Description Formation and Discourse Model Synthesis 
Bonnie Lynn Webber 
Bolt Beranek and Newman Inc. 
50 Moulton Street 
Cambridge MA 02138 <*i> 
I. Introduction 
Many researchers in linguistics, 
psychology, philosophy and artificial 
intelligence have recently begun to 
abandon a purely linguistic approach to 
definite anaphora <*2> in favor of a 
notion of reference into some kind of 
model of the discourse, cf. Karttunen 
\[1976\], Levin & Goldman \[1978\], Lyons 
\[1978\]. Stenning \[1975\]. My own research 
on definite anaphora (cf. Webber 
\[1978a&b\]) follows this approach, in 
particular making the following five 
assumptions: 
i. One objective of discourse is to 
enable a speaker to communicate to a 
listener a model s/he has of some 
situation. Thus the ensuing 
discourse is, on one level, an 
attempt by the speaker to direct the 
listener in synthesizing a similar 
model. 
2. Such a discourse model can be viewed 
as a structured collection of 
entities, organized by the roles 
they fill with respect to one 
another, the relations they 
participate in, etc. 
3. The function of a definite anaphoric 
expression is to refer to an entity 
in the speaker's discourse model 
(DMs). <*3> In using a definite 
anaphor, the speaker assumes 
(a) that on the basis of the 
discourse thus far, a similar entity 
<*i>. The author's current address is: 
Department of Computer and Information 
Sciences, The Moore School, University of 
Pennsylvania, Philadelphia PA 19174. 
<*2>. Although I will soon explain what I 
mean precisely by "definite anaphora", the 
term basically denotes a function that 
some types of syntactic expressions can 
serve. Expressions which can function as 
definite anaphors include definite 
pronouns and definite descriptions. Other 
roles that definite pronouns and 
descriptions can fill are discussed in 
Geach \[1962\], Partee \[1972\], Norman & 
Rumelhart \[1975\] and Webber \[1978a\]. 
<*3>. A similar assumption is made by 
Karttunen \[1976\], Levin & Goldman \[1978\], 
Lyons \[1978\] and Stenning \[1975\]. 
will be in the listener's model 
(DML) as well and (b) that the 
lis£ener will be able to access that 
entity via the given definite 
description or definite pronoun. 
4. The referent of a definite anaphor 
is thus an entity in DMs, which the 
speaker presumes to have a 
counterpart in DM L. Discourse 
entities may have the properties of 
individuals, sets, events, actions, 
states, facts, beliefs, hypotheses, 
properties, generic classes, typical 
set members, stuff, specific 
quantities of stuff, etc. 
5. In deciding which discourse entity a 
definite anaphor refers to, a 
listener's judgments stem in part 
from how the entities in DMT are 
described. (When a discourse ~ntity 
E is the referent of a definite 
anaphor A, one might distinguish 
that description of E conveyed to 
the listener by the immediately 
preceding text and consider it A's 
antecedent.) 
The point of making these assumptions 
explicit is to stress that insofar as 
reasoning about discourse entities is 
mediated by their descriptions, discourse 
entity descriptions are critical to 
anaphor resolution. 
Now one consequence of these 
assumptions about discourse models and 
reference is that the task of 
understanding definite anaphora can be 
decomposed into several complementary 
parts: 
i. deciding whether a definite pronoun 
or definite description is truly 
anaphoric (i.e., is intended to 
refer to some entity presumed to 
already be in DML) or whether the 
term fills some other role in the 
discourse; 
2. synthesizing a discourse model which 
is similar to that of the speaker 
and inhabited by similar discourse 
entities; 
42 
3. constraining the possible referents 
of a given anaphoric expression down 
to one possible choice - the 
"anaphor resolution" problem; 
4. determining what other functions a 
definite description is intended to 
fill besides enabling the listener 
to construct or get to its referent. 
