we take a brief look at 
the theoretical issues raised by our first and third assump- 
tions. 
With regard to the first assumption, suppose that we 
chose Friedmann's alternative and allowed the main and 
98 C~,mputational Linguistics Volume 16, Number 2, June 1990 
Manny Rayner and AmeHe Banks An Implementable Semantics for Comparative Constructions 
comparative clauses to be parallel. For instance, this Would 
give example 28) above a logical form something like 28c): 
28c) 3 N,N'. John bought N books & Mary bought N' 
records & more(N,N'). 
At first glance, this looks simpler. The problems arise when 
we introduce quantified NPs: thus if we replace John with 
something like no one, we are obliged to have more(N,N') 
within the scope of the quantifier representing the new NP. 
Of course, it is possible to require that such NPs always be 
given wider scope than the whole sentence (which is what 
Friedmann does), but to do so ignores the fact that an NP 
that has higher scope than the NP in which the compara- 
tive degree occurs normally has higher scope than the 
comparative degree as well. Making the comparative clause 
a modifier to the degree is from this point of view a more 
principled solution. 
We now consider our third assumption: what scope should 
the "inner" degree receive, and where should the condition 
linking the two degrees appear? Here, there are at least two 
reasonable choices. Alternative A, which is the one we have 
chosen, is to give the inner degree wide scope over the whole 
comparative clause, and conjoin the condition; alternative 
B is to give the inner degree its "natural" scope in the 
comparative clause, and make the relation between the two 
degrees a condition on it. This would give 28) the logical 
form shown in 28d) below. We marginally prefer A, but the 
issues involved are sufficiently unclear to merit further 
discussion. 
28d) "John bought {NIMary bought {N'lmore(N,N')} 
records} books. 
The drawback to A is, once again, that quantified NPs can 
cause problems: thus in a sentence like 33) we do not want 
the interpretation 33a) where most Swedes have traveled 
abroad the same number of times. 
33) Sven has visited Japan more times than most Swedes 
have traveled abroad. 
33a) Sven has visited Japan {N\[(most Swedes have trav- 
eled abroad N' times) & more(N,N')} times. 
To get around this, we have to postulate a rule that gives 
most Swedes wide scope over N'; this is not necessary if we 
choose B, where the natural scoping is 33b): 
33b) Sven has visited Japan {NI (most Swedes have trav- 
eled abroad {N' \[ more(N,N')} times)} times. 
If we are only dealing with extensional sentences, examples 
like 33) would thus make it seem that B was preferable. 
However, serious problems arise with the well-known exam- 
ple 34), due to Russell: 
34) I thought your yacht was longer than it is. 
Here we are more or less forced to choose an interpretation 
that gives the "inner" degree wide scope, i.e. 34a) 
34a) Your yacht is D' long & I thought that your yacht 
was {D \[more(D,D')} long 
If we use alternative A, it is possible to define scoping rules 
that produce this interpretation. However, this appears to 
be out of the question with alternative B; if the comparative 
clause is given wide scope, the degree comparison 
more(D,D') will be outside the scope of D. Although this 
conclusion seems inescapable, we are still somewhat reluc- 
tant to recommend a solution that is motivated entirely by a 
type of example that essentially never occurs in normal 
applications; readers interested in concrete implementation 
may well consider that the practical problems involved in 
formulating suitable scoping rules for alternative A out- 
weigh the theoretical loss of generality. It would appear 
that there is room for further research here: the reader is 
warned that the issues at stake are far from simple, as 
witness for example, Larson (1988). 
4.1 IMPLEMENTATION ISSUES 
Our proposed treatment of clausal comparatives can be 
implemented fairly simply in a framework that contains a 
mechanism for handling long-range dependencies; the ba- 
sic idea was first described in Klein (1980) in the context of 
an early version of GPSG, although we have modified it 
considerably. As already mentioned in Section 3.5, we will 
assume some kind of gap-threading idea. Pinkham observes 
(p. 81) that Quantifier Binding respects island constraints; 
the most obvious way to ensure this is to propagate it using 
the same mechanism as is used to handle WH-movement. 
