Generating Vague Descriptions 
Kees van Deemter 
ITRI, University of Brighton 
Lewes Road, Watts Building 
Brighton BN2 4G J, United Kingdom 
Kees. van. Deemter~itri. brighton, ac. uk 
Abstract 
This paper deals with the generation of definite 
(i.e., uniquely referring) descriptions containing se- 
mantically vague expressions ('large', 'small', etc.). 
Firstly, the paper proposes a semantic analysis of 
vague descriptions that does justice to the context- 
dependent meaning of the vague expressions in 
them. Secondly, the paper shows how this semantic 
analysis can be implemented using a modification of 
the Dale and Reiter (1995) algorithm for the gener- 
ation of referring expressions. A notable feature of 
the new algorithm is that, unlike Dale and Reiter 
(1995), it covers plural as well as singular NPs. This 
algorithm has been implemented in an experimental 
NLG program using ProFIT. The paper concludes by 
formulating some pragmatic constraints that could 
allow a generator to choose between different seman- 
tically correct descriptions. 
1 Introduction: Vague properties 
and Gradable Adjectives 
Some properties can apply to an object to a greater 
or lesser degree. Such continuous, or vague proper- 
ties, which can be expressed by, among other pos- 
sibilities, gradable adjectives (e.g., 'small', 'large', 
e.g. Quirk et al. 1972 sections 5.5 and 5.39), pose a 
difficult challenge to existing semantic theories, the- 
oretical as well as computational. The problems are 
caused partly by the extreme context-dependence of 
the expressions involved, and partly by the resis- 
tance of vague properties to discrete mathematical 
modeling (e.g., Synthese 1975, Pinkal 1995). The 
weight of these problems is increased by fact that 
vague expressions are ubiquitous in many domains. 
The present paper demonstrates how a Natural Lan- 
guage Generation (NLG) program can be enabled to 
-generate uniquely referring descriptions containing 
one gradable adjective, despite the vagueness of the 
adjective. Having presented a semantic analysis for 
such vague descriptions, we describe the semantic 
core of an NLG algorithm that has numerical data as 
input and vague (uniquely referring) descriptions as 
output. 
One property setting our treatment of vagueness 
apart from that in other NLC programs-(e.g. Gold- 
berg 1994) is that it uses ••vague properties for an 
exact task, namely the ruling out of distractors in 
referring expressions (Dale and Reiter 1995). An- 
other distinctive property is that our account allows 
the 'meaning' of vague expressions to be determined 
by a combination of linguistic context (i.e., the Com- 
mon Noun following the adjective) and nonlinguistic 
context (i.e., the properties of the elements in the 
domain). 
2 The Meaning of Vague 
Descriptions 
Several different analyses are possible of what it 
means to be, for example, 'large': larger than aver- 
age, larger than most, etc. But there is not necess- 
rily just one correct analysis. Consider a domain of 
four mice, sized 2,5,7, and 10cm. 1 In this case, for 
example, one can speak of 
1. The large mouse 
(= the one whose size is lOcm), and of 
2. The two large mice 
(= the two whose sizes are 7 and lOcm). 
Clearly, what it takes to be large has not been writ- 
ten in stone: the speaker may decide that 7cm is 
enough (as in (2)), or she may set the standards 
higher (as in (1)). A numeral (explicit, or implicit 
as in (1)), allows the reader to make inferences about 
the standards employed by the speaker3 More pre- 
cisely, it appears that in a definite description, the 
absolute form of the adjective is semantically equiv- 
alent with the superlative form: 
The n large mice - The largest n mice 
The large mice - The largest mice 
The large mouse - The largest mouse. 
1For simplicity, the adjectives involved will be assumed 
to be one-dimensional. Note that the degree of precision re- 
flected by the units of measurement affects the descriptions 
generated, and even the objects (or sets) that can be de- 
scribed, since it determines which objects count as having 
the same size. 
2Thanks are due to Matthew Stone for this observation. 
179 
This claim, which has been underpinned by a small 
experiment with human subjects (see Appendix), 
means that if a sentence containing .one element of 
a pair is true then so is the corresponding sentence 
containing the other. There are bound to be differ- 
ences between the two forms, but these will be taken 
to be of a pragmatic nature, having to do with felic- 
ity rather than truth (see section 5.2). 
