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<?xml version="1.0" standalone="yes"?> <Paper uid="C88-1052"> <Title>Presuppositions as Beliefs</Title> <Section position="3" start_page="0" end_page="255" type="metho"> <SectionTitle> DEFINITION 1: An utterance A pragmatically presup- </SectionTitle> <Paragraph position="0"> poses a proposition B iff A is appropriate only if B is mutually known by participants.</Paragraph> <Paragraph position="1"> These requirements, which reflect the Shared Belief Assumption, are too strict -- presuppositions are often used to introduce new information. Conversely, many definitions accept inferences from the other inference classes as presuppositions. Our definition, to be presented in section 3.2, weakens the overly strict prior knowledge condition 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.</Paragraph> <Paragraph position="2"> The next section describes the unique behavior of presuppositions under negation. In section 3 the details of our Kerry, who is Jay's son, was married last month.</Paragraph> <Paragraph position="3"> >>Kerry is Jay's son.</Paragraph> <Paragraph position="4"> Morn forgot to call.</Paragraph> <Paragraph position="5"> >>Morn intended to call.</Paragraph> <Paragraph position="6"> Tire person who stole Dr. Legg's file used a key.</Paragraph> <Paragraph position="7"> >>There is a person who stole Dr. Legg's file.</Paragraph> <Paragraph position="8"> I congratulated Lois when she finished her thesis. >>For Lois to finish her thesis was a good thing.</Paragraph> <Paragraph position="9"> approach are presented. We then compare our analysis with that of Gazdar, and conclude with a summary.</Paragraph> </Section> <Section position="4" start_page="255" end_page="256" type="metho"> <SectionTitle> 2 Behavior under Negation </SectionTitle> <Paragraph position="0"> 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 defeated by the second sentence.</Paragraph> <Paragraph position="1"> (2) Calvin {did I didn't} stop going to college.</Paragraph> <Paragraph position="2"> >>Calvin had been going to college.</Paragraph> <Paragraph position="3"> (3) I don't wish I had a Porsehe -- I already have one. ~I don't have a Porsche.</Paragraph> <Paragraph position="4"> Our explanation of this behavior is different. Before presenting it, some terminology must be introduced.</Paragraph> <Paragraph position="5"> We will make the following semantic distinction between 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, 187188). External negation focuses on an unspecified component of its scope and therefore has several possible interpretations. The following sentence contains external nega- null tion. It has at least three interpretations: (4) The boogieman didn't blow the door shut.</Paragraph> <Paragraph position="6"> (a) It's stiff open.</Paragraph> <Paragraph position="7"> \[ negating the main proposition \] (b) There is no boogieman.</Paragraph> <Paragraph position="8"> \[ negating a presupposition \] (c) It was already shut.</Paragraph> <Paragraph position="9"> \[ negating a felicity condition \] 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.</Paragraph> <Paragraph position="10"> >>Mark has a Ph.D.</Paragraph> <Paragraph position="11"> (6) Mark, who doesn't have a Ph.D., is the president. ~Mark has a Ph.D.</Paragraph> <Paragraph position="12"> Internal negation that focuses on anything other than a presupposition does not affect that presupposition, because 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.</Paragraph> <Paragraph position="13"> (7) Debbie, who has a dog, {does I doesn't} have cats. >>Debbie has a dog.</Paragraph> <Paragraph position="14"> 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 information, one assumes the intended reading negates that presupposition; 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 presupposition stands. This assumption might be either supported or refuted by information to follow. If it is refuted, then the incorrect presupposition must be retracted.</Paragraph> <Paragraph position="15"> 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.</Paragraph> <Paragraph position="16"> In summary, a presupposition survives semantically internal negation exactly when the negation does not focus 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 may be retracted later if the assumption is shown to be incorrect 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 presuppositions from entaihnents and implicatures.</Paragraph> </Section> <Section position="5" start_page="256" end_page="257" type="metho"> <SectionTitle> 3 Presuppositions as Beliefs </SectionTitle> <Paragraph position="0"> 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.</Paragraph> <Paragraph position="1"> Before continuing, we will point out our assumptions.</Paragraph> <Paragraph position="2"> 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).</Paragraph> <Section position="1" start_page="256" end_page="256" type="sub_section"> <SectionTitle> 3.1 A Logic for Modeling Context </SectionTitle> <Paragraph position="0"> In (Hortoi, 1987) a formal logic of belief is defined.</Paragraph> <Paragraph position="1"> 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 structures, a w~riant of Fagin, Halpern, and Vardi's knowledge structures (1984). A belief structure encodes what Will be called a state -- the truth wdue of each proposition, 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 structures, wewrites ~P;ifnot, wewrites ~P. We also infornmlly describe operations Add Proposition, which updates a belief structure to encode a new belief for some agent, and Retract Proposition, which retracts a proposition 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 operations 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.