Indexical Expressions in the 
Scope of Attitude Verbs 
Andrew R. Haas* 
The University at Albany 
A sentential theory of attitudes holds that propositions (the things that agents believe and know) 
are sentences of a representation language. Given such a theory, it is natural to suggest that the 
proposition expressed by an utterance of natural language is also a sentence of a representation 
language. This leads to a straightforward account of the semantics of attitude verbs. However, this 
kind of theory encounters problems in dealing with indexicals: expressions such as "L" "here," 
and "now." It is hard to explain how an indexical in the scope of an attitude verb can be opaque. 
This paper suggests that while the propositions that agents believe and know are sentences, the 
propositions expressed by utterances are not sentences: they are singular propositions, of the type 
used in Kaplan's theory of direct reference. Drawing on recent work in situation semantics, this 
paper shows how such a theory can describe the semantics of attitude verbs and account for the 
opacity of indexicals in the scope of these verbs. 
1. Introduction 
A sentential theory of attitudes holds that propositions (the things that agents believe 
and know) are sentences of a representation language. The idea has an obvious ap- 
peal to AI workers, who rely heavily on representation languages. Moore and Hendrix 
(1982) gave the classic statement of the case for a sentential theory of attitudes. Kono- 
lige (1986), Haas (1986), and Perlis (1988) are among the authors who have applied 
sentential theories to AI problems. 
A central problem for any theory of attitudes is the opacity of NPs in the scope of 
attitude verbs. Suppose we take a sentence containing an occurrence of the noun phrase 
NP1 and we replace that occurrence with another noun phrase NP2 that refers to the 
same individual. In many cases, the substitution will preserve the truth value of the 
sentence. If "Superman" and "Clark Kent" refer to the same man, then "Superman was 
born on Krypton" and "Clark Kent was born on Krypton" have the same truth value. 
However, if NP1 and NP2 occur in the scope of an attitude verb, the two sentences 
might have different truth values. If "Superman" and "Clark Kent" refer to the same 
man, and Lois Lane knows this man, the sentence "Lois thinks that Superman was 
born on Krypton" might be true even though "Lois thinks that Clark Kent was born 
on Krypton" is false. Then the occurrence of "Superman" in the first sentence is called 
an opaque occurrence. 
Current versions of the sentential theory can explain many examples of opacity, 
but they have trouble when the opaque NP is an indexical. 'T' and "now" are typical 
indexicals. When 'T' occurs in an English utterance, it refers to the speaker of that 
utterance. When "now" occurs in an English utterance, it refers to the time when the 
* Department of Computer Science, The University at Albany, 1400 Washington Avenue, Albany, NY 12222 
© 1994 Association for Computational Linguistics 
Computational Linguistics Volume 19, Number 4 
speaker produces the utterance. In general, indexicals are words and phrases whose 
reference is fixed by a property of the utterance they occur in. Demonstratives are a 
class of phrases akin to indexicals, whose reference often depends on gestures that 
accompany an utterance. If I point at a book and say "Give me that book," the phrase 
"that book" refers to the book I pointed at. Indexicals and demonstratives occur con- 
stantly in human speech, and they present crucial problems for any theory of propo- 
sitional attitudes. In particular, it is essential to explain how an indexical in the scope 
of an attitude verb can be opaque. 
If we adopt a sentential theory of attitudes, it is natural to suggest that the propo- 
sition expressed by an utterance is also a sentence of a representation language. This 
leads to a straightforward account of the semantics of attitude verbs. In Section 2 I 
will describe this approach and show why it fails to explain the opacity of indexicals 
in the scope of attitude verbs. In Section 3 1 will describe a nonsentential semantics for 
attitude verbs due to Crimmins and Perry (1989). This theory can explain the opacity 
of indexicals. In Section 4 1 will describe a new version of the sentential semantics for 
attitude verbs, which incorporates some of Crimmins and Perry's ideas. This theory 
denies that the proposition expressed by an utterance is a sentence in a representation 
language. It follows (given a sentential theory of attitudes) that an utterance expresses 
a proposition that no one can believe or know. This sounds paradoxical, but I will 
argue that the new theory explains the opacity of indexicals while maintaining the 
advantages of a sentential theory of attitudes. 
2. Sentential Semantics for Attitude Verbs--Version One 
2.1 Using Quotation to Represent Attitudes 
Computational linguists often translate sentences of natural language into sentences 
of a representation language. This practice suggests a theory: that the proposition 
expressed by an utterance is a sentence of a representation language. This leads to a 
straightforward analysis of the semantics of attitude verbs. We introduce the quotation 
mark '. If Q is a wff or term of our language, then 'Q is a constant that denotes 
the expression Q. If a sentence P expresses the proposition Q, then an utterance of 
"Mary believes that P" expresses the proposition bel(mary~ 'Q). The symbol "bel" is 
an ordinary predicate letter, not a special modal operator. The first argument of "bel" 
denotes an agent, and the second argument denotes a sentence. The argument of the 
quotation mark may itself contain quotation marks: we might represent "John thinks 
Mary thinks the world is flat" as 
1 think(john, 'think(mary 'flat(world))). 