An important qualification must be made with re- 
spect to the analysis that we propose: to simplify 
matters, we assume that the entire domain of rele- 
vant individuals is: available -and ~ha'g it-is-:this d~: 
main alone which is taken into account when the ad- 
jective is applied. In the case of the example above, 
this means that all mice are irrelevant except the 
four that are mentioned: no other knowledge about 
the size of mice is assumed to be available. 3 
2.1 A Formal Semantics for Vague 
Descriptions 
Let us be more precise. In our presentation, we will 
focus on the adjective 'large', without intended loss 
of generality. For simplicity, 'large' will be treated 
as semantically one-dimensional. 
i. 'The largest n mouse/mice'. Imagine a set 
C of contextually relevant animals. Then the NP 
'The largest n mouse/mice' (n > 0) presupposes 
that there is an S C_ C that contains n elements, 
all of which are mice, and such that (1) C - S ¢ ® 
and (2) every mouse in C - S is smaller than ev- 
ery mouse in S. If such a set S exists then the NP 
denotes S. The case where n = 1, realized as 'The 
\[Adj\]-est \[CN~g\]' (sg = singular), falls out automat- 
ically. 
ii. 'The largest mice'. This account can be 
extended to cover cases of the form 'The \[Adj\]-est 
\[CNpt\]' (pl = plural), where the numeral n is sup- 
pressed: these will be taken to be ambiguous be- 
tween all expressions of the form 'The \[Adj\]-est n 
\[CN\]' where n > 1. Thus, in a domain where there 
are five mice, of sizes 4,4,4,5,6 cm, the only possible 
value of n. is 2, causing the NP to denote the two 
mice of 5 and 6 cm size. 
iii. 'The n large mouse/mice'. We analyse 'The 
n \[Adj\] \[CN\]' (n > 0) as semantically equivalent with 
the corresponding NP of the form 'The \[Adj\]-est n 
\[CN\]'. 'The two large mice', for example, denotes a 
set of two mice, each of which is bigger than all other 
contextually relevant mice. 
iv. 'The large mice'. Expressions of this form can 
be analysed as being of the form 'The n \[Adj\] \[CN\]' 
for some value of n. In other words, we will take 
aln other words, only perceptual context-dependence is 
taken into account, as opposed to no,'maltve or functional 
context-dependence Ebeling and Gehnan (1994). 
them to be ambiguous or unspecific - the difference 
will not matter for present purposes - between 'The 
.2 large mice', 'The 3. large mice', etc. 
3 Generation of Crisp Descriptions 
Generation of descriptions covers a number of tasks, 
one of which consists of finding a set L of properties 
which allows a reader to pick out a given unique in- 
dividual or set of individuals. The state of the art 
is discussed in Dale and Reiter (1995), who present 
a computationally tractable algorithm for character- 
:. izing~i~dividuods.x This,algorithm-(henceforth_D&R), 
deals with vague properties, such as size, to some 
extent, but these are treated as if they were context- 
independent: always applying to the same sets of 
objects. 
In many cases, generating vague descriptions in- 
volves generating a plural and no generally accepted 
account of the generation of plural descriptions has 
been advanced so far. In the following section, there- 
fore, a generalization or D&R will be offered, called 
D& RPlur, which focuses on sets of individuals. Char- 
acterization of an individual will fall out as a special 
case of the algorithm. 
3.1 Plural Descriptions: Dale and Reiter 
generalized 
The properties which form the basis of D&Rpt~r are 
modeled as pairs of the form {Attribute,Value). In 
our presentation of the algorithm, we will focus on 
complete properties (i.e., (Attribute,Value) pairs) 
rather than attributes, as in Dale and Reiter (1995), 
since this facilitates the use of set-theoretic termi- 
nology. Suppose S is the 'target' set of individu- 
als (i.e., the set of individuals to be characterized) 
and C (where S C_ C) is the set of individuals from 
which S is to be selected. 4 Informally - and for- 
getting about the special treatment of head nouns - 
what happens is the following: Tile algorithm iter- 
ates through a list P in which the properties appear 
in order of 'preference'; for each attribute, it checks 
whether specifying a value for that attribute would 
rule out at least one additional member of C; if so, 
the attribute is added to L, with a suitable value. 