A type of dependency we have already seen is that 
between the head of the comparative and the associated 
comparative clause; in this case, the problem is to pass 
rightward the information that a comparative clause is 
being looked for, which will end up as a modifier of a 
comparative degree expression somewhere to its left. Since 
the possible nature of the bound null proforms in the 
comparative clause depends on the structure of the associ- 
ated head, the two types of dependency are interrelated; 
just how, we explain below. We will call the feature associ- 
ated with the first kind of dependency the Q feature, and 
that associated with the second the C_complement fea- 
ture. The values of both of these will as usual be pairs of the 
form (Gaps. in, Gaps_out>. 
Let us now examine in detail how the scheme works. A 
comparative degree expression on a determiner, adjective, 
or adverb causes a non-null value of the C_complement 
feature to move rightwards; that is, a non-null Gaps_out 
on the degree expression successively gives rise to non-null 
Gaps_in values on other constituents to its right. This 
continues until the C_complement feature is "absorbed" 
by a non-null comparative complement. This will be a 
comparative complementizer, followed by a clause with 
suitable C_gaps features. 
The difficult part of the business is getting the right 
Gaps__in value for the Q feature on the comparative clause; 
in other words, making sure that the type of null proform 
that occurs in the comparative clause is one that matches 
the head of the comparison. To begin with, this means that 
the C_complement feature must contain information about 
the permissible values for the associated Q; the rules for 
Computational Linguistics Volume 16, Number 2, June 1990 99 
Mammy Rayner and Amelie Banks An Implementable Semantics for Comparative Constructions 
comparative degree constituents then need to specify this 
information in a suitable way. The following rules are those 
we have implemented: we write H for the head of the 
comparison and B for the bound null proforms, and enumer- 
ate four separate cases. 
1. If H is a determiner, then B is either 
a) aQ 
b) an NP whose determiner is a Q, and whose CN is a copy 
of the CN in the NP where H occurs. 
2. If H is modifying an adjective A in predicate position, 
then B is a Q modifying a copy of A. 
3. If H is modifying a verbal adverb A, then B is a Q 
modifying a copy of A. 
4. If H is modifying an adjective occurring in prenominal 
position in an NP N, then B is a copy of N, where H has 
been replaced by a Q. 
The rules above are a considerable simplification of 
Pinkham's, and there are in particular two major omis- 
sions. First, we copy constituents, instead of introducing 
bound proforms of type PRO A and PROcN. This usually 
makes no difference, but becomes significant in sentences 
like 35): if we copy, getting 35a), we do not guarantee that 
the two occurrences of them refer to the same set. 
35) John gave me more of them than I managed to eat. 
35a) John gave me more of them than I managed to eat (Q 
many of them). 
Secondly, and more critically for practical purposes, we 
have ignored the important distinction Pinkham draws 
between "narrow-scope" and "wide-scope" clausals (p. 
86-91). This was not done for any principled reason, but 
simply for lack of time; implementing it in a satisfactory 
way is an important part of the planned continuation of our 
research. 
5 OTHER ISSUES 
This concludes our analysis, with the exception of some 
minor points that we have postponed until now in the 
interests of expositional clarity. The first concerns noncoref- 
erence of compared objects, the second the question of 
whether "before" and "after" can be regarded as compara- 
tives. 
5.1 NONCOREFERENCE OF COMPARED OBJECTS 
Although speaker judgments tend not to be completely 
unanimous, there is a strong tendency to assume that 
comparison is always between different objects. This point 
becomes important when answering questions like 36). 
36) Has any king ruled as long as Gustav V? 
Most people find "Yes" meaning "Yes, Gustav V did" very 
misleading. To correct this, we make a slight adjustment in 
the analysis we have so far been using, so that an appropri- 
ate inequality is added when the logical form is produced 
from the reshaped quant tree. With this alteration 37) may 
be judged true even if John is present, and 38) may 
correctly be said of one of Mary's articles. 
37) Nobody here has read as many books as John. 
38) Mary has never written an article that is as bad as this 
one. 