This analysis of attitude verbs can certainly account for some examples of opacity. 
Under this analysis, the sentence "Lois thinks Superman was born on Krypton" might 
express the proposition 
2 think(lois, 'born(superman, krypton)) 
while "Lois thinks Clark Kent was born on Krypton" might express 
3 think(lois, 'born(clark_kent,krypton)). 
The terms 'born(superman,krypton) and 'born(clark_kent, krypton) denote two differ- 
ent sentences, so it is quite possible that Lois has one sentence in her knowledge base 
and not the other. 
It is straightforward to introduce this kind of quotation into a first-order language. 
Suppose we are given a first-order language L0. We define the first-order languages 
638 
Andrew R. Haas Indexical Expressions in the Scope of Attitude Verbs 
L1, L2,... by induction as follows: the symbols of Li+l are all symbols of Li, together 
with a new constant 'Q for each term or wff Q in Li. Let L be the union of L0, L1, L2, • • .. 
Then L is a first-order language, and if Q is a term or wff of L, 'Q is a constant of L. Let 
M be a structure for L, and suppose that for each term or wff Q in L, the denotation 
of the constant 'Q in M is Q. Then we say that M is a quotation structure for M. 
These definitions do not take us outside of ordinary first-order logic--we have simply 
defined an interesting subset of the class of all first-order structures. 
Given a system of quotation, we can introduce a predicate called "bel" with three 
arguments: an agent, a sentence, and a time (I omit the time argument in this paper). 
If this predicate represents belief, we must introduce axioms that allow us to make 
the desired inferences about beliefs. Perception can create beliefs; inference creates 
new beliefs from old ones; an agent uses beliefs to choose actions; and so on. Various 
writers have developed theories of this kind, including the present author (Haas 1986). 
This paper is about one problem, opacity, and my arguments do not depend on the 
details of the theory of belief and other attitudes. Therefore I will not develop the 
theory here. 
One issue in the theory of attitudes is so notorious that I must mention it: the 
paradoxes of self-reference. Quotation by itself creates no paradoxes, but if we in- 
troduce a predicate that represents truth or knowledge, it is easy to write plausible- 
looking axioms that are inconsistent. The literature on this topic is large; see Mon- 
tague (1974), Kripke (1975), and Barwise and Etchemendy (1987). It was once thought 
that self-reference paradoxes are particularly troublesome for sentential theories, but 
des Rivi6res and Levesque (1986) have corrected this error. Perlis (1988) has shown 
how we can take a language with quotation and consistently introduce a predicate 
with some (not all) of the properties we expect of a truth predicate. These issues are 
important, but they are not closely related to the problem of indexicals and opacity, 
so I will not consider them further here. See Haas (1991) for more references and 
discussion. 
2.2 Indexicals as Descriptions 
The reference of an indexical depends on the utterance it occurs in. Therefore if we in- 
tend to study indexicals, we can no longer speak of a sentence expressing a proposition. 
An utterance expresses a proposition, and different utterances of the same sentence 
can express different propositions. We must now reformulate the analysis of attitude 
verbs suggested above. Suppose P is a sentence, and consider the sentence "Mary 
believes that P." If a speaker utters "Mary believes that P," he or she also utters P. If 
the utterance of P expresses a proposition Q, the utterance of "Mary believes that P" 
expresses the proposition bel(mary, 'Q). 
If we translate English sentences into a representation language, we must translate 
indexicals into expressions of the representation language. One way to do this is to 
assign a constant to denote each utterance. Suppose the words of a certain utterance 
are "I am now in London," and the constant that denotes the utterance is U729. Then 
the proposition the utterance expresses might be 
4 (3x~ y. speaker(x~ U729) A time(y, U729) A in(x~ london, y)). 
This sentence says that the speaker of U729 is in London at the time when U729 oc- 
curs. The wff speaker(x,U729) is a description of the speaker of U729, and the wff 
time(y, U729) is a description of the time when U729 occurs. This resembles Reichen- 
bach's analysis of indexicals (Reichenbach 1947). 
If indexicals translate into descriptions, it is possible to construct an opaque read- 
ing for an indexical in the scope of an attitude verb. As an example, suppose Clark 
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Computational Linguistics Volume 19, Number 4 
Kent thinks that Lois Lane has discovered his secret identity, but he is mistaken. Kent 
reports his belief to Jimmy Olsen by pointing at a picture of Superman in costume 
and saying 
5 Lois believes I am that man. 
This utterance is false. On the other hand, suppose Kent later says 
6 Lois believes I am me. 
This utterance is true. The NP "that man" in the first utterance and the NP "me" in 
the second utterance refer to the same individual, but one utterance is false and the 
other is true. Therefore the NPs are opaque. 
