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<?xml version="1.0" standalone="yes"?> <Paper uid="E93-1014"> <Title>On the notion of uniqueness *</Title> <Section position="3" start_page="106" end_page="106" type="metho"> <SectionTitle> 1 Restrictive and Non-Restrlctive </SectionTitle> <Paragraph position="0"> Modification in DRT In Discourse Representation Theories (\[Kamp, 1981; Kamp and Reyle, 1990; Helm, 1982\]) no distinction is made between restrictive and non-restrictive modification. This assumption was challenged in e.g. \[Sells, 1985\] who argues for a distinction in meaning between the following minimal pairs: (4) a Anne owns two parrots, which talk to her) b Anne owns two parrots that talk to her.</Paragraph> <Paragraph position="1"> (5) a The talking parrots are happy.</Paragraph> <Paragraph position="2"> b The talking parrots are happy.</Paragraph> <Paragraph position="3"> The examples in a) concern non-restrictive modification. Example (4)a makes a claim about all the parrots that Anne owns: there are two and they talk to her. She owns no others, talking or non-talking. In (4)b on the other hand, no such uniqueness claim is made. She may own other parrots, especially non-talking ones.</Paragraph> <Paragraph position="4"> 1Note that 'which' can also be used in the restrictive sense but in this paper, it is reserved for the non-restrictive reading, to avoid confusion.</Paragraph> <Paragraph position="5"> If we consider continuations of these sentences as in (6) and (7), or a linguistic context as in (8), the distinctions show more clearly: Anne owns two parrots that talk to her.</Paragraph> <Paragraph position="6"> The others never say a word.</Paragraph> <Paragraph position="7"> The talking parrots are happy.</Paragraph> <Paragraph position="8"> * The others ..</Paragraph> <Paragraph position="9"> The ~aiking parrots are happy.</Paragraph> <Paragraph position="10"> The others look depressed.</Paragraph> <Paragraph position="11"> Anne owns a lot of parrots.</Paragraph> <Paragraph position="12"> * She has two parrots, which talk She has two parrots that talk.</Paragraph> <Paragraph position="13"> The NPs in the a)-examples should be interpreted as 'the one and only set X such that all members x</Paragraph> <Paragraph position="15"> This phenomenon has received much attention in the literature, and is known as uniqueness (\[Heim, 1982; Kadmon, 1987\]), maximality (\[Sells, 1985\]) or the E-type effect (\[Evans, 1980\]).</Paragraph> <Paragraph position="16"> In DRT, non-restrictive pronouns, restrictive pro- null nouns and ordinary pronominals are all represented the same. The representation for all the variants in (9) is (10): (9) a b Anne owns two parrots, which talk.</Paragraph> <Paragraph position="17"> Anne owns two parrots that talk.</Paragraph> <Paragraph position="18"> Anne owns two parrots. They talk.</Paragraph> <Paragraph position="20"> A function verifies the representation in (10) iff there is a set of two parrots that Anne owns and that talk. If Anne in fact owns 5 parrots, and 3 of them talk, all sentences in (9) are equally true in DRT.</Paragraph> <Paragraph position="21"> There are two interpretation aspects related to these examples that DRT does not acknowledge: First, if we utter sentences like (9) and that's all we say about those parrots, then most people actually think that Anne owns two talking parrots, not seven or hundred. We take this set of two talking parrots owned by Anne to be unique. Second, in an example like (9)a, the uniqueness-effect is brought about even before 'closing the discourse'. The non-restrictive relative clause has the effect of uniquely determining two parrots that Anne owns. And all of these parrots talk.</Paragraph> </Section> <Section position="4" start_page="106" end_page="108" type="metho"> <SectionTitle> 2 Other Proposals </SectionTitle> <Paragraph position="0"> In the following, two proposals will be discussed that aim at (partially) solving the uniqueness problem. In \[Sells, 1985\] non-restrictive and restrictive pronouns get different interpretations. \[Zeevat, to appear\] relines DRT-interpretation in another way: certain parts of the discourse representation are 'closed', the effect of which is that the reference markers in that part of the discourse get a unique interpretation.