5.2 "BEFORE" AND "AFTER" 
In English, the words before and after can display several 
of the features associated with comparatives. For example, 
sentences like 39) and 40) would appear to have interpreta- 
tions which could be represented as 39a) and 40a): 
39) John arrived before me. 
39a) .John arrived at a time T, T such that I arrived at a 
time T', T before T'. 
40) Henry VIII married Anne Boleyn after Catherine of 
Aragon. 
40a) Henry VIII married Anne Boleyn at a time T, T such 
that he married Catherine of Aragon at a time T', T 
after T'. 
Given examples like these, it is tempting to conclude that 
before and after are the "comparative forms" of adverbials 
that could be represented as "at-early-time" and "at-late- 
time." (Indeed, we made exactly this proposal in an earlier 
paper). However, it must be noted that, even if this analysis 
is correct, these adverbials would appear to be subject to 
certain :restrictions with regard to the comparative comple- 
ments they can take. For example, examples 41 a)-42a) are 
at best dubious, and should be contrasted with the correct 
41b)-42b): 
41a) *John arrived before I expected. 
41 b) John arrived earlier than I expected. 
42a) ?lVlary left before she needed to. 
42b) Mary left earlier than she needed to. 
It thus seems uncertain whether these words should be 
regarded as a special sort of comparative, or as belonging to 
a separate class of their own. The best way to resolve this 
question might perhaps be to consider cross-linguistic data; 
if it turns out that there are other languages that allow a 
full range of comparative complements to the analoguous 
words, it would presumably make sense to hypothesize that 
this was originally the ease for English, and that the 
missing constructions have simply fallen into disuse. Lack- 
ing at: 'the moment any such evidence, we refrain from 
furthe, r speculation on this subject. 
6 DATA FROM CORPUS ANALYSES 
To give our claims concerning relative frequencies of the 
various constructions some substance, we here give the 
results of a small corpus analysis. We took the texts of one 
English and one Swedish novel (Agatha Christie's... And 
Then There Were None; Selma LagerlSf's Kejsaren av 
100 Computational Linguistics Volume 16, Number 2, June 1990 
Manny Rayner and AmeUe Banks An lmplementable Semantics for Comparative Constructions 
Table 7. Data from Corpus Analysis 
Type of No. of 
construction examples Frequency 
1. Discourse comparative: 37 33.9 % 
2. Clausal: 7 6.4 % 
3. Contrastive: 45 41.3 % 
NP: 12 11.1% 
NP + " anaphoric verb": 4 3.7 % 
PP/Adverbial: I 0 9.1% 
S-operator: 5 '4.6 % 
VP-operator." 2 1.8 % 
Internal contrasting in AP: 11 10.1% 
Other: 1 0.9 % 
4. Determiner/Phrasal*: 6 5.5 % 
5. Verb of change + comparative*: 6 5.5% 
6. lnte comparative in att...*: 4 3.7% 
7. Other: 4 3.7 % 
Total: 109 
*Constructions like "more than two" or "less than half." 
*Constructions involving verbs like "grow" or "become" together 
with a comparative, as in "The room grew more cheerful" or "The 
road became harder." The problems involved in giving a correct 
semantics to such sentences derive in our opinion primarily from 
the verbs, and not from the comparatives. 
*A construction peculiar to Swedish, as in Det var inte tyngre i~n 
at__tt han kunde lyfta det. (Lit: "It was not heavier than that he 
could carry" it"). 
Portugalien), and manually extracted all sentences contain- 
ing comparatives. The results are summarized in Table 7. 
One striking fact is immediately apparent; the second 
commonest type of construction (No. 1, "discourse 
comparative") is actually one that we fail to cover! In our 
defense, however, we can at any rate claim that none of the 
other authors we have quoted appear to do so either. By 
discourse comparatives, we mean here comparatives where 
the associated comparative complement (in English nor- 
mally introduced by "than" or "as") is completely absent, 
and must be inferred from the context. Typical examples 
(taken from the Agatha Christie novel) follow below in 
sentences 43)-45). 
43) The abandoned creature.., committed a still graver 
sin. 
44) At eight o'clock the wind was blowing more strongly. 
45) I should be colder if I were dead. 