If u is an utterance, let demonstrate(x, u) mean that x is the object that the speaker 
of u demonstrates to the addressee while uttering u. To get opaque readings for the NPs 
"that man" and "me" in these utterances, we can assign the following representations. 
Let the constant U891 denote the first utterance, and let the representation of this 
utterance be 
7 bel(lois, '(3x, y. speaker(x~ U891) A demonstrate(y, U891) A x = y)). 
Let the constant U144 denote the second utterance, and let the representation of this 
utterance be 
8 bel(lois, '(3x, y. speaker(x, U144) A speaker(y, U144) A x = y)). 
These two representations describe two quite different sentences. It is quite possible 
that Lois believes one sentence and not the other, so it is quite possible that (7) is false 
and (8) is true. So we have opaque readings for the NPs "that man" and "me." 
We get the opaque readings for (5) and (6) by putting the descriptions that rep- 
resent the NPs in the scope of the quotation mark on the second argument of "bel." 
By placing a description in the scope of the quotation mark, we are claiming that this 
description occurs in a sentence that Lois believes. For example, (7) entails that Lois 
believes the sentence 
9 (3x, y. speaker(x, U891) A demonstrate(y, U891) A x = y)) 
which means that Lois knows (or can easily infer) that the speaker of U891 demon- 
strated some object to his or her hearer while uttering U891. So if (7) represents the 
intended meaning of Kent's utterance (5), Kent was implying that Lois knew that 
he demonstrated some object while producing this utterance. This is clearly wrong. 
Kent's statement might easily be true even if Lois was not present when Kent uttered 
U891, and has no idea that the utterance even occurred, let alone that Kent demon- 
strated anything as he spoke. So (7) cannot be a correct representation of the intended 
meaning of Kent's utterance. 
There is another possible representation of Kent's utterance, one that avoids the 
false implication of (7). Let subst(R, \[vl~..., vk\], \[Ul~..., uk\]) be the wff formed by si- 
multaneously substituting the terms Ul,...,uk for free occurrences of the variables 
Vl,..., Vk in R. For example, we have subst('p(x,y), \['x\], \['c\]) = 'p(c,y). Using this no- 
tation, we can form a new representation for "Lois believes I am that man'--one 
that places the description "demonstrate(x, U891)" outside the scope of the quotation 
mark. The new representation says that there exists a term tl of the representation 
language that denotes the demonstratum of U891, and another term t2 which denotes 
the speaker of U891, and Lois believes the sentence tl --- t2. Following Kaplan (1975), 
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Andrew R. Haas Indexical Expressions in the Scope of Attitude Verbs 
we want to indicate that tl and t2 are not just any terms--they must have some signif- 
icance. We write name(a~ t, x) to mean that t is a term of our representation language, 
the denotation of t is x, and t contains information that is significant to the agent a. 
For the moment let us not inquire what this significance amounts to--the question 
does not effect the present argument. 
Using the substitution operator and the predicate "name," we can build the fol- 
lowing representation for Kent's utterance (5): 
10 
(3x, y, tl, t2. speaker(x, U891) A demonstrate(y, U891) 
A name(lois, tl, x) A name(lois, t2, y) 
A bel(lois,subst('(x = y), \['x, 'y\], \[tl, t2\]))) 
And for (6): 
11 
(3x, y, tl, t2. speaker(x, U144) A speaker(y, U144) 
A name(lois~ tl, x) A name(lois~ t2, y) 
A bel(lois,subst('(x = y), \['x, 'y\], \[h, t2\]))) 
To see that (10) is a plausible representation of utterance (5), suppose that k and s 
are terms that denote Clark Kent (and therefore denote Superman), and both terms 
contain information that is significant to Lois. k occurs in the following beliefs of Lois 
(among others): 
12 personal_name(k, "Clark Kent") 
13 profession(k, reporter) 
while s occurs in these beliefs: 
14 personal~name(s, "Superman") 
15 profession(s, superhero). 
Then name(lois, 'k, k) and name(lois, 's, k) are true. Suppose also (contrary to our 
story) that Lois believes the sentence k = s. This is precisely the kind of situation that 
Kent has in mind when he says to himself "Lois has discovered my secret identity," 
and it is this belief that prompts him to produce utterance (5). Let s be an assignment 
such that s(h) is the constant k and s(t2) is the constant s. Then the value of the term 
subst('(x = y), \['x, 'y\], \[tl, t2\]) in s is the sentence k = s. Therefore (10) would be true if 
Lois believed the sentence k = s. In (10) and (11), the translations of the indexicals are 
outside the scope of the quotation marks. Therefore (10) and (11) do not imply that 
Lois has any knowledge of the utterances (5) and (6). This kind of representation for 
attitude reports comes from Kaplan (1975). Haas (1991) presented a formal grammar 
that builds such representations, using a different mechanism for quotation. 
