The detection and representation 
of ambiguities of intension and description 
Brenda Fawcett and Graeme Hirst 
Department of Computer Science 
University of Toronto 
Toronto, Ontario 
CANADA M5S 1A4 
Abstract 
Ambiguities related to intension and their consequent 
inference failures are a diverse group, both syntacti- 
cally and semantically. One particular kind of ambi- 
guity that has received little attention so far is 
whether it is the speaker or the third party to whom 
a description in an opaque third-party attitude 
report should be attributed. The different readings 
lead to different inferences in a system modeling the 
beliefs of external agents. 
We propose that a unified approach to the 
representation of the alternative readings of 
intension-related ambiguities can be based on the 
notion of a descriptor that is evaluated with respect 
to intensionality, the beliefs of agents, and a time of 
application. We describe such a representation, built 
on a standard modal logic, and show how it may be 
used in conjunction with a knowledge base of back- 
ground assumptions to license restricted substitution 
of equals in opaque contexts. 
1. Introduction 
Certain problems of ambiguity and inference failure 
in opaque contexts are well known, opaque contexts 
being those in which an expression can denote its 
intension or underlying concept rather than any par- 
ticular extension or instance. For example, (1) 
admits two readings: 
(1) Nadia is advertising for a penguin with whom she 
could have a long-term meaningful relationship. 
On the transparent (or extensional or de re) reading, 
there is some particular penguin that Nadia is after: 
(2) Nudia is advertising for a penguin with whom she 
could have a long-term meaningful relationship, 
whom she met at a singles bar last week and fell 
madly in love with, but lost the phone number of. 
On the opaque (or intensional or de dicto) reading, 
Nadia wants any entity that meets her criteria: 
(3) Nadia is advertising for any penguin with whom 
she could have a long-term meaningful relation- 
ship. 
On this reading, the rule of existential generalization 
fails; that is, we cannot infer from (3), as we could 
from (2), that: 
(4) There exists a penguin with whom Nudia could 
have a long-term meaningful relationship 
Another rule of inference that fails in opaque con- 
texts is substitution of equals; (5) and (6) do not per- 
mit the conclusion (7): 
(5) Nadia believes that the number of penguins cam- 
paigning for Greenpeace is twenty-two. 
(6) The number of penguins campaigning for Green- 
peace is forty-eight. 
(7) =/~ Therefore, Nadia believes that forty-eight is 
twenty-two. 
Although these facts are familiar, little research 
has been done on how a practical NLU system can 
detect and resolve intensional ambiguities (which can 
occur in many constructions besides the 'standard' 
examples; see Fodor 1980, Fawcett 1985), and con- 
trol its inference accordingly. The same is true of 
certain other complications of opaque contexts that 
are of special relevance to systems that use explicit 
representations of knowledge and belief. In particu- 
lar, the interaction between intensional ambiguities 
192 
and the beliefs of agents has not been studied. The 
present work is a first step towards rectifying this. 
2. Attributing descriptions 
Previous linguistic systems that dealt with opaque 
contexts, such as that of Montague (1973), have 
taken a God's-eye view, in the sense that the speaker 
and listener are assumed to have perfect knowledge, 
as are, in certain ways, the people of whom they 
speak. No account is taken of the limits of the 
knowledge or beliefs of the agents involved. 
To see that beliefs are a complicating factor, con- 
sider the following sentence, usually considered to be 
two ways ambiguous -- transparent or opaque: 
(8) Nadia wants a dog like Ross's. 
These ambiguities, however, cross with an ambiguity 
as to which agent the description a dog like Ross's is 
to be attributed: to the speaker, or to Nadia (the 
agent of the verb of the sentence). This gives a total 
of four possible readings. To see the four cases, con- 
sider the following situations, all of which can be 
summarized by (8): 
(9) Transparent reading, agent's description: 
Nadia sees a dog in the pet store window. "I'd 
like that dog," she says, "It's just like Ross's." 
The speaker of (8), who need not be familiar with 
Ross's dog, reports this. 
(10) Transparent reading, speaker's description: 
Nadia sees an animal in the pet store window. 
"I'd like that," she says. Nadia is not aware of 
it, but the animal is a dog just like the one Ross 
owns. The speaker of (8), however, knows Ross's 
dog (and believes that the listener also does). 