</Paragraph> </Section> <Section position="2" start_page="256" end_page="256" type="sub_section"> <SectionTitle> 3.2 The Definition of Presupposition </SectionTitle> <Paragraph position="0"> We now present a definition of presupposition that embodies the idea of attributing presuppositions to specific agents, and incorporates our view of the behavior of presupposltion.,~ under negation.</Paragraph> <Paragraph position="1"> The presuppositions of an utterance depend not only on the sentence uttered, but also on the speaker, the listener, and the listener's beliefs, since only the listener's beliefs affect the cancdlation of presuppositions for him.</Paragraph> <Paragraph position="2"> One sometimes wishes to speak of presuppositions when not all of this contextual information is known. In particular, 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 proposition were consistent with established information, then the proposition would be a presupposition. We will define potential presupposition to capture this notion of a candidate presupposition that may turn out to hold when the sentence is completely situated, and actual presupposition to denote a potential presupposition that does turn out to hold 4.</Paragraph> <Paragraph position="3"> 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.</Paragraph> </Section> <Section position="3" start_page="256" end_page="257" type="sub_section"> <SectionTitle> Potential Presupposition </SectionTitle> <Paragraph position="0"> The definition of potential presupl)osition for when only the sentence is known is as follows: state a, (a) The utterance of S + by Sp to L in state s would allow L to infer Bs'vP.</Paragraph> <Paragraph position="1"> (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.</Paragraph> <Paragraph position="2"> Clause (a) says that if the a~rmative form of the sentence were spoken, any listener could infer that the speaker believed 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 believed otherwise. A definition with clause (a) alone woukl capture other pragmatic inferences as well as presupposition. Since clause (b) requires that the candidate exhibit the behavior under negation that is unique to presupposition, it excludes the others. See (Herren 1987, sec. 4.5) for exmnples.</Paragraph> <Paragraph position="3"> Actual Presupposition An acttml presupposition of a sentence completely situated in context must be a potential presupposition of that sentence and consistent with the context.</Paragraph> <Paragraph position="4"> 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.</Paragraph> <Paragraph position="5"> (b) If S = S-, s ~ BLBSp~P.</Paragraph> <Paragraph position="6"> In keeping with our philosophy of treating presuppositions as beliefs, clause (b) checks whether the spe~rker believes the potential t)resupposition according to the listener. Since blocking can only occur in negative sentences, 4See section 4 for a comparison of our concepts of&quot; potential and actual presupposition with Gazdt~r's &quot;pre-supl)osition&quot; and &quot;act, ual presupposition.&quot; this check is only performed on negative sentences (see section 3.4 for a qualification).</Paragraph> </Section> <Section position="4" start_page="257" end_page="257" type="sub_section"> <SectionTitle> Example </SectionTitle> <Paragraph position="0"> 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.</Paragraph> <Paragraph position="1"> For any speaker Sp, listener L, and state s, the utterance 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.</Paragraph> <Paragraph position="2"> 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 particular, s ~ BDi~n~B:ro,~P. Therefore, B~'omP is an actual presupposition to Diane of the utterance of sentence S by Tom, in this state. However, Cathie has the previous belief that Tom thinks Chris is not leaving, i.e., s ~ BcathleBTom'~P. Therefore, BTomP is not an actual presupposition to Cathie of the utterance of sentence S by Tom, in this state.</Paragraph> </Section> <Section position="5" start_page="257" end_page="257" type="sub_section"> <SectionTitle> 3.3 Applying the Definitions </SectionTitle> <Paragraph position="0"> Horton (1987, ch. 5) applies the definitions, in the manner shown above, to a representative set of sinlple sentences, and shows that the presuppositions of many sentences 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).</Paragraph> <Paragraph position="1"> (8) Percy criticized Brian for leaving.</Paragraph> <Paragraph position="2"> (9) Percy criticized Brian for leaving, but there was noth null ing wrong with him leaving.</Paragraph> <Paragraph position="3"> 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.</Paragraph> <Paragraph position="4"> ~Brian's leaving was bad.</Paragraph> <Paragraph position="5"> ~ 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.</Paragraph> <Paragraph position="6"> For complex sentences~ one can either again apply the definitions directly or attempt to find rules for determining 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 important. For example, when sentence 11 is embedded in the context of the verb hopes, another level of belief is necessary to expres's the potential presupposition correctly. (11) Lofty is sorry that he upset Willie.</Paragraph> <Paragraph position="7"> >> BLof,u( Lofty upset Willie).</Paragraph> <Paragraph position="8"> (12) Ethel hopes Lofty is sorry that he upset Willie. >> BEtheZBLol~( Lofty upset Willie).