Presuppositions as Beliefs 
Diane HORTON and Graeme HII:tST 
Department of Computer Science 
University of "ibronto 
Toronto, Canada M5S 1A4 
dianeh@ai.toronto.edu (CSNET) 
Abstract 
Most theori~s of presupposition implicitly assume that pre- 
supposition,; are facts, and that all agents involved in a 
discourse share belief in the presuppositions that it gen- 
erates. These unrealistic assumptions can be eliminated 
if each presupposition is treated as the belief of an agent. 
However, it ~s not enough to consider only the beliefs of the 
speaker; we show that the beliefs of other agents are often 
involved. We describe a new model, including an improved 
definition of presupposition, that treats presuppositions as 
beliefs and considers the beliefs of all agents involved in 
the discourse. We show that treating presuppositions as 
beliefs makes it possible to explain phenomena that cannot 
be cxplainecl otherwise. 
1 Introduction 
In addition 'I;o its literM meaning, a sentence or utterance 
conveys a host of indirect information that can be prag- 
matically in~rred. Presuppositions, whidl we mark ">>", 
are one pa~'t of that information. Table 1 gives several ex- 
amples of presupposition with their traditional analyses 1. 
Roughly, a presupposition is a proposition that is con- 
veyed by a sentence or utterance 2 but is not part of the 
main point, and must be consistent with the established 
context in order for that sentence or utterance to be fe- 
licitous. For example, the following is infelicitous because 
the second .,~entence presupposes that Angle quit, which 
contradicts the first sentence: 
(1) *Angle didn't quit. It's surprising that she quit. 
Other types of pragmatic inference include entailment, 
conversational implicature, and conventional implicature 
(see Levinson (1983) for detailed descriptions). Presuppo- 
sitions can be distinguistmd from other sorts of pragmatic 
inference by their unique behavior when the sentence from 
which they originate is negated. These basic ideas are 
generally agreed upon; however, their formalization into a 
theory of presupposition has been difficult. We will now 
introduce two problems and our approach to solving them. 
1 Throughout this paper, we use the sentence itself a.q short form 
for its semantic representation, in order to avoid addressing the or- 
thogonal issu*., of semantic representation. 
2The sentence/utterance distinction will be made clear in the pre- 
sentation of ouc approach. 
Horton (1987) reviews several theories, including 
those of Karttunen (1973, 1974), Karttunen and Pe- 
ters (1979), Wcischedcl (1975, 1979), Gazdar (1979a, 
1979b), Wilson and Sperber (1979), and Atlas and Levin- 
son (1981). One problem is that many theories of 
presupposition iiaplicitly make the' following unrealistic 
assumptions s: 
• Truth Assumption: If sentence S (or its utterance) pre- 
supposes proposition P, then P is true. 
• Shared Belief Assumption: If sentence S (or its ut- 
terance) presupposes proposition P, then all agents 
involved share the prior belief that P is true. 
Weischedel and Gazdar are exceptions; e~tch of them at- 
tributes presuppositions to the speaker as either knowl-. 
edge or belief. However, we will show th~tt the beliefs of 
agents other than the speaker must be considered in order 
to correctly express many presuppositions. Our ai)proach 
is to treat presuppositions as beliefs, but a.lso to consider 
the beliefs of all agents involved in discourse. 
A second difl~culty has been in finding an adequate 
definition of presupposition. Many definitions state that 
the presuppositions of a sentence must be known prior to 
the utterance of that sentence to avoid infelicity. Some 
have the stronger constraint that the presuppositions must 
be mutually known by all participants. The following def- 
inition (Levinson 1983, 205) has these properties: 
DEFINITION 1: An utterance A pragmatically presup- 
poses a proposition B iff A is appropriate only if B 
is mutually known by participants. 
These requirements, which reflect the Shared Belief As- 
sumption, are too strict -- presuppositions are often used 
to introduce new information. Conversely, many defini- 
tions accept inferences from the other inference classes as 
presuppositions. Our definition, to be presented in sec- 
tion 3.2, weakens the overly strict prior knowledge condi- 
tion so that it does not reject valid presuppositions, and 
avoids accepting inferences from other classes by checking 
whether each candidate exhibits the distinctive behavior 
under negation that signifies a presupposition. Hence, the 
new definition captures presupposition more precisely. 
The next section describes the unique behavior of pre- 
suppositions under negation. In section 3 the details of our 
3Here both sentences and utterances are mentioned because the 
assumptions are generally made when either is analyzed. 