(11) Opaque reading, agent's description: 
Nadia feels that her life will be incomplete until 
she obtains a dog. "And the dog that would be 
perfect for me," she says, "Is one just like the one 
that Ross has." The speaker of (8), not neces- 
sarily familiar with Ross's dog, reports this. 
(12) Opaque reading, speaker's description: 
Nadia feels that her life will be incomplete until 
she obtains a pet. "And the pet that would be 
perfect for me," she says, "Is a big white shaggy 
dog, with hair over its eyes." N~lia is not aware 
of it, but Ross owns a dog just like the one she 
desires. The speaker of (8), however, knows 
Ross's dog (and believes that the listener also 
does). 
The agent's-description readings permit the inference 
that Nadia believes that she (either intensionally or 
extensionally) wants a dog like Ross's; the other 
readings do not. Making the distinction is thus cru- 
cial for any system that reasons about the beliefs of 
other agents, such systems being an area of much 
current concern in artificial intelligence (e.g., 
Levesque 1983, Fagin and Halpern 1985). 
Another complicating factor is the time at which 
a description is to be applied. The above readings 
assumed that this was the time of the utterance. 
The intensional readings, however could be referring 
to the dog that Ross will get or (not included in the 
examples below) once had: 
(13) Opaque reading, agent's description, future appli- 
cation: 
Nadia has heard that Ross will buy a dog. Want- 
ing one herself, and trusting Ross's taste in can- 
ines, she resolves to buy whatever kind he buys. 
(14) Opaque reading, speaker's description, future 
applic atio n: 
Nadia finds English sheepdogs attractive, but 
none axe available. She therefore intends to pur- 
chase some other suitably sized dog and spend 
her weekend gluing long shaggy hair onto it. 
Nadia is not aware of it, but Ross owns a dog 
just like the one she wants to end up with. The 
speaker, knowing Ross's dog, can describe Nadia's 
desire as that of having an object that will at 
some future time be describable as a dog like 
Ross's. 
The description in an intensional reading may also 
be used to refer to different entities at different 
times. 
(15) Opaque reading, agent's description, repeated 
application: 
Ross buys a new type of dog every year or so. 
Desperately wanting to keep up with canine 
fashion, Nadia declares her intent to copy him. 
Whatever dog Ross has at any given time, Nadia 
wants to have the same kind. 
We have not been able to find an example in which 
repeated application of the speaker's description 
gives a natural reading. Extensional readings always 
seem to refer to the present time. 2 Thus, there are at 
2It may be objected that an extensional future-application reading 
is also possible. This would be like (14), except that Nadia has 
some particular dog in mind for the cosmetic alterations. If we al- 
low Nadia to use this method repeatedly upon a particular dog, 
then an extensional reading corresponding to (15) would be 
193 
least seven readings for Nadia wants a dog like 
Ross 's. 3 
3. Other intensional ambiguities and 
inference failures 
There are other kinds of intension-related inference 
failures besides those mentioned in the previous sec- 
tions. For example, some opaque contexts forbid 
inferences from postmodifier deletion, while others 
permit it. Both readings of (16) entail the less 
specific (17) (which preserves the ambiguity of (16)): 
(16) Nadia is advertising for a penguin that she hasn't 
already met. 
(17) Nudia is advertising for a penguin. 
However, the same cannot be done with (18): 
(18) Nadia would hate for there to be a penguin that 
she hasn't already met. 
(19) =\]~Nazlia would hate for there to be a penguin. 4 
The examples above have all involved explicit or 
implicit propositional attitudes and such contexts are 
apparently necessary for ambiguities of attribution of 
description and the associated possible inference 
failure and for problems of postmodifier deletion. 
However, there are many other kinds of context in 
which other intension-related ambiguities and infer- 
ence failures can occur. For example, existential 
generalization can also fail in contexts of similarity 
and possibility: 
(20) Nadia is dressed like a creature from outer space. 
(21) =~There is a creature from outer space whom 
derived. That is, Nadia wants her particular dog to once or re- 
peatedly become like Ross's dog. However, we don't see these 
readings as distinct from (14) and (15); Nadia's desire is clearly to- 
wards the goal of having a dog that matches a particular descrip- 
tion, rather than towards that of owning a particular dog. 
3Hofstadter, Clossman, and Meredith (1982) analyze a similar sen- 
tence for the case where the speaker and the agent are the same, I 
want the fastest car in the world, and derive five readings where 
we predict four. However, their two extensional readings are 
identical in our analysis, as they differ only in how many separate 
descriptions the agent has for the entity. 