(The value can be optimized using some further con- 
straints but these will be disregarded here.) Individ- 
uals that are ruled out by a property are removed 
from C. The process of expanding L and contracting 
C continues until C = S. The properties in L can 
be used by a linguistic realization module to pro- 
duce NPs such as 'The white mice', 'The white mice 
• that arepregnant', etc. Schematically, the algorithm 
goes as follows: (Notation: Given a property Q, the 
set of objects that have the property Q is denoted 
\[\[o\]\].) 
• 1Note that C contains r, unlike Dale and Reiter's 'contrast 
set' C, which consists of those elements of the domain from 
which r is set apart. 
180 
L := (D {# L is initialized to the empty set #} 
For each Pie P do 
If S C_ \[\[Pi\]\] ~ :C ~ '\[l~Pi\]\] {# Adding Pi 
would remove distractors from C #} 
then do 
L := L O {Pi} {# Property Pi is added 
to L #} 
C := C n \[\[P~\]\] {# All elements outside 
\[\[Pi\]\] are removed from C #} 
If C = S then Return L {# Success #} 
Return Failure-'{S,d: All-properties in Phave been 
tested, yet C -7= S ~ } 
of one vague property. Case i of section 2.1, 'The 
largest n chihuahuas' will be discussed in some de- 
tail. All the others are minor variations. 
'Success' means that the properties in L are suffi- 
cient to characterize S. Thus, ~{\[\[Pi\]\] : Pie L} = S. 
The case in which S is a singleton set amounts to 
the generation of a singular description: D~RPIur 
becomes equivalent to D&R (describing the individ- 
ual r) when S in D&aPlur is replaced by {r}. 
D&RPlu r uses hill climbing: an increasingly good 
approximation of S is achieved with every contrac- 
tion of C. Provided the initial C is finite, D&apt~,- 
finds a suitable L if there exists one. Each property 
is considered at most once, in order of 'preference'. 
As a consequence, L can contain semantically redun- 
dant properties - causing the descriptions to become 
more natural, of. Dale and Reiter 1995 - and the al- 
gorithm is polynomial in the cardinality of P. 
Caveats. D&RPtur does not allow a generator to in- 
clude collective properties in a description, as in 'the 
two neighbouring houses', for example. Furthermore, 
D~l-tPlur cannot be employed to generate conjoined 
NPs: It generates NPs like 'the large white mouse' 
but not 'tile black cat and the large white mouse'. 
From a general viewpoint of generating descriptions, 
this is an important limitation which is, moreover, 
difficult to overcome in a computationally tractable 
account. In the present context, however, the lim- 
itation is inessential, since what is crucial here is 
the interaction between an Adjective and a (possibly 
complex) Common Noun following it: in more com- 
plex constructs of the form 'NP and the Adj CN', 
only CN affects the meaning of Adj. 5 There is no 
need for us to solve the harder problem of finding an 
efficient algorithm for generating NPs uniquely de- 
scribing arbitrary sets of objects, but only the easier 
problem of doing this whenever a (nonconjunctive) 
NP of the form 'tile Adj CN' is possible. 
4 Generation of Vague Descriptions 
\Ve nOw turn our attention to extensions of D&RPlur 
that generate descriptions containing the expression 
~\[n "The elephant and the big mous(,', for example, the 
mouse does not have to be bigger than any elephant. 
Superlative adjectives. First, 'The largest chi- 
huahua'. We will assume that size is stored (in the 
KB that forms the input to the generator) as an at- 
tribute with exact numerical values. We will take 
them to be of the form n crn, where n is a positive 
natural number. For example, 
type = dog, chihuahua 
• co.lou_v ~_blac, k~ blue, yellow 
size = lcm, 2cm, ..., 10cm. 
With this KB as input, D~R allows us to generate 
NPs based on L = {yellow,chihuahua,9~n}, for ex- 
ample, exploiting the number-valued attribute size. 
The result could be the NP 'The 9cm yellow chi- 
huahua', for example. The challenge, however, is 
to generate superlatives like 'The largest yellow chi- 
huahua' instead. 
There are several ways in which this challenge 
may be answered. One possibility is to replace 
an exact value like 9cm, in L, by a superlative 
value whenever all distractors happen to have a 
smaller size. The result would be a new list L = 
{yellow,chihuahua,largestl}, where 'largestt' is the 
property 'being the unique largest element of C'. 
This list can then be realized as a superlative NP. 
We will present a different approach that is more 
easily extended to plurals, given that a plural de- 
scription like 'the 2 large mice' does not require the 
two mice to have the same size. 