While I cannot hope in this short 
paper to cover even one of these four 
sub-tasks, what I shall try to do is 
illustrate how the explicit data - i.e., 
the actual sentences of the discourse, 
produced by a particular person (or a 
particular computer program) in a 
particular situation - provide material 
for the model synthesis process. In 
particular, I shall show (i) how 
indefinite noun phrases are associated 
with the evocation of new discourse 
entities, independently of any 
higher-level expectations, and (2) how 
those new discourse entities will 
initially be described. I will claim that 
such an initial description (ID) is 
critical to both model synthesis and 
anaphor resolution since it allows the 
listener to reason appropriately about the 
discourse entity in order to assign it to 
an appropriate role vis-a-vis his or her 
higher-level expectations. <*4> 
Moreover, since it is possible for a 
discourse entity's current role assignment 
to be found incorrect, it is the entity's 
ID that allows it to be re-assigned to 
another role with respect to the 
listener's revised expectations. 
In Section 2 I will consider 
indefinite noun phrases vis-a-vis the 
discourse entities they evoke and how 
those entities are described. I will 
contrast them briefly with non-anaphoric 
definite noun phrases and then show that 
all determined noun phrases, including odd 
ones like "few orc eggs", "many lemon gum 
balls", etc. pattern after either 
definites or indefinites vis-a-vis the 
discourse entities they evoke and how 
those entities can be described. In 
Section 3 I will show how this approach to 
definite anaphora in terms of discourse 
entities and their descriptions can 
accommodate certain problematic cases of 
anaphoric reference that have been 
discussed in the linguistics and 
philosophic literatures - the famous 
"donkey" sentence (cf. Bartsch \[1976\], 
Edmundson \[1976\], Hintikka & Carlson 
\[1977\]) and the problem of reference in 
disjunctive contexts (cf. Karttunen 
\[1977\]). Finally, to show that it is not 
<*4>. From different points Of view, 
discussions of the relationship between 
the explicit text and higher-level 
organizing structures can be ~ found in 
Collins, Brown & Larkin \[1977\] and Webber 
\[1978b\]. 
just definite and indefinite noun phrases 
that can evoke entities in the listener's 
discourse model, I will illustrate in 
Section 4 an example of deictically-evoked 
entities and comment on the problem of 
describing them appropriately. 
2. Indefinite Noun Phrases and Discourse 
Entities 
Except after a copula, indefinite 
noun phrases <*5> may evoke a new 
discourse entity into a listener's 
discourse model. <*6> What I want to 
focus on here is appropriate IDs for them. 
Consider the following sentences. 
la. Wendy bought a yellow T-shirt that 
Bruce had liked. 
b. It cost twenty dollars. 
2a. Each third-grade girl brought a 
pelican to Wendy's house. 
b. She is roosting them on her front 
lawn. 
3a. If Bruce manages to catch a fish, 
b. he will eat it for dinner. 
4a. John didn't marry a Swedish woman. 
b. She was Norwegian. 
5a. Whether Bruce buys a mini-computer 
or an Advent TV, 
b. he will have to do the repairs on it 
himself. 
6. Every man who owns a donkey beats 
it. 
I claimed earlier that the initial 
description (ID) of a newly-evoked 
discourse entity is critical for both 
model synthesis and anaphor resolution, 
since the ID mediates all reasoning about 
the entity until its assignment to some 
role within the model. An entity's ID 
should imply neither more nor less about 
it than is appropriate. Now consider what 
an appropriate description would be for 
the discourse entity that "it" refers to 
in sentence lb. It is not "the yellow 
T-shirt that Bruce had liked", since 
sentence la. can be uttered truthfully 
even if Bruce had liked several yellow 
T-shirts (and both speaker and listener 
were aware of that fact). Nor is it "the 
yellow T-shirt that Bruce had liked and 
that Wendy bought", since sentence la. can 
<#5>. i will often .... refer to these as 
"existentials" because of their logical 
interpretation as existential quantifiers. 
<*6>. An indefinite noun phrase following 
a copula functions together with the 
copula as a predicate, e.g. 
Beverly is a bargain hunter. 
Bruce became a librarian. 
As such, it is purely descriptive and does 
not refer to any particular librarian or 
bargain hunter, cf. Kuno \[1970\]. 
43 
be truthfully uttered even if Wendy had 
bought several such T-shirts. What is an 
appropriate description for the referent 
of "it" is something like "the yellow 
T-shirt that Bruce had liked and that 
Wendy bought and that was mentioned in 
sentence la." 
What I am claiming is that in the 
case of a singular existential that is not 
within the scope of either negation, a 
universal quantifier, a hypothetical (e.g. 