4This example is based on one of Fodor's (1980: 188). Fodor 
claims that postmodifier deletion is never valid in an opaque con- 
text; as example (17) shows, this claim is too strong. The problem 
in (19) seems to be that would hate means wants not, and the dele- 
tion is invalid in the scope of a negation. 
Nadia is dressed like. 
(22) It is possible that a creature from outer space 
could interrupt your lecture at the most incon- 
venient moment. 
(23) =/~ There is a creature from outer space who could 
possibly interrupt your lecture at the most incon- 
venient moment. 
The kind of semantic irregularities that we are 
discussing are thus found in a large and syntactically 
diverse set of linguistic constructs. (See Fawcett 
(1985) for a long list, with discussion and examples.) 
Many seem to display idiosyncratic semantic features 
that could necessitate a broad range of operators in a 
representation, destroying any apparent homogeneity 
of the class. It is our suggestion, however, that these 
constructs can be processed in a uniform way. We 
argue that the diversity among the constructs can be 
accounted for by evaluating descriptors according to 
intensionality, agents, time, and states of affairs. 
Introducing the concept of a descriptor preserves the 
homogeneity of the class, while the dimensions along 
which descriptors may vary provide enough detail to 
differentiate among the particular semantics of the 
constructs. 
4. The descriptor representation 
In this section we introduce a representation 
designed to capture the different possible readings of 
opaque constructions. In developing the representa- 
tion, we have tried to move away from previous 
approaches to intensionality, such as that of Mon- 
tague (1973), which use truth conditions and mean- 
ing postulates, and which take no account of the 
beliefs or knowledge of agents. Influenced by recent 
work on situation semantics (Barwise and Perry 
1983, Lespe'rance 1986) and belief logics, we have 
aimed for a more 'common-sense' approach. 
In the representation, we take an intension to be 
a finite representation of those properties that 
characterize membership in a class, and by a descrip- 
tor we mean a non-empty subset of the elements of 
an intension (in practice, often identical to the e0m- 
plete intension). A descriptor provides access either 
to the intension of which it is a part or to its exten- 
sion. This eliminates the need of explicitly listing all 
the known properties of an entity; only properties 
194 
relevant to the discourse situation are mentioned. 
The representation is described in detail in 
Fawcett (1985); below we give a short description of 
the main points, and some examples of its use. 
The representation is based on conventional tem- 
poral modal logic. The general form of.a completed 
sentential clause is a proposition of the form 
(term-list) <predication>. 
The term-list, which can be empty, contains all the 
quantified terms except those which are opaque with 
respect to agents or time; the predication expresses 
the main relation among the various entities referred 
to. The intention is that the term-list provides the 
information to identify referents in the knowledge 
base, and the main predication asserts new informa- 
tion to be added to it. Usually the argument posi- 
tions of the predication will be filled by bound vari- 
ables or constants, introduced previously in the 
term-list. However, within temporal operator or 
agent scopes, argument positions may instead con- 
tain quantified terms. Term-list-predicate pairs may 
be nested inside of one another. 
Quantified terms arise from noun phrases. They 
have the general form 
(Det X." R(X)) 
where Det is a quantifier corresponding to the expli- 
cit or implicit determiner of the noun phrase, X is 
the variable introduced, and R(X) indicates restric- 
tions on X. In the examples below, we restrict our- 
selves to only three quantifiers -- indcf, def, and 
label, introduced by indefinite descriptions, definite 
descriptions, and proper nouns respectively. 5 
To this formalism, we add the following: 
• The agent scope marker ^. 
This marker can apply to a formula or term to 
indicate that any embedded descriptors must be 
evaluated with respect to the beliefs of the agents 
involved (that is, mentioned so far) at the point 
where the scope of begins. The speaker is 
assumed to always be available as an agent, and 
descriptors outside the scope of ^ are attributed 
only to the speaker. 
5For simplicity, we treat names as extensional in our examples. 
However, there is nothing to prevent an opaque treatment, in 
which the different agents are thinking of different individuals 
with the same name. 
• The intensional abstractor int-abs. 
The formula 
int-abs ( C, ( Quant Var : Description)) 
asserts that the quantified term Var is to have an 
intensional referent (i.e., an individual or universal 
concept), which is returned in C. If C is subse- 
quently used, then its referent is a universal (gen- 
eric) concept, which we do not discuss in this paper; 
see Faweett (1985) for details. If Vat is used 
instead, then the referent is an individual concept. 