255 
II' ..... ~!gger 
Faetive verb 
It:cleft 
Change-of-state verb 
Non-restrictive relative clause 
Implicative verb 
Definite description 
Verb of judging 
Example 
Rita is upset that Jenny lied. 
>>Jenny lied. 
It was ~Pauline who told Arthur about Miehelle. 
>>Someone told Arthur about Miehelle. 
Tom finished making dinner. 
>> Tom had been making dinner. 
Kerry, who is Jay's son, was married last month. 
>>Kerry is Jay's son. 
Morn forgot to call. 
>>Morn intended to call. 
Tire person who stole Dr. Legg's file used a key. 
>>There is a person who stole Dr. Legg's file. 
I congratulated Lois when she finished her thesis. 
>>For Lois to finish her thesis was a good thing. 
Table 1: Some common triggers of presupposition, with examples. 
approach are presented. We then compare our analysis 
with that of Gazdar, and conclude with a summary. 
2 Behavior under Negation 
It is often stated that presuppositions are constant under 
negation, as in example 2, but are also defensible. By this 
view, the presupposition in example 3 remains constant 
under the negation in the first sentence, but is later de- 
feated by the second sentence. 
(2) Calvin {did I didn't} stop going to college. 
>>Calvin had been going to college. 
(3) I don't wish I had a Porsehe -- I already have one. 
~I don't have a Porsche. 
Our explanation of this behavior is different. Before pre- 
senting it, some terminology must be introduced. 
We will make the following semantic distinction be- 
tween two kinds of negation. Internal negation has a 
particular element of its scope as its focus, in the sense of 
the terms defined by Quirk and Greenbaum (1973, 187- 
188). External negation focuses on an unspecified com- 
ponent of its scope and therefore has several possible inter- 
pretations. The following sentence contains external nega- 
tion. It has at least three interpretations: 
(4) The boogieman didn't blow the door shut. 
(a) It's stiff open. 
\[ negating the main proposition \] 
(b) There is no boogieman. 
\[ negating a presupposition \] 
(c) It was already shut. 
\[ negating a felicity condition \] 
The focus of internal negation is unambiguous. If that 
focus is on a presupposition, the presupposition, of course, 
does not survive the negation, as in the following: 
(5) Mark, who has a Ph.D., is the president. 
>>Mark has a Ph.D. 
(6) Mark, who doesn't have a Ph.D., is the president. 
~Mark has a Ph.D. 
Internal negation that focuses on anything other than a 
presupposition does not affect that presupposition, be- 
cause presuppositions do not depend on tile truth of any 
other thing expressed by the sentence. For example, the 
presupposition of sentence 7 still holds when the main 
proposition is negated. 
(7) Debbie, who has a dog, {does I doesn't} have cats. 
>>Debbie has a dog. 
External negation is inherently vague. We argue that 
it is handled as follows. One first checks to see if there is 
any evidence favoring one of the possible interpretations. 
If a presupposition contradicts any established informa- 
tion, one assumes the intended reading negates that pre- 
supposition; hence the presupposition is never believed to 
hold. We will call this the blocking of a presupposition. 
In the absence of any evidence to guide one in choosing 
an interpretation, one assumes that negation of the main 
proposition was intended, and hence that the presupposi- 
tion stands. This assumption might be either supported 
or refuted by information to follow. If it is refuted, then 
the incorrect presupposition must be retracted. 
Our analysis of example 3 then, is as follows. The 
negation in the first sentence is ambiguous and, on hearing 
that sentence alone, the hearer assumes a reading where 
the focus of negation is on wish and the presupposition 
is left intact. That is, the hearer assumes the intended 
reading was I don'~ have a Porsehe, and I don't want one. 
On hearing the second sentence, the hearer learns that this 
assumption was incorrect, and the presupposition that I 
don'~ have a Porsche is retracted. 
In summary, a presupposition survives semantically 
internal negation exactly when the negation does not fo- 
cus on the presupposition itself. It is assumed to survive 
semantically external negation unless there is evidence to 
the contrary, in which case it is blocked. If not blocked, it 
256 
may be retracted later if the assumption is shown to be in- 
correct by evidence that follows. We use the term defeat 
to subsmne both blocking and retraction. Horton (1987, 
sec. 1.2) shows that this behavior distinguishes presuppo- 
sitions from entaihnents and implicatures. 
3 Presuppositions as Beliefs 
The at)proach proposed here is to treat each presupposition 
as the belief of some particular agent in order to avoid ~he 
assumptions of truth and shared belief and thereby arts.in 
a more reatistie account of presupposition. In addition, we 
propose considering all agents when deciding to whom tim 
belief should be attributed. 