</Paragraph> <Section position="1" start_page="107" end_page="107" type="sub_section"> <SectionTitle> 2.1 Maximality </SectionTitle> <Paragraph position="0"> In \[Sells, 1985\], it is argued that a distinction needs to be made between restrictive and non-restrictive modification. Sells proposes an alternative interpretation for non-restrictive relative pronouns, in which the pronoun is evaluated with respect to every way the antecedent was satified.</Paragraph> <Paragraph position="1"> (11) a John owns some sheep, which graze (11) b Bz,v,z \[ John=x & sheep(Y) &5 owns(x,Y)</Paragraph> <Paragraph position="3"> The function g verifies K' iff Vf verifying K, Vale e f(Y) ~ a * g(Z)\] So, for each and every sheep that John owns, it must hold that the sheep grazes. This contrasts to a restrictive interpretation, in which case the pronoun is evaluated with respect to the one particular embedding function currently specified for the an-</Paragraph> <Paragraph position="5"> The function f verifies K iff Va \[a E f(Y) iff a e f(Z)\] The restrictive interpretation requires that there be a set of sheep for which it holds that every sheep in the set grazes and is owned by John. There is no maximality (or uniqueness) effect with restrictive modification.</Paragraph> <Paragraph position="6"> This approach predicts that one cannot utter (13) when John owns ten sheep, of which only 5 graze: (13) John owns 5 sheep, which graze There are ways in which the antecedent is verified but the anaphoric extension is not. However, note that, according to this proposal, (13) is a correct utterance in case John owns 10 sheep, and all of them graze. This prediction will be discussed more extensively in section 2.3.</Paragraph> </Section> <Section position="2" start_page="107" end_page="107" type="sub_section"> <SectionTitle> 2.2 Exhaustiveness </SectionTitle> <Paragraph position="0"> In \[Zeevat, to appear\] the notion of exhaustiveness (cf. \[Groenendijk en Stokhof, 1984\]) is used, to account for the maximality effect. Zeevat expresses exhaustification as a condition on truthful embeddings.</Paragraph> <Paragraph position="1"> (14) A function f embeds a DI~ A exhaustively iff: embeds A and Vh =din(A) f : h embeds A =~ Vx E din(A) h(x) C f(x) \] The function f will assign sets of the domain of individuals to the discourse markers. These sets must be such that there are no other sets - to be assigned by any other function h - that have the same properties but are not contained in the sets assigned by f. Take the following examples: (15) a Bill owns sheep. John shears them.</Paragraph> <Paragraph position="2"> b There is a doctor in London. He is Polish. The exhaustive verifying function necessarily picks the maximal set of sheep Bill Owns (else there would be other another set chosen by some function h that would contain the current set). All of these sheep are sheared by John. Similarly, 'a doctor' in b) necessarily refers to a unique individual who is a doctor in London. That explains the weirdness of (15)b since we expect London to have more than one doctor.</Paragraph> </Section> <Section position="3" start_page="107" end_page="108" type="sub_section"> <SectionTitle> 2.3 Discussion </SectionTitle> <Paragraph position="0"> In this subsection I would like to summarize some of the predictions made by the approaches discussed above.</Paragraph> <Paragraph position="1"> One major distinction between Sells' approach and Zeevat's is that Sells 'blames' the anaphor for the maximality effect whereas in Zeevat's approach, constituents have a unique interpretation by virtue of their being in focus.</Paragraph> <Paragraph position="2"> In Sells' theory, the antecedent is evaluated in the same way as in the original Dl~T-analysis. So, for a discourse as (16), this means that Anne may have more than two hikes. Furthermore, Sells claims that for all of the bikes Anne has - even if she has 15 it must be true that she got them from her brother. In my opinion, this is not the interpretation of (16). Indeed, it is possible that Anne has more than two bikes - bikes we don't care about in this story - but theses bikes were not necessarily from her brother.</Paragraph> <Paragraph position="3"> On the contrary, the preferred reading is that they were not.</Paragraph> <Paragraph position="4"> (16) Anne has two bikes. She got them from her brother.