</Paragraph> <Paragraph position="9"> 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.</Paragraph> <Paragraph position="10"> (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 incorrectly 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 considers only the beliefs of the speaker, cannot capture this presupposition.</Paragraph> <Paragraph position="11"> 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 beliefs of agents other than just the speaker.</Paragraph> </Section> <Section position="6" start_page="257" end_page="257" type="sub_section"> <SectionTitle> 3.4 Defeat in Affirmative Sentences </SectionTitle> <Paragraph position="0"> The presuppositions of an affirmative sentence usually cannot 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.</Paragraph> <Paragraph position="1"> For example, sentence 14 potentially presupposes 15 because of the definite reference Barney's loud music.</Paragraph> <Paragraph position="2"> (14) If Fred's in his office, Barney's loud music will bother him.</Paragraph> <Paragraph position="3"> (15) Barney is playing loud music.</Paragraph> <Paragraph position="4"> However, in the context of 16, the presupposition does not hold.</Paragraph> <Paragraph position="5"> (16) Barney plays loud music when Fred's in his office, just to bother him.</Paragraph> <Paragraph position="6"> In this case, the contextual information combines with the /\]-clause of 14 to establish that the potential presupposition 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 established as hypothetical by a clause of the sentence in combination with contextual information. Horton (1987) enumerates these relatively infrequent cases.</Paragraph> <Paragraph position="7"> 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 possible. In this section we discuss two ways to do so. Both are compatible with our approach.</Paragraph> <Paragraph position="8"> 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 affirmative 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.</Paragraph> <Paragraph position="9"> 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.</Paragraph> <Paragraph position="10"> (b) If S = S-, s ~k BLBs,,-~P.</Paragraph> <Paragraph position="11"> (e) ,~ ba B~B~,Q.</Paragraph> <Paragraph position="12"> 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.</Paragraph> <Paragraph position="13"> 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 regarding defeat in affirmative sentences is to treat affirmative and negative sentences uniformly, that is, to perform the consistency check on both types of sentence. This approach, adopted by Gazdar (1979a, 1979b), requires no special mechanism to account for felicitous defeat in affirmative 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 &quot;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.</Paragraph> <Paragraph position="14"> (18) I'm sorry that I didn't see it.</Paragraph> <Paragraph position="15"> However, I didn't ace Les Miadrables is also an entaihnent of 18 (bec~mse factive verbs entail their complements). 5Gazdar's &quot;pre-suppositions&quot; correspond roughly to onr porchtim 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 cumulative context and sentence 18 is therefore predicted to be infelicitous in the context of 17.</Paragraph> <Paragraph position="16"> 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.</Paragraph> <Paragraph position="17"> Casting the &quot;uniform&quot; approach in our terms, wc get the following definitions: DEFINITION 6: Sentence S potentially presupposes proposition P ill&quot; 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.</Paragraph> <Paragraph position="18"> 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.</Paragraph> <Paragraph position="19"> (b) s \[/= BLBsv~P.</Paragraph> <Paragraph position="20"> We are at present undecided as to which of these two methods to prefer. Both explain the t)henomena. Treating 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 approach 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)position under negation. In contrast, the earlier definitions 4 and 5 can distinguish presupposition from other kinds of impli cation.</Paragraph> <Paragraph position="21"> 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.</Paragraph> </Section> </Section> <Section position="6" start_page="257" end_page="259" type="metho"> <SectionTitle> 4 Comparison with Gazdar's Approach </SectionTitle> <Paragraph position="0"> 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. Consistency is also central to our analysis. In addition, the structure of our account is similar to Gazdar's. In particular, both accounts first compute preliminary propositions in our case potential presuppositions and in Gazdar's, &quot;pre-suppositions&quot; -- and then perform a consistency-based context check to find the presuppositions of the sen6Gazdar 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.</Paragraph> <Paragraph position="1"> tence or utterance in context. Despite the structural similarities, there are important differences between the two approaches. We will now describe some of these.</Paragraph> <Paragraph position="2"> First, for Gazdar a sentence may &quot;pre-suppose&quot; a proposition that it can never, on any occasion of use, presuppose. His &quot;pre-suppositions&quot; are simply convcnient intermediate 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 &quot;pre-suppositions&quot; 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 account of presupposition to be our main contribution.</Paragraph> </Section> class="xml-element"></Paper>