Before continuing, we will point out our assumptions. 
Following Griee (1975), we assmne tlrst that no speaker 
will deliberately try to deceive the listener, and second 
that no speaker will use irony or sarcasm. Deceit, irony, 
and sarca,;m cart affect presuppositions, and the possibility 
of handling them is discussed by tIorton (1987). 
3.1 A Logic for Modeling Context 
In (Hortoi, 1987) a formal logic of belief is defined. 
Its syntax allows the expression of propositioils such as 
.l~JohnBMary-'P (that is, dohn believes that Mary believes 
P is not true). Its semantics is based on belief struc- 
tures, a w~riant of Fagin, Halpern, and Vardi's knowl- 
edge structures (1984). A belief structure encodes what 
Will be called a state -- the truth wdue of each proposi- 
tion, as well as the beliefs of each agent regarding these 
propositions, their beliefs about the other agents' beliefs, 
and so on. If a proposition P is true for a belief struc- 
tures, wewrites ~P;ifnot, wewrites ~P. We also 
infornmlly describe operations Add Proposition, which up- 
dates a belief structure to encode a new belief for some 
agent, and Retract Proposition, which retracts a proposi- 
tion from an agent's beliefs. These operations can bc used 
to model the acquisition and retraction of presuppositiomfl 
information by agents. Formal definitions of these opera- 
tions raise difficult problems that wc have not solved. See 
(Horton 1987, 37--42). However, the logic does provide a 
notation a,ll,:l formal semantics for the expression of beliefs. 
3.2 The Definition of Presupposition 
We now present a definition of presupposition that em- 
bodies the idea of attributing presuppositions to specific 
agents, and incorporates our view of the behavior of pre- 
supposltion.,~ under negation. 
The presuppositions of an utterance depend not only 
on the sentence uttered, but also on the speaker, the lis- 
tener, and the listener's beliefs, since only the listener's 
beliefs affect the cancdlation of presuppositions for him. 
One sometimes wishes to speak of presuppositions when 
not all of this contextual information is known. In partic- 
ular, it is desirable to be able to discuss presuppositions 
of a sentence independent of any context of utterance. In 
such cases, it is not possible to perform a consistency check 
to determine whether or not a candidate will actually turn 
out to be a presupposition; but one can say that if the 
necessary information were available and if the proposi- 
tion were consistent with established information, then the 
proposition would be a presupposition. We will define po- 
tential presupposition to capture this notion of a can- 
didate presupposition that may turn out to hold when the 
sentence is completely situated, and actual presupposi- 
tion to denote a potential presupposition that does turn 
out to hold 4. 
In the definitions below, S ~ is used to rel)resent tile 
affirmative form of sentence S, and S- to represent the 
externally negated form of the sentence. We will use the 
term state to refer to a state of affairs, as represented by 
a belief structure. 
Potential Presupposition 
The definition of potential presupl)osition for when only 
the sentence is known is as follows: 
DEHNI'rlON 2: Sentence S potentially presui)poses 
t)roposition P iff for any speaker Sp, listener L, and 
state a, 
(a) The utterance of S + by Sp to L in state s would 
allow L to infer Bs'vP. 
(b) The utterance of S- by Sp to L in state s would 
allow L to infer BspP unless L already believed 
Bsp~P, i.e., unless s ~ BLBsp'-P. 
Clause (a) says that if the a~rmative form of the sentence 
were spoken, any listener could infer that the speaker be- 
lieved P. Clause (b) says that even if the negative ibrm 
of the sentence were spoken, any listener could still infer 
that the speaker believed P, unlc'ss the listener already be- 
lieved otherwise. A definition with clause (a) alone woukl 
capture other pragmatic inferences as well as presupposi- 
tion. Since clause (b) requires that the candidate exhibit 
the behavior under negation that is unique to presupposi- 
tion, it excludes the others. See (Herren 1987, sec. 4.5) for 
exmnples. 
Actual Presupposition 
An acttml presupposition of a sentence completely situ- 
ated in context must be a potential presupposition of that 
sentence and consistent with the context. 
DEFINITION 3: The utterance of sentence S by speaker 
Sp in state s actually presupposes proposition 
BspP for listener L iff 
(a) P is a potential presupposition of S. 
(b) If S = S-, s ~ BLBSp~P. 