</Paragraph> <Paragraph position="5"> In Zeevat's approach, exhanstification of the antecedent is induced independently of the nature of the anaphor. If an NP is (in) a focussed constituent, it is maximized. Let us consider the example that motivated this analysis, (15)b, repeated here.</Paragraph> <Paragraph position="6"> (15) b There is a doctor in London. He is Polish. Now suppose I am addressing a friend of mine, who is Polish and very ill. She's telling me that she dreads going to a doctor in England, everything being unfamiliar to her etc. I think in such a situation, it is completely natural to tell her the following. (17) There is a doctor in London. He is Polish.</Paragraph> <Paragraph position="7"> It seems best that you go and see him.</Paragraph> <Paragraph position="8"> You can talk to him in your own language.</Paragraph> <Paragraph position="9"> I'm sure he'll understand you.</Paragraph> <Paragraph position="10"> Summarizing, the idea of exhaustification accounts for uniqueness by demanding that the verifying embedding is unique. The problem is to explain why it should uniquely verify the DRS related to the first sentence in (15)b - to explain the weirdness - but not so in (16). Sells' maximMity proposal accounted for uniqueness claims imposed by anaphora, but has some undesirable empirical consequences.</Paragraph> </Section> </Section> <Section position="5" start_page="108" end_page="108" type="metho"> <SectionTitle> 3 An alternative account </SectionTitle> <Paragraph position="0"> We have discussed two proposals that made an attempt to clarify the uniqueness problem. In one approach, it is the anaphor that imposes a unique interpretation on the antecedent. In the other, the closing off of (partial) DRS's causes this effect. Below it will be claimed that these two ideas should be combined (and modified) to yield correct results.</Paragraph> <Paragraph position="1"> I assume that the uniqueness effect stems from two sources: * the closed world assumption (implicit) * linguistic means (explicit) These assumptions will be discussed in the sections to follow.</Paragraph> <Section position="1" start_page="108" end_page="108" type="sub_section"> <SectionTitle> 3.1 Closed World </SectionTitle> <Paragraph position="0"> The closed world assumption has the effect that, for a discourse as a whole, the reference markers are maximized. Consider the following paradigm: (18) I dropped a wine glass (19) I dropped a wine glass It was very expensive.</Paragraph> <Paragraph position="1"> (20) I dropped a wine glass last night.</Paragraph> <Paragraph position="2"> It was very expensive.</Paragraph> <Paragraph position="3"> The glass was dear to me, I inherited it from my grandmother.</Paragraph> <Paragraph position="4"> last night.</Paragraph> <Paragraph position="5"> last night.</Paragraph> <Paragraph position="6"> If someone drops a line as (18), it creates the impression she dropped one and only one wine glass. If, on the other hand, (19) is uttered, it may be that she dropped an entire tray of glasses. But, only one of them was expensive. Similarly, in (20), the thing that is unique is the x such that</Paragraph> <Paragraph position="8"> herited_fromJny_grandmother(x).</Paragraph> <Paragraph position="9"> So, this sense of uniqueness is not triggered by anything in particular in the discourse. It is a side effect of closing off the discourse.</Paragraph> </Section> <Section position="2" start_page="108" end_page="108" type="sub_section"> <SectionTitle> 3.2 Explicit Uniqueness </SectionTitle> <Paragraph position="0"> As Sells has observed correctly, there are linguistic means to mark uniqueness explicitly. We present some examples in this subsection.</Paragraph> <Paragraph position="1"> Nonrestrictive modifiers Uniqueness, or maximality, is forced by non-restrictive modification, as can be the case in relative clauses and adjective-noun phrases.</Paragraph> <Paragraph position="2"> were training for the match (cf. I caught a glimpse of two players that/who were training for the match) The aggressive police officers were to blame for the incident (cf. The aggressive police officers were to blame for the incident) In both a) examples, one is forced to conclude that there is a unique set of people - two players, police officers respectively - of which all of its members were involved in the action reported on.