If the discourse comparatives are excluded, however, we 
are clearly capable of dealing with the vast majority of 
those left. Thus we feel fairly well justified in claiming that 
our treatment covers most of the common cases of compar- 
ison that occur in practice. 
7 SUMMARY AND FURTHER DIRECTIONS 
We have presented a treatment of comparative construc- 
tions that can claim to cover most of the commonly occur- 
ring cases, and is also capable of being implemented in a 
reasonably standard framework. Several of the key ideas 
are adapted from the theoretical work of Pinkham. In 
particular, we divide comparatives into two separate classes, 
clausals and phrasals. Clausals are interpreted by a version 
of Pinkham's "quantifier binding," which treats the miss- 
ing material in the comparative clause as null proforms 
bound by the comparative head (Section 4); phrasals are 
interpreted directly, using an adaption of Pinkham's "dis- 
tributive copying." The semantics of phrasals are summa- 
rized in the key formulas (*), (**), and (***) from Section 
3.2. 
At the beginning of Section 1, we presented a selection of 
comparative constructions, classified according to a more 
or less traditional approach. Table 8 shows the same exam- 
pies, this time with our classification. 
Particularly in our analysis of contrastive phrasals, we 
have gone to some lengths to describe how the ideas can be 
implemented in a reasonably efficient way. Here, the key 
idea has been to use a level of representation intermediate 
between syntax and logical form, which we call quasi- 
logical form, or QLF. At QLF level, phrasal comparatives 
are linked to their heads, but not to the constituent they are 
contrasted against. Rewriting rules then reshape the QLF 
until it is in a form where the comparative complements are 
at the same level as their "correlates." We also make use of 
features for defining long-range dependencies. These occur 
in several varieties: the bound null proforms in clausal 
comparatives, the missing sentential and VP complements 
in S- and VP-operators, and finally the comparative comple- 
ments, which in general are separated from their heads in 
surface syntax. 
Weighing up the strengths and weaknesses of our ap- 
proach, it is most natural to compare it with Friedmann's. 
Since Friedmann gives the comparative degree wide scope 
by default, her system needs extra rewriting rules for 
dealing with quantified NPs, both in the main clause and 
the comparative complement; we have argued that a "nar- 
row scope" default is in general preferable. We have also 
claimed that it is difficult in Friedmann's syntactically 
oriented approach to give a formulation of the comparative 
deletion rule that will extend to the harder cases. 
However, we have also seen, in Section 3.4.6, that our 
semantics runs into problems when attempting to derive the 
"wide-scope" reading for sentences like 27), where the 
comparative head occurs within the scope of a modal 
operator. Rather than postulate more ad hoc rewriting 
rules, we tentatively suggested that there may be alternate 
wide-scope versions of the key formulas from Section 3.2; 
this fits in well with Pinkham's remarks on wide- and 
narrow-scope clausals, which we refer to at the end of 
Section 4. Further investigation of these issues seems like 
one of the most important items on our agenda for future 
research. 
Another topic that urgently needs study is the interaction 
between comparatives and coordination; in certain cases, 
illustrated in sentences 46)-49), our first impression is that 
problems will occur. Since these obviously depend on the 
Computational Linguistics Volume 16, Number 2, June 1990 101 
Mammy Rayner and Amelie Banks An Implementable Semantics for Comparative Constructions 
Table 8. Typical Examples of Comparatives: Our Classification 
Clausal comparatives 
1) Mary was happier in New York than John was in London. 
2) John has more books than Mary has newspapers. 
3) The table is longer than it is wide. 
Contrastive phrasal comparatives 
4) John is taller than Mary. 
5) Few people run as fast as John. 
6) John bought more books than Mary. 
7) John was happier in New York than in 
London. 
8) Mary had more friends than John thought. 
9) John hit Mary harder than he meant to. 
10) More men than women bought the book. 
11) More people vote~l for the proposal than 
against. 
12) Mary needs a larger car than this Fiat. 
13) John ran faster than the world record. 