Unfortunately, the representations (10) and (11) do not account for the opacity of 
the NPs. If "that man" in U891 and "me" in U144 refer to the same individual, then the 
demonstratum of U891 and the speaker of U144 are the same man. Therefore the wffs 
demonstrate(y, U891) and speaker(y, U144) have the same denotation: a function that 
maps a substitution s to True if s(y) is the speaker of U891 (= the demonstratum of 
U144). The wffs speaker(x, U891) and speaker(x, U144) also have the same denotation. 
It follows that (10) and (11) must have the same truth value. According to our story, 
(10) is true--as the reader can see by considering an assignment s such that s(x) = 
Kent = Superman, s(y) = Kent = Superman, and s(tl) = s(t2) = the constant k. 
Therefore (10) cannot express the intended meaning of Kent's utterance (5)--because 
the proposition Kent was trying to express is false. 
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Our attempt to translate indexicals into a representation language has ended in 
a dilemma. If we represent an indexical as a description, that description must spec- 
ify the utterance that the indexical occurs in--because the reference of the indexical 
depends on that utterance. We might represent "I am that man" as "the speaker of 
U891 is the man demonstrated by the speaker of U891." Suppose the indexical occurs 
in the scope of an attitude verb, and it is opaque--as in "Lois thinks I am that man." 
In order to account for the opacity, we must put the description that represents the 
indexical within the scope of a quotation mark. This entails that the description is 
part of Lois's belief--which means that Lois knows about the utterance U891. This is 
clearly wrong. If "Lois thinks I am that man" is true, it doesn't follow that Lois thinks 
that the speaker of U891 is the same as the individual demonstrated by the speaker 
of U891. It is quite possible that Lois knows nothing about the utterance U891. 
We can get rid of this implication by moving the description up, out of the scope 
of the quotation mark--but then we lose our explanation of opacity. Either way, we 
get it wrong. It seems that translating indexicals into descriptions will not help us to 
explain the opacity of indexicals in the scope of attitude verbs. 
3. Direct Reference and Singular Propositions 
3.1 Direct Reference and Semantic Interpretation 
We have considered a theory claiming that indexicals are represented by descriptions. 
Let us now consider a very different approach: Kaplan's theory of direct reference 
(Kaplan 1989). Suppose an utterance contains an indexical expression referring to an 
entity x. According to Kaplan, this utterance expresses a proposition that contains x 
itself--not a concept of x, or a description of x in a representation language. Kaplan 
called such a proposition a singular proposition. He writes: 
Don't think of propositions as sets of possible worlds, but rather as 
structured entities looking something like the sentences which express 
them. For each occurrence of a singular term in a sentence there will 
be a corresponding constituent in the proposition expressed .... in the 
case of a singular term which is directly referential, the constituent of 
the proposition is just the object itself. (Kaplan 1989, p. 494) 
Kaplan never denied that a proposition might contain concepts or descriptions--he 
only said that indexicals refer to entities without introducing any concept or descrip- 
tion into the proposition. He argued that the same is true for proper names, but for 
convenience I will ignore this and translate proper names as constants of the repre- 
sentation language. 
Suppose direct reference is right. Consider an utterance that contains indexicals 
referring to people, places, or times. These people, places, or times must be constituents 
of the proposition expressed by that utterance. It follows that this proposition is not 
a sentence of a representation language--because people, places, and times cannot 
be constituents of sentences. If we maintain a sentential theory, we must conclude 
that this utterance expresses a proposition that no one can believe or know--because 
the propositions that people believe and know are sentences, but the proposition the 
utterance expresses is not a sentence. Then we cannot interpret "Mary believes that 
P" as meaning that Mary believes the proposition that P expresses. Instead she must 
believe a sentence that is somehow related to the proposition P expresses. What can 
this relation be? 
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Andrew R. Haas Indexical Expressions in the Scope of Attitude Verbs 
3.2 A New Semantics for Attitude Reports 
Crimmins and Perry (1989) proposed a new approach to NPs in the scope of attitude 
reports. They proposed the idea as a modification of situation semantics, but it is easily 
incorporated into a sentential theory. I will first consider their work and then describe 
a sentential version of their ideas. 
Crimmins and Perry begin by distinguishing between beliefs and propositions. 
Beliefs are mental entities--they would not exist if there were no thinking beings. A 
proposition is not a mental entity. It consists of a property or relation and a sequence 
of arguments. The proposition that John loves Mary consists of the relation of loving 
and the sequence of John and Mary. This proposition contains the people themselves, 
not concepts or representations. So it is a singular proposition. It also contains the 
relation of loving, which is not a symbol or a concept, any more than John or Mary is. 