</Paragraph> </Section> <Section position="3" start_page="108" end_page="108" type="sub_section"> <SectionTitle> Focusing Adjuncts </SectionTitle> <Paragraph position="0"> (23) a Only John knew how to behave b (cf. Even John knew how to behave) Here, in the a) example, the only x such that x knew how to behave is John. In b), on the other hand, it is implied that others knew how to behave, too.</Paragraph> </Section> <Section position="4" start_page="108" end_page="108" type="sub_section"> <SectionTitle> Structural Focusing </SectionTitle> <Paragraph position="0"> (24) a It was John who gave a present to Mary b It was to Mary that John gave a present c It was a present that John gave to Mary None of the above are logically equivalent. As for a), John could easily have given presents to girls other than Mary. This in contrast with b), which claims that Mary was unique in receiving a present from John. And vice versa, b) is compatible with Mary getting presents from other boys, whereas a) is not. And c) is again different, for similar reasons.</Paragraph> </Section> </Section> <Section position="6" start_page="108" end_page="109" type="metho"> <SectionTitle> 4 The Analysis </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="108" end_page="109" type="sub_section"> <SectionTitle> 4.1 Uniqueness of Discourse </SectionTitle> <Paragraph position="0"> For the closed world assumption, we adopt exhaustiveness for discourses along the line of \[Groenendijk en Stokhof, 1984\] en \[Zeevat, to appear\]. Exhaustilication applies to the verification of the entire discourse, and as such, it is more natural to define the condition on the function that embeds the discourse (as in Zeevat) than in the grammar (as in Groenendijk & Stokhof).</Paragraph> <Paragraph position="1"> (25) The embedding function f uniquely verifies the DRS K in M iff: f verifies the conditions in M and Vh \[Vx * rm(K) =C/, h(x) C f(x)\] Note that uniqueness is a property of closed off discourses (or discourse units).</Paragraph> <Paragraph position="2"> Let me explain the unique verification in view of the following examples: (26) a I spoke to two students yesterday.</Paragraph> <Paragraph position="3"> They thought the exam was too difficult.</Paragraph> <Paragraph position="4"> b I spoke to at least two students yesterday. They thought the exam was too difficult.</Paragraph> <Paragraph position="5"> If I spoke to exactly two students who thought the exam was too difficult, a) en b) are both true. The verifying function maps the reference marker onto the maximal set of students, 2 in this case. Both a) and b) are also compatible with the situation where I spoke to many students during that day but only two of them thought that the exam was too difficult. What discriminates a) from b) is when I spoke to 5 students who reported this complaint about the exam. In a), f maps the reference marker onto a set of two students who complained about the exam. There are other sets with the same properties, though, sets that are not contained in the set verifyied by f. Discourse b) can in this scenario not be understood as referring to only 2, 3 or 4 students. The embedding function must map the reference marker onto the maximal set, i.e the set of</Paragraph> </Section> </Section> <Section position="7" start_page="109" end_page="110" type="metho"> <SectionTitle> 5 students. </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="109" end_page="110" type="sub_section"> <SectionTitle> 4.2 Uniqueness of Antecedents </SectionTitle> <Paragraph position="0"> For the analysis of uniqueness forced by linguistic means, I distinguish three cases: The a) examples of (21)-(23), and (24)a-c all explicitly mark uniqueness: (21) by the non-restrictive clause, (22) by the lack of stress on the modifier, (23) a focusing adjunct, and (24)a-c, uniqueness is forced by the clefting construction. Similarly, the b) examples in (21)-(23) mark non-uniqueness. In (22)b, for example, the stressed modifier 'aggressive' indicates that there were non-aggressive police officers - else we should have uttered (22)a.</Paragraph> <Paragraph position="1"> Note that this list of linguistic 'tools' to mark (non)uniqueness is, of course, far from exhaustive. The point I want to make is that sometimes the context forces a (non)unique interpretation, but in absence of such explicit indicators, the interpretation is vague about (non)uniqueness.