(Without int-abs, use of Vat refers to an extension.) 
• Descriptors. 
The notation \[d X l indicates that the properties d 
are being used as a descriptor of entity X Thus its 
intensionality, time of application, and agent must 
be considered. (Variables over such descriptors are 
permitted, so we can manipulate them indepen- 
dently of the entities to which they might refer.) 
Thus, opacity with respect to agents and opacity 
with respect to time are both treated as scope ambi- 
guities, while intensionality is marked as a binary 
distinction. In general, all quantified terms are left- 
extraposed to the outermost term list. Those 
quantified terms marked as intensionally ambiguous 
may be prefixed by int-abs. Those quantified terms 
originating within the scope of the agent scope 
marker ^ may remain inside its scope and be 
evaluated relative to the agents available at that 
point. Similarly, those quantified terms originating 
in the scope of the temporal operators F and P 
(future and past) may stay inside their scope, thus 
indicating a future or past application of the descrip- 
tor. 
The following example shows the representations 
of the first four readings of (8) (i.e., those with the 
description applied at the time of the utterance), and 
an extensional counterpart. (In the examples, the 
quantifier indef corresponds to the English deter- 
miner a, and the quantifier label is used for proper 
nouns. The structure of the descriptor dog-like- 
Ross's, orthogonal to our concerns here, is not 
shown.) 
(24) Transparent reading, agent's description: 
There is a dog Nadia wants, and she describes it 
as being like Ross's dog. 
(label Y: Nadia) 
<want Y, ^ (indef X: \[dog-like-ross's X\]):> 
195 
(25) Transparent reading, speaker's description: 
There is a dog Nadia wants, and the speaker 
describes it as being like Ross's dog. 
(label Y : Nadia) 
(indef X: \[dog-like-ross's 4) 
<want Y, ^X~ 
(26) Opaque reading, agent's description: 
Nadia wants something she describes as being a 
dog like Ross's. 
(label Y : Nadia) 
<want Y, 
^ int-abs (C, (indef X: \[dog-like-ross's 4))> 
(27) Opaque reading, speaker's description: 
Nuciia wants something that the speaker describes 
as being a dog like Ross's. 
(label Y: Nadia) 
int-abs (C, (indef X: \[dog-like-ross's X~)) 
<wants Y, ^X> 
Note that the fourth reading has no representation in 
a conventional first-order modal language. For com- 
parison, here is a non-opaque sentence of the same 
structure. 
(28) Nadia buys a dog like Ross's. 
(label Y : Nadia) 
(indef X: \[dog-like-ross's X\]) 
<buy Y, X:> 
Within the scopes of the opaque operators F, P, 
and ^, special checks must be made before standard 
inference rules can apply. 6 We do nc'~ assume that all 
arguments are intensional; we favour a policy 
towards intensional scopes of "introduce when 
required" to minimize the amount of extra process- 
ing needed. Our use of the symbol ^ is quite 
different from that of Montague. For Montague, ^x 
denotes an object that is intensional. We instead use 
this notation to delimit the agent scope of an opaque 
construct; descriptors in x are potentially ascribed to 
any of the agents preceding the ^ marker. 
Our approach to determiners is a compromise 
between other common approaches. The first, com- 
mon in computational linguistics, is to represent 
determiners by three-place quantifiers of the general 
6This is analogous to the restricted rules that Montague presents 
for substitution of identicals and lambda conversion in his inten- 
sional logic (Dowty, Wall, and Peters 1981: 165). We seek a more 
flexible scheme that, rather than prohibiting inference, restricts its 
use to certain special cases. 
form 
d,t (., P(.)) 
where x is the variable introduced, R is the restric- 
tion on the variable, and P is the new predication on 
the variable. This reflects observations of Moore 
(1981) and others that determiners rarely have a 
direct correlation with the existential and universal 
quantifiers of first-order logic. In many of the mean- 
ing representations used with logic grammars (Dahl 
(1981), for example), determiners provide the basic 
structure of the meaning representation formula. 
The determiners are translated into quantifiers and 
are all left-extraposed (to be later scoped relative to 
one another on the basis of some reasonably simple 
set of rules). As a result, the main predication of a 
clause will always be nested in the rightmost predica- 
tion position. 