NP contrasting, adjective 
NP contrasting, adverbial 
NP contrasting, determiner 
PP contrasting 
S-operator contrasting 
VP-operator contrasting 
CN contrasting 
Preposition contrasting 
Internal contrasting in AP 
Internal contrasting in adverbial 
Determiner/phrasal 
14) More than 50 people signed the petition. 
Unclear cases: possibly contrastive phrasals 
15) John was born in the same city as Mary. 
16) John arrived before Mary. 
17) John likes Mary's house better than Mary John's. 
way in which we intend to handle coordination, we post- 
pone discussion to a later paper. 
46) No one could have a safer and more promising future 
than John. 
47) Mary is more attractive than Jane and Sarah. 
48) John visits the U.S. more often than Mary, but less 
frequently than Carol. 
49) The results were better than John claimed, but worse 
than we had hoped. 
Several other open questions also deserve mention. We 
have not been very specific in giving rules about where 
comparative complements may occur, and our treatment of 
phrasal contrastives also appear to allow more readings 
than really exist. It would certainly be desirable to find 
rules to eliminate these, or at least heuristics to say which 
readings can be regarded as unlikely. Another interesting 
question is whether it is possible to make the theory more 
compact, by collapsing the three formulas (*), (**), and 
(***) into one; they are so similar that this seems intu- 
itively quite feasible. We speculate that one may be able to 
do this in a framework like that described in Pereira and 
Pollack (1988), which allows conditional interpretation. 
Finally, we say a few more words about the "discourse 
comparatives" mentioned in Section 6. A cursory examina- 
tion of the example sentences would suggest that most of 
the missing comparative complements are of one of the 
following: "than previously," "than the one just mentioned," 
or "than is the case." For example, taking another look at 
sentences 43)-45), we can postulate that the complement is 
as given below in italics. 
43) The abandoned creature ... committed a still graver 
sin (than the one just mentioned). 
44) At eight o'clock the wind was blowing more strongly 
(than previously). 
45) I should be colder (than is the case) if I were dead. 
To fill in these missing complements, it as usual seems clear 
that pragmatic information is needed; researchers working 
in discourse theory may find these problems worth investi- 
gating:. 
ACICNOWLEDGMENTS 
We would like to thank the following people: several anonymous referees, 
for insighl:ful criticism of earlier versions of this paper; James Allen, Jerry 
Hobbs, Fernando Pereira and Remko Scha for useful comments and 
general encouragement; and, last but not least, Rune Gustavsson and 
Siwert Sundstrtim for helpfulness and flexibility with regard to financing 
our research. 
NOTES 
1. Earlier versions of several of the results herein have already been 
published in Banks (1986), Rayner and Banks (1986), Banks and 
Rayner (1987), and Rayner and Banks (1988a; 1988b). Since a 
number of important changes have been made, this report is to be 
taken as superseding all five. 
2. Current address: ZYX Sweden AB, Styrmansg. 6, 114 54 Stockholm. 
3. It appears, for example, that Japanese allows essentially the same 
range of comparative complements, and assigns a parallel semantics 
to them. 
4. We borrow this useful term from the Core Language Engine project 
(Alshawi et al. 1988; 1989). 
5. Those familiar with Montague semantics will realize that the version 
we are using here is in several respects fairly different from that in 
PTQ. Most important, we more or less completely dispense with the 
mechanisms for dealing with intentionality; since this isn't our con- 
cern here, we feel that it would only confuse the issue. Readers who 
disapprove of these ideas should have no great difficulty in converting 
out derivations into more conventional ones. 
6. There is some disagreement between applied and theoretical linguists 
concerning the correct division of credit here. Although Woods and 
his colleagues were the first people to realize the idea in practice, they 
made no attempt to justify their work in formal terms; this was later 
achieved independently by Cooper (1983), working within the Mon- 
tague grammar school. Our work has to some extent been influenced 
by both of these sources. 
7. Mean bastard. 
8. Excluding "discourse comparatives": see Sections 6 and 7. 
9. We would like to thank Carol Friedmann for bringing this example to 
our attention. 
Computational Linguistics Volume 16, Number 2, June 1990 lO3 
Manny Rayner and Amelie Banks An Implementable Semantics for Comparative Constructions 

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