The beliefs that Crimmins and Perry consider in their paper are similar to atomic 
sentences of a representation language. Each belief involves a k-ary idea (similar to 
a k-ary predicate of representation language) and a sequence of k notions (similar to 
closed terms of representation language). To represent the structure of the belief we 
write 
16 (Ideak,Notionl .... Notionk). 
An idea is normally an idea of some property or relation. We write Of(Idea k) for the 
property or relation that Idea k is an idea of. Likewise a notion is usually a notion of 
something, and we write Of(Notion1) for the individual that Notion~ is a notion of. 
In Crimmins and Perry the object of a notion can change over time, and the function 
"Of" takes a time as one of its arguments. I have simplified by omitting this argument. 
The content of a belief is a proposition. In particular, if (16) describes the structure 
of a certain belief, then its content is a proposition consisting of the relation Of(Idea k) 
and the sequence of individuals Of(Notion1) ..... Of(Notionk). We write this proposition 
as 
17 ((Of(Ideak); Of(Notion1),...,Of(Notionk))). 
In this case we say that the notion Notionj is responsible for filling the j-th argument 
position in proposition (17). 
According to Crimmins and Perry, an attitude is a ternary relation. Its argu- 
ments are an agent, a proposition, and a sequence of notions. Let us take belief as 
an example. The belief relation holds between agent a, proposition p, and notions 
Notion1 .... Notionk iff a has a belief whose content is p, and that belief has the form 
18 (Ideal,NOtion1 .... Notionk). 
That is, the notions Notion1,... Notionk are the ones responsible for filling the argument 
positions in the proposition p. The belief report says that the agent has a belief whose 
content is p, but it says more: it specifies the notions that appear in that belief. 
Consider the Superman example above. Lois has two notions of Superman/Kent-- 
call them k and s. The notion k occurs in the beliefs that Lois would express in English 
as "Kent was born on Earth" and "Kent cannot fly." The notion s occurs in beliefs that 
Lois would express as "Superman was born on Krypton" and "Superman can fly." Let 
"Identity" be the identity relation, which holds between x and y iff x -- y. When Kent 
points at the picture and says "Lois thinks I am that man," he asserts that the belief 
relation holds between Lois, the proposition 
19 ((Identity;Superman,Superman)l, 
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Computational Linguistics Volume 19, Number 4 
and the sequence of k and s. The assertion is true if Lois has a belief whose content is 
(19), and that belief has the form 
20 (Ideal;k,s). 
Since the content of this belief is (19), Ideal must be Lois's idea of the identity relation. 
Kent is not just saying that Lois has a belief whose content is (19)--he is also asserting 
that this belief contains particular notions k and s. Because k and s are distinct, belief 
(20) is not a trivial inference from the belief that everything is equal to itself. 
When Kent says "Lois thinks I am me," he is describing a trivial belief that Lois 
would express in English as "Kent is Kent." He is asserting that the belief relation 
holds between Lois, the proposition (19), and the sequence of k and k. The assertion 
is true if Lois has a belief whose content is (19), and that belief has the form 
21 (Ideal,k,k). 
Then Kent's two assertions express two different propositions. Each proposition con- 
sists of the belief relation and a triple containing Lois, proposition (19), and a sequence 
of two notions. In the first assertion the sequence is \[s,k\], while in the second assertion 
it is \[k,k\]. Since the two assertions express different propositions, it is quite possible 
that one is true and the other false. Thus Crimmons and Perry are able to explain the 
opacity of indexicals. 
This simple solution to the problem has one drawback. We claim that when Kent 
points and says "Lois thinks I am that man," he expresses a proposition that refers 
directly to two notions k and s that appear in Lois's beliefs. The sentence "Lois thinks 
I am that man" contains a proper name that refers to Lois, and indexicals that refer to 
Kent, but it contains no word or phrase that refers to k or s. k and s are constituents 
of the proposition Kent expressed, but his words do not name or describe them in any 
way. k and s are what Crimmins and Perry call unarticulated constituents. 
There is clear evidence for unarticulated constituents in cases that do not involve 
attitudes. For example, the verb "rain" takes two logical arguments: a time and a 
place. Sometimes they are both articulated: "It rained in New York last night." Often 
the place is unarticulated. If you return from Bermuda I might meet you and say "Hi, 
how was your trip?" You might reply "It rained every day." You have expressed a 
proposition with Bermuda among its constituents, though you did not use any name, 
description, or indexical expression that refers to Bermuda. Such examples show that 
we cannot object to the ideas of Crimmins and Perry because they rely on unarticulated 
constituents. 
The reader should note that we must generalize Crimmins and Perry's idea in 
order to handle quantification into the scope of attitudes. Suppose we have "Every 
man thinks his wife is smart." Each man has a notion of his wife, and the speaker 
is presumably referring to a function that maps each man to the correct notion. We 
cannot represent this example in Crimmins and Perry's notation, because it is not clear 
how they intend to represent quantifiers. 