Another approach focuses more on the main verbs 
by first translating them into predicates, and subse- 
quently finding appropriate fillers for their arguments 
that contain the necessary quantifiers. However, this 
does not allow a convenient way to represent relative 
scoping ambiguities. Montague combines the two 
approaches. All quantifiers introduce two predicates: 
a restriction predicate and a main predication as in 
kR kP (3z (R{z} AND P{z})), 
which translates the determiner a. 
Our approach is a compromise. Quantified terms 
consist of a variable and restriction, but do not 
incorporate the main predication. All quantified 
terms (except those that are opaque with respect to 
time or agent) are left-extraposed and assimilated 
into a single list structure followed by a single main 
predication. 
5. Substitution of equals 
Given our descriptor logic, we can now turn to the 
question of when substitution-of-equals inferences 
can and can't be made. 
The failure of substitution of equivalent phrases 
appears to be a gradable notion; the degree of substi- 
tution allowed varies with the type of construct 
under consideration. We can think of a scale of sub- 
stitutivity, with the lower bound being a strictly de 
196 
dicto reading in which no substitutions are permitted 
and the upper bound a strictly de re reading in 
which co-extensional phrases can be substituted in 
any context. 
For example, sentences that refer directly to the 
form of the expression admit no substitution: 
(29) The Big Bopper was so called because of his size 
and occupation. 
(30) The Big Bopper was J. P. Richardson. 
(31) 5ff J. P. Richardson was so called because of his 
size and occupation. 
In sentences of propositional attitude, certain 
descriptors can be substituted for, provided the con- 
tent of the proposition, relative to the speaker and 
the hearer, is not affected. It is easy to recognize 
such cases, but not always easy to specify what exact 
criteria determine terms that are interchangeable. 
Consider: 
(32) Nadia thinks that the Queen of England is a 
lovely lady. 
(33) Nadia thinks that Queen Elizabeth is a lovely 
lady. 
(34) Nadia thinks that the titular head of the Church 
of England is a lovely lady. 
The assumption is that since the filler of the role 
Queen of England is not likely to change within the 
time of the conversation and the speaker, the hearer, 
and Nadia are all aware of who fills that role, it is 
acceptable to substitute the filler for the role and 
vice versa. Thus, sentence (33) can be inferred from 
(32). But to substitute the phrase the titular head of 
the Church of England, as in (34), seems to attribute 
more knowledge to Nadia than was in the original 
statement. 
The problem of substitution in opaque contexts 
stems from the failure to recognize how descriptors 
relate, and not, as in classical logical approaches, 
from the failure of expressions to be "co- 
intensional". The emphasis should be on identifying 
the relation between descriptors with respect to 
appropriate agents rather than on co-intensionality 
alone; in most cases co-intensionality is too strong a 
condition for substitution. Rather, the background 
assumptions of the discourse determine whether a 
substitution of one descriptor for another is 
permitted. 
A typical substitution replaces the target descrip- 
tor, dl, with an equivalent descriptor, d2, from the 
background assumptions, but otherwise preserves the 
form of the target sentence, i.e., 
RESULT ~ TARGET \[dl/d2\]. 7 
To see whether a descriptor substitution is valid in 
an opaque context, three factors must be checked in 
the following order: the intensionality of the descrip- 
tor, the time of reference of the descriptor, and the 
agents of the descriptor. We must establish the 
"level" of each factor in the target sentence and 
then determine whether the background assumptions 
authorize substitutions at that level. That is, we 
must relate the intensionality, time, and agent of the 
descriptor equivalence asserted in the background 
assumptions to those of the target descriptor, and 
then assert the intensionality, time, and agent of the 
descriptors in the resulting clause (after any substitu- 
tions). 
The background assumptions will have already 
been derived from earlier input (in a manner 
described by Fawcett 1985, section 5.5) and assimi- 
lated into the system's general knowledge base. In 
order to compare descriptors in the target to descrip- 
tors in the background assumptions, we extract the 
relevant aspects from the representation of each, and 
express them explicitly by the use of the following 
descriptor predicates, which can then be used to 
query the knowledge base. 
• dese (a, e, dl). 
Ascribes a particular descriptor to an individual; 
"agent a would use the descriptor dl to describe the 
entity e". 
• label (a, c, name). 
Indicates that the label name is known by agent a 
to be a label for the (individual) constant c. 
• time (t, e, dl). 
Asserts that descriptor dl describes entity e at 
time t. 