In keeping with our philosophy of treating presupposi- 
tions as beliefs, clause (b) checks whether the spe~rker 
believes the potential t)resupposition according to the lis- 
tener. Since blocking can only occur in negative sentences, 
4See section 4 for a comparison of our concepts of" potential and 
actual presupposition with Gazdt~r's "pre-supl)osition" and "act, ual 
presupposition." 
257 
this check is only performed on negative sentences (see sec- 
tion 3.4 for a qualification). 
Example 
Consider the utterance of S = I'm not glad that Chris is 
leaving by Tom. Let P be Chris is leaving, and the state 
be s where s ~ BDianeB:romP, s ~ BDia,~eBTom~P, and 
s ~ BcothieBTorn~P. The sentence is Mready externally 
negated, so o e- = S, and S + = It is ndt true that l'm not 
glad that Chris is leaving, which is equivalent to I'm glad 
that Chris is leaving. 
For any speaker Sp, listener L, and state s, the utter- 
ance of S + by Sp would allow L to conclude BspP. We 
can confirm this by noting that the utterance of I'm glad 
that Chris is leaving, but he isn't would be infelicitous. In 
addition, the utterance of S- by any speaker Sp would 
also allow any listener L to conclude BspP, unless it were 
inconsistent with L's beliefs. Therefore, P is a potential 
presupposition of sentence S. 
P may or may not be an actual presupposition of 
the utterance of S by Tom in this state, depending on 
who is the listener. Diane has no particular belief about 
whether or not Tom thinks Chris is leaving. In partic- 
ular, s ~ BDi~n~B:ro,~P. Therefore, B~'omP is an ac- 
tual presupposition to Diane of the utterance of sentence 
S by Tom, in this state. However, Cathie has the pre- 
vious belief that Tom thinks Chris is not leaving, i.e., 
s ~ BcathleBTom'~P. Therefore, BTomP is not an ac- 
tual presupposition to Cathie of the utterance of sentence 
S by Tom, in this state. 
3.3 Applying the Definitions 
Horton (1987, ch. 5) applies the definitions, in the man- 
ner shown above, to a representative set of sinlple sen- 
tences, and shows that the presuppositions of many sen- 
tences must be treated as beliefs. For example, sentence 8 
does not potentially presuppose Brian's leaving was bad, as 
shown by the felicity of 9. However, under our assumption 
that all speakers are sincere, it does potentially presuppose 
Bpe~(Brian's leaving was bad). 
(8) Percy criticized Brian for leaving. 
(9) Percy criticized Brian for leaving, but there was noth- 
ing wrong with him leaving. 
In the case of utterances, all presuppositions must be 
treated as the beliefs of the speaker, but many can be 
correctiy expressed only if the beliefs of agents other than 
the speaker can also be mentioned. For example, consider 
the following utterance of 8: 
(10) Mavis: Percy criticized Brian for leaving. 
~Brian's leaving was bad. 
~ BM~i~( Brian's leaving was bad) 
>>BM~,i,Bpercy( Brian's leaving was bad) 
Because our approach models the beliefs of all agents, it is 
capable of correctly handling these cases. 
For complex sentences~ one can either again apply the 
definitions directly or attempt to find rules for determining 
25~1 
the potential presuppositions of the sentence from those of 
its constituents. Horton (1987, chapter 6) examines this 
projeetion problem and shows that beliefs are again im- 
portant. For example, when sentence 11 is embedded in 
the context of the verb hopes, another level of belief is nec- 
essary to expres's the potential presupposition correctly. 
(11) Lofty is sorry that he upset Willie. 
>> BLof,u( Lofty upset Willie). 
(12) Ethel hopes Lofty is sorry that he upset Willie. 
>> BEtheZBLol~( Lofty upset Willie). 
The felicity of sentenee 13 below shows that 12 does not 
simply carry the potential presupposition, BLoltu(L@y 
upset Willie), of its constituent 11. 
(la) Ethel hopes Lofty is sorry that he upset Willie. She 
doesn't reMize that Lofty doesn't even know he did. 
Any account that does not treat presuppositions as beliefs 
cannot capture the presupposition in 12 and must incor- 
rectly consider verbs of propositional attitude such as hopes 
(as well as verbs of saying) to block this projection, Even 
an account that treats presuppositions as beliefs, but con- 
siders only the beliefs of the speaker, cannot capture this 
presupposition. 
The initial motivation for treating presuppositions as 
beliefs was to avoid two unrealistic assumptions. We have 
now seen that some cases of projection cannot be handled 
otherwise, and that many presuppositions do involve be- 
liefs of agents other than just the speaker. 