"if", "suppose") or one of several other 
special contexts (cf. Webber \[1978a\]), the 
entity it evokes will be appropriately 
described via a conjunction of (i) the 
description inherent in the noun phrase 
(e.g. "yellow T-shirt that Bruce had 
admired"); (2) a predicate that embodies 
the remainder of the sentence (e.g. "which 
Wendy bought"); and (3) a predicate that 
relates that entity to the utterance 
evoking it (e.g. "which was mentioned in 
(or evoked by) sentence 6a."). This is 
the description that I am calling the 
entity's "initial description" or ID. 
Given how I specified its components then, 
it should not be surprising that I will 
claim that the ID of an 
existentially-evoked discourse entity can 
be derived from an appropriately 
structured sentence-level logical 
representation. Such a representation is 
independently motivated by its use in 
regular inference procedures. 
Using a somewhat simplified version 
of the formalism described in Webber 
\[1978a\], a simple rule can be stated for 
forming the ID of an existentially evoked 
discourse entity - i.e., 
(Ex:C) F x ==> 
(Ezi z = ix: Cx & F x & evoke S,x 
Here (Ex:C) is an example of restricted 
quantification, in which C represents an 
arbitrary predicate which x satisfies. Fx 
represents an arbitrary open sentence in 
which x is free; i stands for Russell's 
definite operator, iota; and S is the 
label assigned to the proposition on the 
left-hand side of the arrow. Informally, 
this rule, which I shall call \[RW-I\], says 
that if a proposition S states that there 
is a member x of class C which makes F. 
true, then there exists an individua~ 
describable as "the C which F's which was 
evoked by proposition S". This individual 
is taken to be the discourse entity evoked 
by the existential noun phrase. For 
example, let Y stand for the predicate 
corresponding to "yellow T-shirt that 
Bruce had liked". <*7> Then sentence la. 
can be represented simply as 
<*7>. I will soon be more precise about 
the representation of relative clause 
containing noun phrases. Here, where the 
descriptive part of the noun phrase can be 
treated as an unanalyzed unit, the 
predicate name Y is an adequate 
representation. 
(Ex:Y) . Bought Wendy, x 
Since this matches the left-hand side of 
the above rule, it follows that 
(Ez) . z = ix: Y x & Bought Wendy,x 
& evoke Sla,X 
That is, there is an individual 
describable as "the yellow T-shirt that 
Bruce had liked, that Wendy bought and 
that was evoked by sentence la." The 
discourse entity so described is the 
referent of "it" in sentence lb. 
Examples 2-6 illustrate singular 
indefinite noun phrases in some of the 
special contexts noted above. While I 
will only be discussing examples 5 and 6 
in this paper, notice that in all five 
cases, the entity evoked by the indefinite 
noun phrase is appropriately described by 
taking into account at least the three 
factors mentioned above. That is, in 
example 2 the referent of "them" can be 
described uniquely as "the set of 
pelicans, each of which, mentioned in 
sentence 2a., some third grade girl 
brought to Wendy's house." <*8> In 
example 3, the referent of "it" can be 
described as "the fish mentioned in clause 
3a. that Bruce has managed to catch, if 
Bruce has managed to catch a fish". In 
example 4, the negation appears intended 
to scope only "Swedish". Thus the 
discourse entity referent of "she" can be 
described as "the woman mentioned in 
sentence 4a. that John married". (We 
later learn in sentence 4b. that she is 
Norwegian rather than Swedish.) IDs for 
the two other existentially-evoked 
discourse entities in examples 5 and 6 
will be discussed in Section 3. 
Notice that a definite noun phrase in 
the same context as an indefinite noun 
phrase will also evoke a discourse entity, 
but one whose ID is somewhat different. 
To see this, consider the following 
sentences. 
<'8> A rule simii&r {o \[RWLi\] is g~ven 
in Webber \[1978a\] for existentials scoped 
by universals. In all, six such rules are 
given, covering 
i. independent existentials (sg/pl) 
"I saw {a cat, three cats} on the 
stoop." 
2. definite descriptions (sg/pl) 
"I saw the {cat, cats\] which hate(s) 
Sam." 
3. distributives 
"Each cat on the stoop hates Sam." 
"The three cats each scratched Sam." 
4. universally quantified existentials 
"Each boy gave each girl {a peach, 
three peaches}." 