Suppose size is the only vague property in the KB. 
Vague properties are less 'preferred' (in the sense 
of section 3.1) than others (Krahmer and Theune 
1999).6 As a result, when they are taken into consid- 
eration, all tile other relevant properties are already 
in L. For instance, assume that this is the KB, and 
that the object to be described is c4: 
type(cl, c~. c3, c,l) =chihuahua 
type(ph) =poodle 
size(c1 )=3cnl 
size(c.2)=hcnl 
size(ca)=8cm 
size(c4) =size(ps) =9cm 
At this point, inequalities of tile form size(x) > 
m cm are added to the KB. For every value of 
,the form n ~n oecuring in-the oldKB, all..inequat- 
ities of the form size(x) > n an are added whose 
truth follows from the old I<B. Inequalities are more 
6Note, by contrast, that vague properties tend to be real- 
ized first (Greenbaum et al. 1985, Shaw and Hatzivassiloglou 
1999). Surface realization, however, is not the topic of lids 
paper. 
181 
preferred than equalities, while logicaUy stronger in- 
equalities are more preferred than logically weaker 
ones. 7 Thus, in order of preference .... 
size(c4),size(ps) > 8cm 
size(c3),size(c4),size(ps) > 5cm 
size (c2),size(ca ),size(c4 ),size(p5) > 3cm. 
The first property that makes it into L is 'chi- 
huahua', which removes Ps but not ca from the con- 
text set. (Result: C = {cl,...,c4}.) Now size is 
taken into account, and the property size(x) > 8cm 
singles out c4..The .resulting.listA s L =,~cchihuahua , 
> 8cm}. This implies that c4 is the only chihuahua 
in the KB that is greater than 8cm and consequently, 
the property size(x) > 8cm can be replaced, in L, by 
the property of 'being larger than all other elements 
of C'. The result is a list that may be written as 
L = {chihuahua, largesh }, which can be employed 
to generate the description 'the largest chihuahua'. 
Plurals can be treated along analogous lines. Sup- 
pose, for example, the facts in the KB are the same 
as above and the target set S is {ca, c4}. Its two ele- 
ments share the property size(x) > 5cm. This prop- 
erty is exploited by n&Rm~ to construct the list 
L = {chihuahua,>5cm}. Analogous to the singular 
case, the inequality can be replaced by the property 
'being a set all of whose elements are larger than 
all other elements of C' (largestm for short), leading 
to NPs such as 'the largest chihuahuas'. Optionally, 
the numeral may be included in the NP ('the two 
largest chihuahuas'). 
- 'Absolute' adjectives. The step from the su- 
perlative descriptions of case i to the analogous 'ab- 
solute' descriptions is a small one. Let us first turn 
to case iii, 'The n large mouse/mice'. Assuming the 
correctness of the semantic analysis in section 2, the 
NP 'The n large mouse/mice' is semantically equiv- 
alent to the one discussed under i. Consequently, 
an obvious variant of the algorithm that was just 
described can be used for generating it. (For prag- 
matic issues, see section 5.2) 
Finally. case iv, 'The large mice'. Semantically, 
this does not introduce an 3" new problems, since 
it is to case iii what case ii is to case i. Accord- 
ing to the semantic analysis of section 2.1 'The 
large mice' should be analysed just like 'The n large 
mouse/mice', except that the muneral n is sup- 
pressed. This means that a simplified version (i.e., 
without a cardinality check) of the algorithm that 
takes care of case iii will be sufificient to generate 
descriptions of this kind. 
rE.g, size(x) > m is preferred over sZze(x) > n iff m > n. 
The preference for inequalities causes the generator to avoid 
the mentioning of measurements unless they are needed for 
the identification ~ff the target object. 