3.4 Defeat in Affirmative Sentences 
The presuppositions of an affirmative sentence usually can- 
not be defeated without an infclicity. For example, It's 
a good thing that Tom didn't .fall presupposes that Tom 
didn't fall. There is no context for this sentence in which 
the presupposition does not hold and hence no context in 
which it can be contradicted. However, there is a small 
class of affirmative sentences in which defeat is possible. 
For example, sentence 14 potentially presupposes 15 be- 
cause of the definite reference Barney's loud music. 
(14) If Fred's in his office, Barney's loud music will 
bother him. 
(15) Barney is playing loud music. 
However, in the context of 16, the presupposition does not 
hold. 
(16) Barney plays loud music when Fred's in his office, 
just to bother him. 
In this case, the contextual information combines with the 
/\]-clause of 14 to establish that the potential presupposi- 
tion of the then-clause, 15, is merely a possibility, thereby 
blocking it as an actual presupposition of the sentence. 
We argue that a presupposition of an affirmative sentence 
can be defeated only in this manner, i.e., only if it is es- 
tablished as hypothetical by a clause of the sentence in 
combination with contextual information. Horton (1987) 
enumerates these relatively infrequent cases. 
Definitions 2 and 3, given above, correctly handle the 
cases in which attempted defeat of a presupposition arising 
from an affirmative sentence leads to an infelicity; however, 
they do not handle those cases where such defeat is pos- 
sible. In this section we discuss two ways to do so. Both 
are compatible with our approach. 
We define an anti-eondltlon to be any background 
information that helps to establish as hypothetical, and 
therefore to dethat, a potential presupposition of an af- 
firmative sentence. Clauses involving anti-conditions are 
added to ~\[le definitions as follows: 
DEFINITION 4: Sentence S potentially presupposes 
proposition P with anti-condition Q iff for any speaker 
Sp, listener L, and state s, 
(a) Tt~e utterance of S + by Sp to L in state s would 
allow L to infer BSpP unless L already believed 
BsvO, i.e., unless s I= BLBsp@ 
(b) The utterance of S- by Sp to L in state s would 
allow L to infer BSvP unless L already believed 
Bsp~.P or BsvQ, i.e., unless .s ~= BLI3&,~P or 
s ~ BLBSvQ. 
DEFINITION 5: The utterance of sentence S by speaker 
Sp in state s actually presupposes proposition 
B&I-' for listener L iff 
(a) 1 ) is a potential presupposition of S, with anti- 
condition Q. 
(b) If S = S-, s ~k BLBs,,-~P. 
(e) ,~ ba B~B~,Q. 
For examt,le, sentence 14 potentially presupposes 15 
with 16 as an anti-condition. As long ~s the anti-condition 
is not believed, the presupposition is actual. 
As mentioned above, defeat can only occur in a few 
types of positive sentence, so the anti-condition is usually 
nil; in such cases the simpler definitions, 2 and 3, suffice. 
An alternative method of handling the phenomena re- 
garding defeat in affirmative sentences is to treat affirma- 
tive and negative sentences uniformly, that is, to perform 
the consistency check on both types of sentence. This ap- 
proach, adopted by Gazdar (1979a, 1979b), requires no 
special mechanism to account for felicitous defeat in af- 
firmative sentences. To explain the infelicity that arises 
in moat. cases when defeat of a presupposition of an affi> 
mative sen/;enee is attempted, the help of entaihnents is 
enlisted. For exmnpie, Gazdar's theory says that 1 didn't 
see Lea Miadrablea is a "pre-supposition ''5 of 18, but not 
an actual presupposition in the context of 17, because this 
would be inconsistent. So far no infelicity is detected. 
(17) I saw Lea Mis&ables. 
(18) I'm sorry that I didn't see it. 
However, I didn't ace Les Miadrables is also an entaihnent 
of 18 (bec~mse factive verbs entail their complements). 
5Gazdar's "pre-suppositions" correspond roughly to onr porch- 
tim presuppo:dtions (see section 4). We will use quotation marks to 
distinguish his hyphem~ted term from the generic one. 
This entailment introduces an inconsistency into tile cu- 
mulative context and sentence 18 is therefore predicted to 
be infelicitous in the context of 17. 
Unfortunately, Gazdar does not say exactly where 
such entailments occur. We argue that the entaihnents 
exist exactly where anti-conditions do not, and thus that 
the distinction between Mfirmative sentences that allow 
defeat and those that do not can be drawn either by anti~ 
conditions or by tile existence of entaihnents. 