5. class dependent definites 
"Each boy gave a woman he knew the 
{peach, two peaches} she wanted." 
6. class dependent distributives 
"Each boy I know loves every woman 
he meets." 
44 
7a. Wendy bought the yellow T-shirt that 
Bruce had liked. 
b. It cost twenty dollars. 
8a. Each third grade girl has seen the 
pelican on Wendy's lawn. 
b. They prefer it to the plastic 
flamingo she had there before. 
9a. John didn't marry the Swedish woman. 
b. He threw her over for a Welsh 
ecdysiast. 
In each case, an appropriate description 
for the discourse entity evoked by the 
singular definite noun phrase is just that 
singular definite noun phrase itself - 
"the yellow T-shirt that Bruce had liked", 
"the pelican on Wendy's lawn", "the 
Swedish woman". While it is certainly 
true that the definiteness of these noun 
phrases may be contingent on context 
(i.e., identifiability within the 
speaker's model of the underlying 
situation), nevertheless unlike entities 
evoked by indefinite noun phrases, those 
evoked by definites do not depend for 
their appropriate IDs on the particular 
sentences the definite noun phrases 
appeared in. 
The same characteristic behavior of 
definites and indefinites discussed for 
singular noun phrases holds for plural 
noun phrases as well. That is, while both 
indefinite and definite plural noun 
phrases evoke discourse entities, the 
unique initial descriptions that can be 
assigned to those entities will differ in 
the two cases. To see this, consider the 
following example. 
10a. I saw the guys from "Kiss" on TV 
today. 
b. I saw the three guys from "Kiss" on 
TV today. 
c. I saw all three guys from "Kiss" on 
TV today. 
d. I saw some guys from "Kiss" on TV 
today. 
e. I saw three guys from "Kiss" on TV 
today. 
ii. They were being interviewed by Dick 
Cavett. 
Sentences 10a-c each contains a definite 
plural noun phrase. That noun phrase 
should evoke a discourse entity into the 
listener's model, one appropriately 
described as "the (set of) guys from 
'Kiss'" This can be verified by 
following either of these sentences by 
sentence ii and considering what is the 
referent of the definite pronoun "they". 
<*9> 
<*9>. While Sentences 10b&c. prov{de the 
additional information that the number of 
guys in "Kiss" is three \[not actually true 
- BLW\], that information is not needed in 
order to describe the set uniquely. 
Sentences 10d&e, on the other hand, 
each contains an i~definite plural noun 
phrase. That noun phrase will evoke a 
discourse entity appropriately described 
as "the (set of) guys from 'Kiss' that I 
saw on TV today and that was mentioned in 
Sentence 10d(e)." This is because either 
sentence is consistent with there being 
other members of "Kiss" whom I didn't see 
on TV today, as well as other members whom 
I did see but whom I don't mean to include 
in my statement. <'10> Notice again that 
the set size information provided in 
sentence 10e. is not necessary for 
describing that set uniquely. However, it 
too may be useful later in resolving 
definite anaphora. 
An interesting point is that there 
seem to be no other patterns that English 
determiners follow vis-a-vis discourse 
entity IDs. To see this consider the 
following sentences. 
12a. Few linguists smoke since they know 
it causes cancer. 
b. Few linguists were at the party, but 
they drank more than the whole Army 
Corps of Engineers. 
13a. Many linguists smoke although they 
know it causes cancer. 
b. Not many linguists smoke since they 
know it causes cancer. 
c. Many linguists don't smoke since 
they know it causes cancer. 
In sentence 12a, the referent of "they" is 
the discourse entity appropriately 
described as "(the entire set of) 
linguists". That is, "few <x>s" can evoke 
the same discourse entity as the definite 
noun phrase "the <x>s". However as 
However, it should not be ignored, as it 
may be needed later in resolving a 
definite anaphor like "the three guys". 
<'10>. This latter point is a subtle one, 
and usage may vary from person to person. 
That is, some people intend an indefinite 
plural noun phrase contained in a sentence 
S - "Some <x>s P" - to refer to the 
maximal set - i.e., "the set of <x>s which 
P". Other people intend it to refer to 
some subset of that set - "the set of <x>s 
which P which I (the speaker) intended to 
mention in sentence S". For a system to 
cope with this variation in usage, it 
would be better for procedures to derive 
the latter, non-maximal set description, 
which is always appropriate. If a system 
is sophisticated enough to associate a 
"belief space" with the speaker (cf. Cohen 
\[1978\]), other procedures can later access 
that belief space (if necessary or 
desirable) to judge whether the maximal 
set interpretation might have been 
intended. (This will again become an 
issue when I discuss other determiners 
like "many" and "several".) 