</Paragraph> <Paragraph position="2"> The neutral counterparts of (21)-(23) are the following: null (21) c (22) c I caught a glimpse of two players.</Paragraph> <Paragraph position="3"> They were training for the match.</Paragraph> <Paragraph position="4"> The aggressive police officers were to blame for the incident 2 (23) c John knew how to behave (24) d John gave a present to Mary For the neutral interpretation of pronouns, we adopt the standard DRT-analysis for anaphora. The Anaphora Condition below is logically equivalent to the interpretation of '=' in 'x=y' for anaphora in DRT.</Paragraph> <Paragraph position="5"> Given a function 2&quot;, and g an extension of f:</Paragraph> <Paragraph position="7"> The non-restrictive interpretation is forced when we add to the anaphora condition that the antecedent is verified in such a way that there is no other set that has the same properties and is not a subset of the set denoted by the antecedent.</Paragraph> <Paragraph position="9"> Note that we need the Uniqueness Condition independently for precision adverbs such as 'exactly' in 'exactly 2'.</Paragraph> <Paragraph position="10"> The non-uniqueness condition requires that besides the set that satisfies the antecedent for this contingent function, there is at least another element with the same properties.</Paragraph> <Paragraph position="12"> 2In spoken language, there would be no neutral form. The stress pattern would always indicate (non)restrictivity. In writing, which is what (22)c. refers to, it usually vague, or ambiguous between the two readings.</Paragraph> </Section> <Section position="2" start_page="110" end_page="110" type="sub_section"> <SectionTitle> 4.3 ~rther Predictions </SectionTitle> <Paragraph position="0"> First, note that my approach deviates from the traditional view that non-restrictive pronouns and ordinary pronouns should be interpreted equally.</Paragraph> <Paragraph position="1"> So, the objection against the unique interpretation in examples like (25) does not hold for the analysis presented above. Pronouns could indicate uniqueness but do not so necessarily. (25) is not a counterexample, the pronoun can be used in this non-unique interpretation.</Paragraph> <Paragraph position="2"> (25) If a man is in Athens, he is not in Rome However, if we consider examples where both a unique and a non-unique interpretation are possible, the non-restrictive pronoun forces uniqueness, whereas the ordinary pronoun can be interpreted either way.</Paragraph> <Paragraph position="3"> (26) a b If I want to marry a 16-year old, who I happen to love, then that's my business.</Paragraph> <Paragraph position="4"> If I want to marry a 16-year old and I happen to love him, then that's my business.</Paragraph> <Paragraph position="5"> The differences are subtle but (26)a seems to be appropriate only when there actually exists such a boy the speaker wants to marry or, in other words, there is a unique candidate in the world. (26)b could easily be uttered in a situation where there is no unique boy that fits the description. The discussion is about the age difference between lovers and (26)b is uttered not to report on an actual (unique) situation but to generalize over possible situations. The analysis also explains why proper names can never be modified restrictively. After all, a proper name is mapped unto a unique element from the start. There is no way that a subset can be taken from that one element.</Paragraph> <Paragraph position="6"> Rambo-movies than the one I didn't like. The restrictive clause picks a subset from the set of movies. A similar argument holds for &quot;generic&quot; uses of NPs: (28) a Cats, which are ugly, are not allowed in my house.</Paragraph> <Paragraph position="7"> b Cats that are ugly are not allowed in my house.</Paragraph> <Paragraph position="8"> When uttering (28)a, I run the risk of offending all my. cat-loving friends. There is no doubt that I claim that all cats are ugly animals. It would be more diplomatic to utter b), where I only talk about a subset of cats (excluding, of course, my friends' cats ..).</Paragraph> </Section> </Section> class="xml-element"></Paper>