As an example, consider the four readings of this 
sentence in which the description is applied at the 
time of utterance: 
7Not all substitutions are of this form; see Fawcett 1985, section 
5.4. 
197 
(35) Nadia wants the fastest car in the world. 
speaker's description: 
E ^x> 
speaker% description: 
(i) Extensional reading, 
(label Y: Nadia) 
(def X: \[fcw )~) <want 
(ii) IntenMonal reading, 
(label Y: Nadia) 
int-abs (C, (def X: \[fcw X\])) <want Y, ^X> 
(iii) Extensional reading, agent's description: 
(label Y : Nadia) 
<want Y, ^(def X: \[fcw X\])> 
(iv) Intensional reading, agent's description: 
(label Y : Nadia) 
<want Y, ^int-abs (C, (def X: \[few X\]))> 
(fcw stands for the descriptor fastest-car-in-the- 
world.) 
Table I lists some different possible background 
assumptions. We will show the different effects of 
each. Background assumption I asserts the co- 
extensionality of the descriptors fastest ear in the 
world and Ross's Jaguar 300, while assumption II 
asserts co-intensionality of the descriptors. Assump- 
tions llI and IV express the same equivalences, and, 
additionally, knowledge of them is also attributed to 
Nadia. 
When the beliefs of agents (other than the 
listener) are not involved, the following rule licenses 
certain substitutions of equivalents: 
• If the target descriptor is intensional 8 then co- 
intensional or definitionally equivalent descriptors in 
the background assumptions may be substituted. 
Background assumptions I and II thus allow substitu- 
tions in readings (i) and (ii), as shown in table H. 
(For simplicity, the quantifier 
(label Y: Nadia) 
is omitted from each example.) 
When attribution of descriptions is involved, as in 
readings (iii) and (iv) of (35), we must determine 
whether the other agents are (believed by the listener 
to be) aware of the equivalence. The general rule for 
substituting descriptors which are ambiguous with 
respect to descriptive content is this: 
• If the assertion of descriptor equivalence in the 
background assumptions in the listener's knowledge 
base is part of the knowledge base of the agent to 
8In this rule, the descriptor must not be generic. Rules for gener- 
ics (universal concepts) are described in Fawcett 1985, section 5.4. 
TABLE I 
BACKGROUND ASSUMPTIONS 
I The fastest car in the world is Ross's Jaguar 300. 
II The fastest car in the world (always) is a Jaguar 300. 
III Nadia believes that the fastest car in the world is 
Ross's Jaguar 300. 
IV Nadia believes that the fastest car in the world is 
a Jaguar 300. 
TABLE II 
SUBSTITUTIONAL INFERENCES 
(i) + I Nadia wants Ross's Jaguar 300. 
(def X: \[ross's-jag300 X\]) <wants Y, ^X> 
(i) + II Nadia wants a Jaguar 300. 
(def X: \[jag300 X\]) <wants Y, ^X> 
(ii) + I No substitution possible. 
(ii) + II Nadia wants a Jaguar 300. 
int-ab,(C, (def X: \[jag300 X\])) 
<wants Y, ^X> 
(iii) + Ill 
(iii) + rv 
(i~) + Ill 
(i~) + Iv 
Nadia wants Ross's Jaguar 300. 
<wants Y, ^ (def X: \[ro~'sqag300 X\])> 
Nadia wants a Jaguar 300. 
<wants Y, ^ (indef X: \[jag300 X\])> 
No substitution possible. 
Nadia wants some Jaguar 300. 
<wants Y, 
^ int-abs (C, (indef X: \[jag300 X\]))> 
whom the target descriptor is ascribed, then the 
descriptor can be substituted in the target. The 
resulting clause will have the substituted descriptor 
attributed to the same agents as the descriptor in 
the original target. 
Reading (iii) requires a co-extensional descriptor that 
Nadia is aware of. Background assumptions IlI and 
IV both provide such a descriptor. Reading (iv) also 
requires a descriptor that Nadia is aware of, but it 
must be co-intensional with the target descriptor; 
only assumption IV provides such a descriptor which 
can then be substituted. The results are shown in 
table II. 
198 
Substitution rules for other intensional constructs, 
and details of interactions between rules, can be 
found in Fawcett (1985, section 5.4). 