45 
sentence 12b. shows, "few <x>s" can also 
pattern after the indefinite plural: the 
referent of "they" is the entity 
appropriately described as "the 
just-mentioned set of linguists who were 
at the party". (We learn from "few" that 
this set is small or smaller than the 
speaker expects.) 
"Many", on the other hand, seems to 
pattern only after the indefinite plural. 
In sentence 13a., the referent of "they" 
is appropriately described as "the 
just-mentioned set of linguists who 
smoke". (We learn from "many" that this 
set of linguists is large or larger than 
the speaker expects.) Sentence 13b. shows 
that the reverse polarity "not many" acts 
like "few" vis-a-vis evoking discourse 
entities: the referent of "they" is the 
entire set of linguists. However as 
sentence 13c. shows, a NEG which occurs in 
the sentence auxiliary does not effect 
this same change in behavior: "they" 
refers to the just-mentioned set of 
linguists who don't smoke. 
3. TWo Interesting Reference Problems 
Recall that the purpose of this paper 
is to point out the importance of 
description formation to both discourse 
model synthesis and reference resolution 
and to show that this process can, to an 
important degree, be formalized. I have 
taken as given the notion that a listener 
is using both the discourse and his or her 
knowledge of the world to synthesize a 
model of what s/he believes to underlie 
the discourse. Definite anaphora are 
viewed as means by which the speaker 
refers to entities in DM s that are 
presumed to have counterparts in the 
listener's model. What I want to show in 
this section is that this approach to 
definite anaphora can accommodate not only 
straight-forward cases as discussed above, 
but certain problematic cases as well. 
3.1 Parameterized Individuals 
The problem of formally 
characterizing the referent of "it" in 
examples like 6 below has often been 
discussed in the linguistics and 
philosophy literatures, cf. Bartsch 
\[1976\], Edmundson \[1976\], Hintikka & 
Carlson \[1977\]. 
6. Every man who owns a donkey beats it. 
The problem has been taken to be that 
while "it" intuitively seems related to 
the embedded noun phrase "a donkey", there 
is no way to represent this logically in 
terms of simple quantifier scoping. What 
I shall show is that an approach in terms 
of discourse entities and their IDs makes 
this intuitive relationship simple both to 
explain and to represent. 
First notice that this problem arises 
independently of how the matrix noun 
phrase is determined. 
14. A man I know who owns a donkey beats 
it. 
15. The man who owns a donkey beats it. 
16. Which man who owns a donkey beats 
it? 
17. No man who owns a donkey beats it. 
In all these examples, "it" seems 
intuitively related to "a donkey". 
Informally, one might describe its 
referent as "the just-mentioned donkey he 
owns", where "he" is bound to whatever 
value that "(each, a, the, which, no) man 
who owns a donkey" may take. But this is 
just a discourse entity of a rather 
special type - one with a parameterized 
ID, rather than a rigid one. I call such 
entities "parameterized individuals", 
borrowing the term from Woods & Brachman 
\[1978\]. <*ii> 
Notice that parameterized individuals 
behave somewhat differently from the 
"actual" discourse entities the sentences 
evoke. <'12> That is, parameterized 
individuals all have the same ID, 
independent of how the noun phrase 
containing the relative clause is 
determined. On the other hand, the actual 
discourse entities evoked by these 
sentences do not. For example, 
18a. Each man who owns a donkey beats it. 
it = the donkey he owns 
b. However, the donkeys are planning to 
get back at them. 
the donkeys = the set of donkeys, 
each of which some man 
who owns a donkey owns 
them = the set of men, each of whom 
owns a donkey 
19a. The man I know who owns a donkey 
beats it. 
it = the donkey he owns 
b. But the donkey is planning to get 
back at him. 
the donkey = the just-mentioned 
donkey that the man I 
know who owns a donkey 
owns 
him = the man I know who owns a 
donkey 
20a. Which man who owns a donkey beats 
it? 