4. Sentential Semantics for Attitudes--Version Two 
4.1 Singular Propositions and Sentences 
Crimmins and Perry firmly deny that a proposition is a sentence or an internal rep- 
resentation. Yet in order to account for opacity, they need to use notions, which are 
internal representations. Since internal representations play an essential role in their 
explanation of opacity, it is natural to ask if we can find a similar explanation within 
a sentential theory. 
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Andrew R. Haas Indexical Expressions in the Scope of Attitude Verbs 
If direct reference is right, the proposition that an utterance expresses cannot be 
a sentence. However, it might still be a lot like a sentence. Let us assume that a 
singular proposition is an ordered pair, containing a wff with free variables and an 
assignment of values to those variables. For example, an utterance of "I am now 
in London" might express a proposition consisting of the wff in(x, london,y) and a 
function that maps x to the speaker and y to the time of the utterance. I will write 
this singular proposition as ('in(x,london,y),f), where f is a function mapping x to the 
speaker and y to the time. This account of singular propositions is consistent with 
Kaplan's description: the referents of indexicals are constituents of the proposition, 
and propositions are "structured entities looking something like the sentences which 
express them." Kaplan's description obviously gives us a lot of leeway; I am taking 
advantage of that leeway to make singular propositions as much like sentences as 
possible. I will show that by adopting this view of singular propositions, we can 
account for the opacity of indexicals within a sentential theory of attitudes. 
Suppose, as in Section 2.2 above, that Lois's beliefs contain two constants k and 
s that denote Superman/Kent, and these constants occur in beliefs (12-15), among 
others. 
12 personal_name(k, "Clark Kent") 
13 profession(k,reporter) 
14 personal~name(s,"Superman") 
15 profession(s,superhero) 
When Kent says "Lois thinks I am that man," he is expressing a singular proposition 
that refers directly to the terms k and s. This proposition says that k and s denote 
Superman/Kent, and that Lois believes the sentence k = s. The proposition is (P,f), 
where P is the wff 
22 denote(z, x) A denote(w, y) A believe(lois,subst('(x = y), \['x, 'y\], \[z, w\])) 
and f is the function that maps x and y to Superman, z to k, and w to s. Note that 
the variables x and y have both quoted and unquoted occurrences in this wff. The 
unquoted occurrences refer directly to Superman, while the quoted occurrences are in 
the arguments of the function letter "subst." These occurrences serve to indicate the 
places where the ground terms z and w, denoting Superman, occur in Lois's belief. 
This double use of the variables is a little confusing, but it will simplify the semantic 
interpretation rules for attitude verbs. 
When Kent makes the uninteresting assertion "Lois thinks I am me," he expresses 
a different singular proposition. This proposition is (P, g), where P is wff (22) and g is 
a function that maps x and y to Kent, z to the constant k, and w also to the constant k. 
These two singular propositions contain the same wff--they differ oMy in the values 
they assign to the variables in that wff. The second proposition says that Lois believes 
the trivial sentence k = k. Since they describe different beliefs, it is quite possible that 
one is true and the other false--even if Kent and Superman are the same person. So 
this analysis can account for opaque indexicals. 
Suppose we accept direct reference and also maintain a sentential theory of atti- 
tudes. Then in "Mary believes that P," the utterance of P expresses a singular proposi- 
tion, while Mary's belief is a sentence. We must somehow construct this sentence from 
the singular proposition expressed by P. Our proposal for this construction is in two 
parts. First, we suggest that a singular proposition is a pair (Q,f), where Q is a wff 
and f is a function that maps the free variables of Q to their values. This is consistent 
with Kaplan's ideas about singular propositions, and it suggests an obvious way of 
constructing a sentence: we replace each free variable x in Q with a ground term that 
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Computational Linguistics Volume 19, Number 4 
denotes the value f(x). To complete the construction, we must choose a ground term 
for each free variable of Q. Here we rely on Crimmins and Perry's notion of unartic- 
ulated constituents. We claim that the ground terms we need are constituents of the 
proposition expressed by "Mary believes that P" even though they are not named 
or described by any words of the utterance. Given these ground terms, we take the 
proposition expressed by P and construct the sentence that Mary believes. In this way 
we can reconcile direct reference with a sentential theory of attitudes. 
4.2 Further Examples 
Suppose John says "I am smart." Hearing his words, one would naturally describe 
John's belief by saying "He thinks he is smart." In this sentence the pronoun "he" 
appears in the scope of an attitude verb, and it represents the subject's use of a first 
person pronoun. Castafieda (1968) coined the term quasi-indicator for an occurrence 
of a pronoun that is in the scope of an attitude verb and that represents the subject's 
use of some indexical expression. 