5 Conclusions and loose ends 
We have shown how vague descriptions can be gen- 
.. ~erated .that'.make.use-of-one vague-propeift~. We be- 
lieve our account to be an instructive model of how 
the 'raw data' in a standard knowledge base can be 
presented in English expressions that have a very dif- 
ferent structure. The numerical data that are the in- 
put to our algorithm, for example, take a very differ- 
ent form in the descriptions generated, and yet there 
is, in an interesting sense, no loss of information: a 
description has the same reference, whether it uses 
• ...:,..exaet~.anforroataon:(~he:3c~zz.mouse.) ~or ...~ague:. m,-- 
formation ('The large mouse'), s 
5.1 Limitations of the semantic analysis 
Our proposal covers the generation of vague descrip- 
tions 'from absolute values', which is argued in Dale 
and Reiter (1995, section 5.1.2) to be most practi- 
cally useful. When vague input is available (e.g., in 
the generation component of a Machine Translation 
system, or in WVSlWYM-style generation (Power and 
Scott 1998)), simpler methods can be used. Our own 
account is limited to the generation of definite de- 
scriptions and no obvious generalization to indefinite 
or quantified NPs exists. Other limitations include 
a. Descriptions that contain properties for other 
than individuating reasons (as when someone 
asks you to clean 'the dirty table cloth' when 
only one table cloth is in sight). This limitation 
is inherited directly from the D&R algorithm 
that our own algorithm extends. 
b. Descriptions containing more than one vague 
property, such as 'The fat tall bookcase', whose 
meaning is more radically unclear than that of 
definite descriptions containing only one vague 
term. (The bookcase may be neither the fattest 
nor the tallest, and it is not clear how the two 
dimensions are weighed.) 
c. Descriptions that rely on the salience of con- 
textually available objects. Krahmer and The- 
une (1998) have shown that a contextually 
more adequate version of D~:R can be obtained 
when degrees of salience are taken into account. 
Their account can be summarized as analysing 
'the black dog' as denoting the unique most 
salient object in the domain that is both black 
and a dog. (Generalizations of this idea to 
D&Rmu~ are conceivable but nontrivial since 
not all elements of the set S have to be equally 
salient.) Our own extensions of D&R (and per- 
haps O&Rmu~) could be 'contextualized' if the 
SThis may be contrasted with the vague expressions gem 
crated in (Goldberg et al. 1994), where there is a real -- and 
intended Ioss of information. (E.g., 'Heavy rain fell on Tues- 
day', bmsed on the information that the rainfall on 'lhlesday 
equalled ,15rnm.) 
182 
role of salience is changed slightly: focusing on 
the singular case, the algorithm can, for exam- 
ple, be adapted, to, legislate.that:'the, large(est) : 
mouse' denotes the largest of all those mice 
that are salient (according to some standard of 
salience). Note that this analysis predicts am- 
biguity when the largest mouse that is salient 
according to one standard is smaller than the 
largest mouse that is salient according to a more 
relaxed standard. Suppose, for example, 
then 'the large(est) mouse' may designate ei- 
ther m2 or m3 depending on the standards 
of salience used. What this illustrates is that 
salience and size are both vague properties, and 
that - as we have seen under point b - combin- 
ing vague properties is a tricky business. 
5.2 Pragmatics 
An experimental ProFIT (Erbach 1995) program has 
implemented the algorithms described so far, gen- 
erating different descriptions, each of which would 
allow a reader/hearer to identify an object or a set 
of objects. But of course, an NLG program has to do 
more than determine under what circumstances the 
use of a description leads to a true statement: an 
additional problem is to choose the most appropri- 
ate description from those that are semantically cor- 
rect. This makes NLG an ideal setting for exploring 
issues that have plagued semanticists and philoso- 
phers when they studied the meaning of vague ex- 
pressions, such as whether it can be true for two 
objects x and y which are indistinguishable in size 
that x is large and y is not (e.g. Synthese 1975). 
The present setting allows us to say that a statement 
of this kind may be true yet infelicitous (because 
they conflict with certain pragmatic constraints), 
and consequently to be avoided by a generator. 
As for the choice between the 'absolute'/superlative 
forms of the gradable adjective, we conjecture that 
the following constraints apply: 
C1. Distinguishability. Expressions of the form 
'The (n) large \[CN\]' are infelicitous when the 
smallest element of the designated set S (named 
x) and the largest CN smaller than all elements 
of S (named y) are perceptually indistinguish- 
able. 
C2. Natural Grouping. Expressions of the form 
'The (n) large \[CN\]' are better avoided when the 
difference in size between x and y is 'compara- 
tiveh small. One way of making this precise is 
by requiring that the difference hetween x and 
C3. 
y cannot be smaller than that between either 
x or y and one of their neighbouring elements. 
Consider, for. example,.: a domain .consisting .of 
mice that are lcm, lcm, 2cm, 7cm, 9cm and 
9cm large; then C2 predicts that the only felic- 
itous use of 'the large mice' refers to the largest 
three of the group. 