<*ii>. The phrase "parameter~zed 
individual" is being used somewhat loosely 
to include "parameterized" sets, stuff, 
etc. For example, 
(i) No man who owns two donkeys beats 
them. 
them = the two donkeys he owns 
<'12>. By "actual" discourse entities, I 
mean ones that can be referred to 
anaphorically in subsequent sentences. 
46 
it = the donkey he owns 
-- "None" 
b.*Are the donkeys planning to get back 
at {him, them, ???}? 
the donkeys = ??? 
c.*Is the donkey planning to get back 
at {him, them, ???}? 
the donkey = ??? 
To show that this approach to 
definite anaphora in terms of discourse 
entities and their descriptions can 
explicate "donkey" sentences as well, I 
will have to introduce a bit more of the 
formalism described in Webber \[1978\]. 
That bit involves an extension of 
restricted quantification, cf. \[RW-I\] 
above. In restricted quantification, a 
quantification operator (e.g. ¥,E), the 
variable of quantification and the class 
it ranges over (noted implicitly as a 
predicate) constitute a structural unit of 
the representation. For example, "Every 
boy is happy" can be represented as 
(¥x:Boy) Happy x 
This is truth functionally equivalent to 
(¥x) . Boy x ==> Happy x 
Similarly "Some boy is happy" can be 
represented as 
(Ex:Boy) Happy x 
which is truth functionally equivalent to 
(Ex) Boy x & Happy x 
The extension I will introduce will 
permit the representation of noun phrases 
with relative clauses as well as simple 
noun phrases. Semantically, a relative 
clause can be viewed as a predicate. One 
way to provide for arbitrary predicates is 
through the use of the abstraction 
operator, represented as " " by Hughes & 
Cresswell \[1968\], following Church \[1941\]. 
For example, the noun phrase "a peanut" 
can be represented as 
(Ex:Peanut) 
while the noun phrase "a peanut that Wendy 
gave to a gorilla" can be represented as 
(Ex: ~(u:Peanut) \[(Ey:Gorilla) 
Gave Wendy,u,y\]) 
In this case 
~(u:Peanut) \[(Ey:Gorilla) 
Gave Wendy,u,y\] 
names a unary predicate which is true if 
its argument is a peanut that Wendy gave 
to some gorilla. 
Using this notation, sentence 6 can 
be represented as 
(¥x:~(u:Man) \[ (Ey:Donkey) . Own u,yJ) . 
Beat x,IT 
By applying rule \[RW-I\] to the embedded 
clause \[(Ey:Donkey) . Own u\], the entity 
evoked by the existential can be 
identified as 
iy: Donkey y & Own u,y & evoke S6.l,U 
"the just-mentioned donkey that u owns" 
<'13> 
As I mentioned above, the semantics of 
restricted quantification is such that the 
variable of quantification, here x, 
satisfies the predicate in the 
restriction. Thus if x satisfies 
~(u:Man) \[(Ey:Donkey) . Own u,y\], there 
must be an entity identifiable as 
iy: Donkey y & Own x,y & evoke S 6 l,y 
"the just-mentioned donkey x owns ~ 
This is a parameterized individual - 
parameterized by the variable in (¥x:...) 
- that is a possible referent for "it" in 
the matrix sentence - i.e., 
(¥x:~(u:Man) \[(Ey:Donkey) . Own u,y\]) 
Beat x, iy: Donkey y & Own x,y 
& evoke S6.l,y 
"Every man who owns a donkey beats the 
just-mentioned donkey he owns" 
I noted above that a sentence like 
"Every man who owns a donkey beats it" 
could sensibly be followed by a sentence 
like "However, the donkeys are planning to 
get back at them" (cf. example 18). Given 
that I have shown how to account for the 
referent of "it" in the first sentence in 
terms of discourse entities and their 
formally derivable descriptions, can the 
referent of "the donkeys" be account for 
in the same way? <'14> 
To show that it can, I need to 
present the rule for dealing with class 
dependent definite descriptions that I 
mentioned in footnote 8. This rule is 
motivated by examples such as 21, where 
the referent of "them" is presumably the 
discourse entity evoked by the noun phrase 
"the flower she picked", where "she" 
stands for the variable bound by "each 
girl in the class". 