We can analyze this example as follows. John's belief is the sentence smart(i), 
where i is the constant that John normally uses to refer to himself. This constant will 
play a special role in perception, introspection, and planning. If John sees a lion in 
front of him, his sensors will create the belief (3x. lion(x) A inXront_of(x, i)). If he 
learns by introspection that he believes the world is round, he will form the belief 
bel(i, 'round(world)). If John wants to achieve a goal represented by a sentence P, he 
will try to identify an action x such that (do(i, x) --* P) is true. See Haas (1986) for 
further examples of how an agent can use a standard constant to refer to himself or 
herself. Such a constant is called the agent's selfnarne. 
An utterance of "John thinks he is smart" would normally express a singular 
proposition (Q,f), where Q is the wff 
23 denote(z,john) A believe(john,subst('smart(x),\['x\], \[z\])) 
and f is a function that maps the variable z to John's selfname. It is possible that there 
are other terms in John's internal language that denote John, and in some unusual 
situation, an utterance of "John thinks he is smart" might refer to one of those other 
terms. But a person who says "John thinks he is smart" would normally be referring 
to John's selfname. 
Let us give an informal statement of the semantic rule for attitude verbs that 
we are proposing. Consider a sentence of the form "John believes that P," where P 
is a clause. P will express a singular proposition (Q,g), where Q is a wff with free 
variables Xl, • • •, xn and g is a function mapping these variables to their values. We can 
refer to Q by the constant 'Q. Let tl, • • •, tn be closed terms of representation language-- 
terms that (in the speaker's opinion) appear in John's belief and denote the individuals 
g(xl),... ~ g(Xn). Let R be formed by substituting tl,..., tn for free occurrences of Xl, . . . ~ 
Xn in Q. Then R is the sentence that (the speaker claims) John believes. 
To refer to R, we must be able to refer to h,. •., tn. For this purpose we choose new 
variables yl,. •., yn, distinct from Xl, • .., Xn. We will use the variable yi to refer directly 
to the closed term ti. Therefore we define a new assignment of values to variables. Let 
f be a function whose domain consists of the variables Xl, • •., xn and yl~ • •., yn, with 
f(xi) = g(xi) for i from 1 to n, and f(yi) = ti for i from 1 to n. 
If the free variables yl~...,y~ have the values given by f, then the term 
subst('Q, \['Xl,..., 'Xn\], \[Yl,..., yn\]) denotes the sentence R. The sentence "John believes 
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Andrew R. Haas Indexical Expressions in the Scope of Attitude Verbs 
that P" can express a singular proposition (S,f), where S is the following wff: 
24 denotes(y1, X1) A'.-A denotes(yn, xn) A believe(john, subst('Q, \['Xl,... , 'Xn\], 
~!~1,-.', Yn\]). 
This proposition says that for i from 1 to n, ti is a closed term of representation 
language that denotes the individual g(xi), and John believes the sentence R formed 
by substituting each ti for the variable xi in the wff Q. Since Xl,.. •, x, includes all free 
variables of Q, and there are no free variables in tl,.. •, tn, the result of this substitution 
is indeed a sentence, not a wff--just as the sentential theory requires. Note that the 
variables Xl,...,x, have both quoted and unquoted occurrences in this wff. These 
variables were already present in the singular proposition (Q,g) expressed by the 
sentence P, where they referred directly to the individuals g(xl),... ,g(x,). The wff Q 
appears under a quotation mark in wff (24), but the occurrences of Xl,. •., x~ under the 
quotation mark do not refer directly. Instead they serve to indicate where the closed 
terms tl,..., tn occur in John's belief. For i from 1 to n, the variable xi also occurs 
unquoted in (24), as the second argument of the predicate "denote." The unquoted 
occurrence of xi refers directly to the individual g(xi) = f(xi). We could avoid this 
double use of the variables xl,..., Xn by complicating the semantic interpretation rule. 
Notice that h,. •., t~ can be any closed terms of the representation language. For 
each choice of tl, • • •, tn we get a possible interpretation for an utterance of the sentence 
"John thinks that P." This interpretation is "possible" in the sense that it is consistent 
with the syntax and semantics of English. The speaker of the utterance intends to 
refer to a particular sequence of terms tl,.. •, tn, and the hearer must use knowledge 
of the speaker and situation to make some inferences about tl,..., tn. It is possible 
that the hearer will infer enough about tl,. • •, t~ to identify each of them uniquely, but 
we should not assume that the hearer must actually identify h,..., tn. It is possible 
that the hearer can learn something from the utterance, or produce a helpful response, 
given only a limited knowledge about the terms tl,..., tn that the speaker intends to 
refer to. 
The object of an attitude verb may itself be an attitude report: for example, "I 
think you think you are smart." Let us check that our proposal allows a reasonable 
semantic interpretation for this example. Suppose the speaker is John and the hearer 
is Mary. John knows that in Mary's belief about her own smartness, the term that 
denotes Mary is her selfname. He does not know which constant is Mary's selfname, 
but he can refer to that constant as selfname(mary). Then John's belief about Mary's 
belief would be 
25 bel(mary, subst('smart(x), \['x\], \[selfname(mary)\]). 