Minimality. Otherwise, preference is given to 
the absolute form. This implies that when ob- 
jects of only two sizes are present, and the differ- 
Salient (strict): ence is perceptually distinguishable, the abso- 
ml (2em);,m~.(Scm) ................ .~ • : .,~.~Ante~formds~pr.eferEedover:t~hes~perta'~iv~fovm. 
Salient (relaxed): (For example, in a domain where there are two 
ml (2cm), m2 (5cm), m3 (7cm); sizes of pills, we are much more likely to speak 
of 'the large pills' than of 'the largest pills'.) 
In s in which the superlative form is 
morphologically more complex than the abso- 
lute form, constraint C3 can be argued to follow 
from general Gricean principles (Grice 1975)). 
As for the presence/absence of the numeral, we 
conjecture that the disambiguating numeral (as 
in 'the n large mice' or 'the n largest mice') can 
be omitted under two types of circumstances: (1) 
when any ambiguity resulting from different values 
of n is likely to be inconsequential (see Van Deemter 
and Peters (1996) for various perspectives); (2) 
when the domain allows only one 'natural grouping' 
(in the sense of C2). Before and until a more 
accurate version of the notion of a natural grouping 
is available (perhaps using fuzzy logic as in Zim- 
mermann 1985), generators could be forbidden to 
omit the numeral, except in the case of a definite 
description in the singular. 
Appendix: A Supporting Experiment 
Human subjects were asked to judge the correctness 
of an utterance in a variety of situations. The ex- 
periment was set up to make plausible that, in a sit- 
uation in which only perceptual context-dependence 
(see section 1) is relevant, expressions of the form 
'the n. large CN' can be used whenever certain sim- 
ple conditions are fullfilled. Note that this (0) di- 
rection of the hypothesis is most directly relevant 
to the design of a generator, since we expect a gen- 
erator to avoid mistakes rather than ahvays use an 
expression whenever it is legitimate. 
Hypothesis (=>): In a situation in which 
the domain D represents the set of percep- 
tually relevant objects, an expression of the 
form 'the n large CN' (where n 2 2 1), can 
be used to refer to a set S of cardinality n 
if all objects in D - S are smaller than anv 
of the n.. 
183 
The experiment explores whether 'the n large CN' 
can refer to the n largest objects in the domain, 
whether or not this set of objects is held together by 
spatial position or other factors. Subjects were pre- 
sented with 26 different situations, in each of which 
they had to say whether the sentence 
The two high numbers appear in brackets 
would constitute a correct utterance. The literal text 
of our question was: 
Suppose you want to inform a hearer 
*.which numbers:.,irr~'a:,gi~ren.list:,appeav in- 
brackets*, where the hearer knows what 
the numbers are, but not which of them ap- 
pear in brackets. For example, the hearer 
knows that the list is 1 2 1 7 7 1 1 3 1. 
You, as a speaker, know that only the 
two occurrences of the number 7 appear 
in brackets: 1 2 1 (7) (7) 1 1 3 1. Our 
question to you is: Would it be *correct* 
to convey this information by saying "The 
two high numbers appear in brackets"? 
(...). 
All subjects were shown the 26 situations in the 
same, arbitrary, order. Each situation presented to 
the subjects contained a list of nine numbers. In 24 
cases, the lists had the following form: 
lllxyzlll, 
where each of x, y, z equalled either 6 or 9, and where 
there were always two numbers among x, y, z that 
appear in brackets. In 16 out of 24 cases, the two 
bracketed positions are right next to each other, al- 
lowing us to test whether spatial contiguity' plays 
any role. Subjects were presented with two addi- 
tional situations, namely 1 1 1 (6) 1 (7) 1 1 1 and 
1 1 1 (7) 1 (6) 1 1 1 in which, unlike the other 24 
situations, the two largest numbers are not equally 
large, to make sure that the descriptions do not re- 
quire the elements in their denotation to be similar 
in that respect. Our questions were presented via 
email to 30 third-year psychology/cognitive science 
students at the University of Durham. UK. all of 
whom were native speakers of English and ten of 
which responded. 