<'13>. In labeling each clause of a 
complex sentence, I use the following 
convention: if the matrix clause is 
labelled S, its leftmost embedded clause 
will be labelled S.I, the leftmost 
embedded clause in S.I will be labelled 
S.I.I, etc. 
<'14>. I shall not take the time here to 
discuss the path from the phrase "every 
man who owns a donkey" to the discourse 
entity informally describable as "the set 
of men, each of whom owns a donkey", since 
it is rather straightforward, cf. Webber 
\[1978a\]. This entity is a possible 
referent for "them" in sentence 18b. 
47 
21a. Each girl in the class gave Ivan the 
flower she picked. 
b. He arranged them artfully in an 
empty Glenfiddach bottle. 
This is a definite noun phrase, but 
because of its binding to the 
distributively quantified noun phrase 
"each girl", it will evoke a discourse 
entity with the properties of a set rather 
than an individual (cf. example 8). In 
this case, it will be "the set of flowers, 
each of which was the flower that some 
girl in the class picked". Simplifying 
for brevity here, this rule can be written 
(Vx:K) . P x,iy:C x,y ==> 
(Ez) . z = {ul (Ex:K) . u = iy:C x,y} 
where K represents an arbitrary unary 
predicate which x satisfies and both P and 
C represent arbitrary binary predicates. 
The right-hand side of this rule implies 
that in case the left-hand side matches 
some sentence, there will be a discourse 
entity roughly describable as "the set of 
u's, each of which is the thing that 
stands in relation C to some member of K". 
Notice now that after the "it" is 
resolved in "Every man who owns a donkey 
beats it" (see above), the sentence 
matches the left-hand side of the above 
rule - i.e., "Every man who owns a donkey 
beats the just-mentioned donkey he owns. 
Thus it follows that there is a discourse 
entity describable as "the set of donkeys, 
each of which is the just-mentioned donkey 
that some man who owns a donkey owns" - 
i.e., 
{wl (Ex:~(u:Man) \[(Ey:Donkey) Own u,y\]) 
w = iz: Donkey z & Own x,z 
& evoke Sl8,Z} 
This is a possible referent for "them" in 
sentence 18b. 
3.2 Disjunction 
The other class of problematic 
examples that I want to discuss here in 
terms of discourse entities and their 
descriptions is one I first encountered in 
Karttunen \[1977\]. Karttunen presents 
examples like the following. 
22. If Wendy has a car or Bruce has a 
bike, it will be in the garage. 
23. Bruce can have either a bike or a 
car, but he must keep it in the 
garage. 
24. Either Bruce has ~a new car or he has 
borrowed his brother's. In any 
case, it is blocking my driveway. 
25. Whether Bruce buys a car or his 
brother buys a bike, he will have to 
keep it in the garage. 
The problem is again to determine just 
what it is that "it" refers to. 
I see two ways of approaching this 
problem in terms of discourse entities and 
their IDs. One way holds that in each 
sentence, each term of the disjunction 
evokes a different discourse entity into 
DML, each with a different ID: 
(22) "the car that Wendy has (if she has 
a car)" 
"the bike that Bruce has (if he has 
a bike)" 
(23) "the bike that Bruce will have (if 
he chooses a bike)" 
"the car that Bruce will have (if he 
chooses a car)" 
(24) "the new car that Bruce has (if 
Bruce has a new car)" 
"Bruce's brother's car" 
(25) "the car Bruce will have bought (if 
he buys a car)" 
"the bike Bruce's brother will have 
bought (if Bruce's brother buys a 
bike)" 
The truth of the disjunction (which seems 
in each case to be interpreted as 
exclusive "or") then guarantees there 
being one and only one entity in the model 
to which "it" refers. Notice that if the 
terms were conjoined rather than 
disjoined, the truth of the conjunction 
would imply the simultaneous existence of 
two entities within the model. In that 
case, either the referent of "it" would be 
ambiguous or the sentence would just be 
bizarre. 