According to our semantics, an utterance of "I think you think you are smart" has 
many possible interpretations. I will show that there is one possible interpretation 
that is true iff John believes (25). 
The clause "you are smart" expresses a singular proposition consisting of wff 
26 smart(x) 
and a function that assigns Mary as the value of the variable x. According to our 
semantics, the clause "you think you are smart" expresses a singular proposition con- 
sisting of the wff 
27 denotes(n, x)A think(y, subst('smart(x), \['x\], In\])) 
and a function f that assigns values to the free variables of this wff. The variable x 
occurred in wff (26), and the function f assigns it the same value that it had in (26): 
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f(x) is Mary. The variable y represents the pronoun "you," and the hearer is Mary, so 
f(y) is also Mary. The variable n could refer to any closed term denoting Mary. Let n 
refer to Mary's selfname; then f(n) is Mary's selfname. We have now chosen one of 
the possible interpretations for an utterance of "you think you are smart." 
The interpretation of "I think you think you are smart" will consist of the wff 
28 denotes(m1, x) A denotes(m2, y) A denotes(m3, n) 
A think(z, subst('(denotes(n~ x) A think(y, subst('smart(x)~ \['x\], \[n\]))), 
\['x, % % 
\[ml~ m2~ m3\] ) ). 
and a function g that assigns values to the free variables of this wff. The variable z 
represents the pronoun "I," so g(z) is John himself. The variables x, y, and n occurred 
in the wff (27), so the function g assigns them the same values that f assigned. Since 
x and y refer to Mary, g(ml) and g(m2) must be closed terms that denote Mary. Let 
g(ml) = g(m2) = the constant mary. Since n refers to Mary's selfname, g(m3) must be a 
closed term that denotes Mary's selfname. Let g(m3) be the term selfname(mary). We 
have now chosen one of the possible interpretations for an utterance of "I think you 
think you are smart." 
To find the belief described by (28), we take the first argument of "subst" and we 
substitute the constant "mary" for x and y and the term "selfname(mary)" for n. The 
result is 
29 denotes(selfname(mary),mary) A think(mary, subst('smart(x), \['x\], 
\[selfname(mary)\])) 
If John believes (29), he can trivially infer (25). Conversely, suppose John believes (25). 
It is common knowledge that an individual's selfname denotes that individual, so 
John can easily infer the conjunction (29). So we have found a possible interpretation 
of the utterance that is true iff John believes (25). 
5. Conclusions 
We are given a belief report: "Mary believes that P." We have a parser and semantic 
interpreter that can identify the proposition expressed by P. We want to use this 
information to predict Mary's behavior--say, her answer to a given question. Suppose 
we know the algorithm that Mary uses for answering questions. Since the algorithm's 
input is a set of representations, we need to find Mary's internal representation for 
the proposition expressed by the clause P. 
If the proposition expressed by a clause is a sentence of a representation lan- 
guage, our problem is already solved: Mary's representation of the proposition just 
is the proposition. Unfortunately, we have seen that this kind of theory cannot ex- 
plain opaque indexicals. It seems that Mary's representation must be distinct from the 
proposition it represents, and if we are given the proposition it will take some reason- 
ing to find the representation. If we are going to distinguish between a proposition 
and its internal representation, we would like a clear and simple picture of how they 
are related, and how we are to find the representation when the proposition is known. 
We have proposed that the proposition expressed by P is a pair, containing a wff and 
an assignment of values to the free variables of the wff. To find Mary's representation 
we must find the terms she uses to represent the values of the free variables, and 
substitute these terms for the corresponding variables in the wff. In Crimmins and 
Perry's work, a proposition and its representation are two quite different objects. A 
proposition consists of objects and relations, while a representation consists of "ideas" 
648 
Andrew R. Haas Indexical Expressions in the Scope of Attitude Verbs 
and "notions." If we need both internal representations and singular propositions, it is 
simpler to assume that they are closely similar objects--instead of radically different 
objects, as in Crimmins and Perry. 
The examples that motivate this work are unfortunately remote from the texts 
that computational linguists currently work on. In studying opacity we concentrate 
on cases where an agent uses two different representations without realizing that they 
refer to the same entity. Such cases are popular in fiction, but rare in applications like 
machine translation or question-answering from a database. So it will be some time 
before these ideas are helpful in the practice of computational linguistics. However, 
indexicals occur constantly in human speech, and opacity is a crucial issue in any 
theory of propositional attitudes. So if we are serious about a sentential theory of 
attitudes, it is important to be certain that such a theory can explain opaque indexicals. 
Acknowledgment 
This work was supported by the National 
Science Foundation under grant number 
IRI-9006832. 
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