Casting the "uniform" approach in our terms, wc get 
the following definitions: 
DEFINITION 6: Sentence S potentially presupposes 
proposition P ill" for any speaker Sp, listener L, and 
state s, the utterance of ,5' by Sp to L in state s would 
allow L to infer BspP unless s ~: BLBsp~P. 
DEHNITION 7: The utterance of sentence S by speaker 
oep in state a actually presupposes proposition 
BspP for listener L iff 
(a) P is a potential presupposition of S. 
(b) s \[/= BLBsv~P. 
We are at present undecided as to which of these two 
methods to prefer. Both explain the t)henomena. Treat- 
ing af\[irmative and negative sentences uniformly leads to 
simpler definitions; in addition, the use of entaihnents to 
explain defeat phenomena in positive sentences is more 
gmmral than relying on anti--conditions, which are specific 
to the type of sentence under question, ttowevcr, this ap- 
proach does not capture the intuition that defeat differs in 
negative and atfirmative sentences. In addition, uniform 
definitions do not capture only presupposition, because 
they do not mention the unique hehavior of presui)posi- 
tion under negation. In contrast, the earlier definitions 4 
and 5 can distinguish presupposition from other kinds of 
impli cation. 
It is inlportant to note that the choice between these 
two methods is orthogonal to our goal of developing a 
model that treats presuppositions as beliefs. 
4 Comparison with Gazdar's 
Approach 
Gazdar's (1979a, 1979b) is perhaps the most influential 
theory of presupposition. It attempts to explain diverse 
phenomena regarding the behavior of presuppositions in 
context ~ with a single rule, based on consistcucy. Con- 
sistency is also central to our analysis. In addition, the 
structure of our account is similar to Gazdar's. In particu- 
lar, both accounts first compute preliminary propositions 
in our case potential presuppositions and in Gazdar's, 
"pre-suppositions" -- and then perform a consistency- 
based context check to find the presuppositions of the sen- 
6Gazdar refers to this as tile projection problem. We use the 
term differently, as Levinson does, to mean the problem of finding 
the presuppositions of a complex sentence from the presuppositions 
of its constituents. 
259 
tence or utterance in context. Despite the structural sim- 
ilarities, there are important differences between the two 
approaches. We will now describe some of these. 
First, for Gazdar a sentence may "pre-suppose" a 
proposition that it can never, on any occasion of use, pre- 
suppose. His "pre-suppositions" are simply convcnient in- 
termediate results. In our theory, on the contrary, to say 
that a sentence S potentially presupposes proposition P is 
to make a general statement about sentence S: it tends to 
imply P. Second, Gazdar computes his "pre-suppositions" 
using a set of unconnected and unmotivated rules, whereas 
our definition of potential presupposition lends coherence 
to the diverse class of potential presuppositions. The key 
difference between the present work and Gazdar's is that 
our emphasis is not on the behavior of presuppositions 
in context, but on the relevance of agents' beliefs to all 
aspects of presupposition. Gazdar does not address this 
issue. 7 We consider our integration of beliefs into an ac- 
count of presupposition to be our main contribution. 
5 Summary 
We have found that agents' beliefs are relevant to an ac- 
count of presupposition, and that it is necessary to consider 
all agents involved in discourse when deciding to whom be- 
lief in a presupposition should be attributed. We have de- 
scribed an account of presupposition that therefore makes 
beliefs central. This account includes a new definition of 
presupposition that captures it more precisely than earlier 
ones. 
Treating presuppositions as beliefs -- with full con- 
sideration given to all agents' beliefs -- not only allows a 
more correct analysis by avoiding the Truth Assumption 
and the Shared Belief Assumption; it also makes it possi- 
ble to account for presuppositionM phenomena that could 
not be explained otherwise. 
Acknowledgements 
This paper is based on thesis work by the first au- 
thor, under the supervision of the second. The authors 
wish to thank Brenda Fawcett, Gerhard Lakemeyer, Hec- 
tor Levesque, and Bart Selman for helpful discussions, 
and Chrysanne DiMarco and Susan McRoy for help in 
preparing this paper. Financial support was received from 
the Natural Sciences and Engineering Research Council of 
Canada. 
7As mentioned above, Gazdar does treat all presuppositions as 
knowledge of the speaker; however, he does not consider the knowl- 
edge or beliefs of other agents, or examine the relevance of beliefs or 
knowledge to a theory of presupposition. 
260 

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