Results: Eight subjects responded in exact confor- 
mance with the analysis of section 2.1, marking all 
and only those five sequences in which the highest 
2 numbers appeared in brackets. Only two subjects 
deviated slightly from this analysis: one of the two 
(subject 9) described all the expected situations as 
'correct' plus the two cases in which two contiguous 
6-es appeared in brackets: the other subject (subject 
10) appears to have made a typing err~n, confusing 
two subsequent situations in the experiment? All 
other responses of subjects 9 and 10 were as pre- 
dicted. This means: tha t all .sub.jects except subject 
10 were consistent with our '=#' hypothesis. The ex- 
periment suggests that the converse of the hypoth- 
esis might also be true, in which it is claimed that 
expressions of the form 'the n large CN' cannot be 
employed to refer to the set S unless S consists of 
the n largest objects in D: 
Hypothesis (.¢=): In a situation in which 
the domain D represents the set of percep- 
t_..: .......... ~ ~.t.ually: relevmtt, ob_jects>a~:-expressionof t~he. 
form 'the n large CN' (where n _> 1), can 
only be used to refer to a set S of cardi- 
nality n if all objects in D - S are smaller 
than any of the n. 
Again disregarding subject 10, eight out of nine 
subjects act in accordance with Hypothesis .¢=, 
while only one appears to follow a somewhat more 
liberal rule. Given these findings, it appears to 
be safe to build a generator that implements both 
hypotheses, since none of our subjects would be 
likely to disagree with any of the descriptions 
generated by it. 
This experiment has evident limitations. In partic- 
ular, it has no bearing on the pragmatic constraints 
suggested in section 5.2, which might be tested in a 
follow-up experiment. 
Acknowledgements 
Thanks are due to: Richard Power for discussions 
and implementation; Emiel Krahmer, Ehud Reiter 
and Matthew Stone for comments on an earlier 
draft; Hua Cheng for observations on linguistic 
realization; Rosemary Stevenson and Paul Piwek 
for their help with the experiment described in the 
Appendix. 

References 
- Dale and Reiter 1995. R. Dale and E. Reiter. Con> 
putationat Interpretations of the Gricean Maximes 
in the Geueration of Referring Expressions. Co.qni- 
tive Science 18: 233-263. 
- Ebeling and Gelrnan 1994. Ebeling, K.S.. Gehnan 
S.A. 1994. Children's use of context in interpreting 
"big" and "little". Child Development 65(4): 1178- 
1192. 
- Erbach 1995. G. Erbach. Web page on the ProFIT 
programming , http://coli.uni-sb.de/ er- 
bach/formal/profit/profit.html. 
.... Goldberg et al. 1994. .E. Goldberg,.tN. Driedger, 
and R. Kitteridge. Using Natural-Language Pro- 
cessing to Produce Weather Forecasts. mEE Expert 
9 no.2: 45-53. 
- Greenbaum et al. 1985. "A Comprehensive Gram- 
mar of the English Language". Longman, Harlow, 
Essex. 
- Grice 1975. P. Grice. Logic and Conversation. 
In P. Cole and J. Morgan (Eds.), "Syntax and Se- 
mantics: Vol 3, Speech Acts"!- 43~-58. New Ym'k, 
Academic Press. 
- Krahmer and Theune 1999. E. Krahmer and M. 
Theune. Generating Descriptions in Context. In 
R. Kibble and K. van Deemter (Eds.), Procs. of 
workshop The Generation of Nominal Expressions, 
associated with the llth European Summer School 
in Logic, Language, and Information (ESSLLI'99). 
- Pinkal 1995. M. Pinkal. "Logic and Lexicon". Ox- 
ford University Press. 
- Power and Scott 1998. R. Power and D. Scott. 
Multilingual Authoring using Feedback Texts. In 
Proc. COLING/ACL, Montreal. 
- Quirk et al. 1972. R. Quirk, S. Greenbaum, and 
G. Leech. "A Grammar of Contemporary English". 
Longman, Harlow, Essex. 
- Shaw and Hatzivassiloglou 1999. Ordering Among 
Premodifiers. In Proes. of ACL99, Univ. Maryland. 
- Synthese 1975. Special issue of the journal Syn- 
these on semantic vagueness. Synthese 30. 
- Van Deemter and Peters 1996. K. van Deemter 
and S. Peters (Eds.) "Semantic Ambiguity and Un- 
derspecification". CSLI Publications, Stanford. 
- Zimmermann 1985. H. J. Zimmermann. "Fuzzy 
Set Theory - and its Applications". Kluwer Aca- 
demic Publishers, Boston/Dordrecht/Lancaster. 