The other, I think nicer, way of 
approaching the problem holds that each 
sentence evokes only a single discourse 
entity into the model, with the indecision 
(i.e., the disjunction) embodied in its 
ID. That ID is of the form "A if P, 
otherwise B". For example, the entity 
evoked by sentence 22 would be describable 
as "the car that Wendy has (if she has a 
car) or the bike that Bruce has 
otherwise"; that evoked by sentence 23 
would be describable as "the bike that 
Bruce will have (if he chooses a bike) or 
the car that Bruce will have otherwise"; 
that evoked by sentence 24, as "the new 
car that Bruce has (if he has a new car) 
or Bruce's brother's car otherwise"; and 
that evoked by sentence 25, as "the car 
Bruce will have bought (if he buys a car) 
or the bike Bruce's brother will have 
bought otherwise". 
One advantage to this approach is 
that additional properties which 
truthfully follow from either ID can be 
ascribed to the entity without committing 
oneself to one description or the other. 
This can be useful in anaphor resolution. 
For example, in sentence 24, the subject 
48 
of "block my driveway" must be a physical 
object, preferably large and somewhat 
mobile. This condition is satisfied by 
the discourse entity evoked by sentence 
24, independent of which ID is 
appropriate. 
Although there may be other ways to 
approach the problem of disjunction, the 
"donkey" problem, and the whole problem of 
definite reference in general, what I hope 
to have shown in these two sections is the 
robustness of an approach based on notions 
Of a discourse model, discourse entities 
and their formally derived descriptions. 
4. Conclusion 
In arguing for the importance of 
description formation to both discourse 
model synthesis and reference resolution, 
I concentrated on how indefinite noun 
phrases evoke new entities into the 
listener's discourse model and how their 
appropriate initial descriptions (IDs) 
could be derived from a formal 
sentence-level representation of the text. 
There are many other ways in which 
discourse entities can be evoked, and many 
interesting problems in forming 
appropriate descriptions of them. I will 
conclude therefore with a brief discussion 
of deictically-evoked discourse entities 
and the problem of describing them 
appropriately. 
The example comes from the children's 
book Babar Loses his Crown by Laurent de 
Brunhoff, and involves the following 
situation: Babar, King of the Elephants, 
decides to take his wife Celeste and his 
family on a trip to Paris. In packing for 
the trip 
"Babar puts his crown in a little 
red bag." (p.3) 
They travel by train and then by taxi to 
their hotel in Paris, and when they arrive 
"Celeste opens all the bags. Last 
of all, she opens the little red 
one. 'Look!' she cries. 'What is 
this? A flute! Babar! This is not 
your bag!' " (p.l~) 
Before this point in the story, there 
should have been one little red bag in 
DM L. Now there should be two. The first 
is the existentially-evoked discourse 
entity (say, e43 ) - "the little red bag 
mentioned in sentence <x> that Babar put 
his crown in". However if "this" on 
page 10 is not that entity, then it must 
be some other one (say, e~8) ~ How should 
it be described? Since "thlS presumably 
points to the little red bag Celeste is 
opening, e48 can appropriately be 
described as "the just-mentioned little 
red bag which Celeste is opening, which 
contains a flute and not Babar's crown, 
and which is not equivalent to e43". <'15> 
The problem here is to be able to 
articulate clearly what each of these 
properties derives from since they do not 
come from a single sentence. In this 
case, one must determine what things 
relevant to the story do or do not follow 
from e48's not being Babar's bag. 
* * * * * * * * 
In this paper, I have tried in as 
brief a way as possible to reveal an 
aspect of understanding definite anaphora 
that precedes the more frequently 
discussed problem of "anaphor resolution". 
This aspect involves accounting for what 
it is that definite anaphors refer to and 
how such things become available. I moved 
from the notion of reference into a model 
to problems of how that model is 
synthesized, and in particular, how the 
entities in it are appropriately 
described. In this endeavor, I focused on 
the initial descriptions (IDs) ascribed to 
existentially-evoked entities, briefly 
touching upon deictically-evoked entities 
as well. This paper has just skimmed the 
surface of a very large problem. In 
particular, one must still account for, 
inter alia, reference to actions, events, 
processes, stuff, quantities of stuff, 
etc.; relativization of descriptions to 
the speaker's beliefs (cf. Cohen \[1978\], 
Prince \[1978\]); additional ~ descriptions 
derived from the various roles in 
higher-level situations that an entity is 
assigned to; effects of tense, modality, 
negation, etc. on description formation; 
and how descriptions change over time. 
Some of these problems (as well as others) 
are discussed further in Webber \[1978a&b\], 
and much interesting work remains to be 
done. 

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