6. Implementation 
We have implemented a prototype system that incor- 
porates the ideas discussed above. The system is 
written in Prolog, and is built on top of Popowich's 
SAUMER formalism for syntactic and semantic rules 
(Popowich 1984, 1985). 
7. Plans and goals 
Now that we have looked at the problem of detect- 
ing these ambiguities and representing the possible 
readings, the next step is to study how the ambigui- 
ties may be resolved, and what factors influence the 
preference for one reading over another. We expect 
that in most cases pragmatic factors will be central, 
although there may be default preferences in some 
constructions. In addition, another member of our 
group, Diane Horton, is studying the interaction 
between agents' descriptions and the presuppositions 
of a sentence (Horton 1986). 
Acknowledgements 
This paper is based on thesis work by the first author 
under the supervision of the second, who also wrote the 
paper. The authors acknowledge helpful discussions with 
each other, Diane Horton, and Hector Levesque, and finan- 
cial support from IBM, the Natural Sciences and Engineer- 
ing Research Council of Canada, and the University of 
Toronto. They are also grateful to Nick Cercone and Fred 
Popowich for making the SAUMER system available to 
them. 
References 
BARWISE, Jon and PERRY, John (1983). Situations and 
attitudes. Cambridge, M.A: The MIT Press / Bradford 
Books, 1983. 
DAHL, Veronica (1981). "Translating Spanish into logic 
through logic." American journal of computational 
linguistics, 7(3), 149-164. 
DowTY, David R; WALL, Robert E; and P~TERS, Stanley 
(1981). Introduction to Montague semantics (Synthese 
language library 11). Dordrecht: D. Reidel, 1981. 
FAGIN, Ronald and HALPERN, Joseph Y (1985). "Belief, 
awareness, and limited reasoning: Preliminary report." 
Proceedings of the Ninth International Joint Confer- 
ence on Artificial Intelligence, Los Angeles, August 
1985. 491-501. 
FAWCETT, Brenda (1985). The representation of ambiguity 
in opaque constructs. MSc thesis, published as techni- 
cal report CSRI-178, Department of Computer Science 
University of Toronto, October 1985. 
FODOR, Janet Dean (1980). Semantics: Theories of mean- 
ing in generative grammar (The language and thought 
series). Cambridge, Mass.: Harvard University Press, 
1980. 
HOFSTADTER, Douglas R; CLOSSMAN, Gary A; and 
MEREDITH, Marsha J (1982). " 'Shakespeare's plays 
weren't written by him, but by someone else of the 
same name.' An essay on intensionality and frame- 
based knowledge representation." Bloomington, Indi- 
ana: Indiana University Linguistics Club, November 
1982. 
HORTON, Diane (1986). Incorporating agents' beliefs in a 
model of presupposition, MSc thesis, Department of 
Computer Science, University of Toronto, forthcoming 
(June 1986). 
LESP~RANCE, Yves (1986). "Toward a computational 
interpretation of situation semantics." Computational 
intelligence, 2(1), February 1986. 
LEVESQUE, Hector (1983). "A logic of implicit and explicit 
belief." Proceedings of the National Conference on 
Artificial Intelligence (AAAI-88), Washington, D.C., 
August 1983, 198-202. 
MONTAGUE, Richard (1973). "The proper treatment of 
quantification in ordinary English." \[11 In: Hintikka, 
Kaarlo Jaakko Juhani; Moravcsik, Julius Matthew Emil 
and Suppes, Patrick Colonel (editors). Approaches to 
natural language: Proceedings of the 1970 Stanford 
Workshop on Grammar and Semantics. Dordrecht: D. 
Reidel, 1973. 221-242. \[2\] In: Thomason, Richard 
Hunt (editor). Formal Philosophy: Selected Papers of 
Richard Montague. New Haven: Yale University Press, 
1974. 247-270. 
MOORE, Robert C (1981). "Problems in logical form." 
Proceedings of the 19th Annual Meeting, Association 
for Computational Linguistics, Stanford, June 1981, 
117-124. 
POPOWICH, Fred (1984). "SAUMER: Sentence analysis using 
metarules." Technical report 84-2, Laboratory for Com- 
puter and Communications Research, Simon Fraser 
University, Burnaby, B.C., Canada. August 1984. 
PoPowIG~, Fred (1985). "The SAUMER user's manual." 
Technical report 85-4, Laboratory for Computer and 
Communications Research, Simon Fraser University, 
Burnaby, B.C., Canada. March 1985. 
199 
