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<Paper uid="W00-1424">
  <Title>Generating Vague Descriptions</Title>
  <Section position="7" start_page="181" end_page="183" type="concl">
    <SectionTitle>
5 Conclusions and loose ends
</SectionTitle>
    <Paragraph position="0"> We have shown how vague descriptions can be gen.. ~erated .that'.make.use-of-one vague-propeift~. We believe our account to be an instructive model of how the 'raw data' in a standard knowledge base can be presented in English expressions that have a very different structure. The numerical data that are the input to our algorithm, for example, take a very different form in the descriptions generated, and yet there is, in an interesting sense, no loss of information: a description has the same reference, whether it uses * ...:,..exaet~.anforroataon:(~he:3c~zz.mouse.) ~or ...~ague:. m,-formation ('The large mouse'), s</Paragraph>
    <Section position="1" start_page="181" end_page="182" type="sub_section">
      <SectionTitle>
5.1 Limitations of the semantic analysis
</SectionTitle>
      <Paragraph position="0"> Our proposal covers the generation of vague descriptions 'from absolute values', which is argued in Dale and Reiter (1995, section 5.1.2) to be most practically useful. When vague input is available (e.g., in the generation component of a Machine Translation system, or in WVSlWYM-style generation (Power and Scott 1998)), simpler methods can be used. Our own account is limited to the generation of definite descriptions and no obvious generalization to indefinite or quantified NPs exists. Other limitations include a. Descriptions that contain properties for other than individuating reasons (as when someone asks you to clean 'the dirty table cloth' when only one table cloth is in sight). This limitation is inherited directly from the D&amp;R algorithm that our own algorithm extends.</Paragraph>
      <Paragraph position="1"> b. Descriptions containing more than one vague property, such as 'The fat tall bookcase', whose meaning is more radically unclear than that of definite descriptions containing only one vague term. (The bookcase may be neither the fattest nor the tallest, and it is not clear how the two dimensions are weighed.) c. Descriptions that rely on the salience of contextually available objects. Krahmer and Theune (1998) have shown that a contextually more adequate version of D~:R can be obtained when degrees of salience are taken into account.</Paragraph>
      <Paragraph position="2"> Their account can be summarized as analysing 'the black dog' as denoting the unique most salient object in the domain that is both black and a dog. (Generalizations of this idea to D&amp;Rmu~ are conceivable but nontrivial since not all elements of the set S have to be equally salient.) Our own extensions of D&amp;R (and perhaps O&amp;Rmu~) could be 'contextualized' if the SThis may be contrasted with the vague expressions gem crated in (Goldberg et al. 1994), where there is a real -- and intended Ioss of information. (E.g., 'Heavy rain fell on Tuesday', bmsed on the information that the rainfall on 'lhlesday equalled ,15rnm.)  role of salience is changed slightly: focusing on the singular case, the algorithm can, for example, be adapted, to, legislate.that:'the, large(est) : mouse' denotes the largest of all those mice that are salient (according to some standard of salience). Note that this analysis predicts ambiguity when the largest mouse that is salient according to one standard is smaller than the largest mouse that is salient according to a more relaxed standard. Suppose, for example, then 'the large(est) mouse' may designate either m2 or m3 depending on the standards of salience used. What this illustrates is that salience and size are both vague properties, and that - as we have seen under point b - combining vague properties is a tricky business.</Paragraph>
    </Section>
    <Section position="2" start_page="182" end_page="182" type="sub_section">
      <SectionTitle>
5.2 Pragmatics
</SectionTitle>
      <Paragraph position="0"> An experimental ProFIT (Erbach 1995) program has implemented the algorithms described so far, generating different descriptions, each of which would allow a reader/hearer to identify an object or a set of objects. But of course, an NLG program has to do more than determine under what circumstances the use of a description leads to a true statement: an additional problem is to choose the most appropriate description from those that are semantically correct. This makes NLG an ideal setting for exploring issues that have plagued semanticists and philosophers when they studied the meaning of vague expressions, such as whether it can be true for two objects x and y which are indistinguishable in size that x is large and y is not (e.g. Synthese 1975).</Paragraph>
      <Paragraph position="1"> The present setting allows us to say that a statement of this kind may be true yet infelicitous (because they conflict with certain pragmatic constraints), and consequently to be avoided by a generator.</Paragraph>
      <Paragraph position="2"> As for the choice between the 'absolute'/superlative forms of the gradable adjective, we conjecture that the following constraints apply: C1. Distinguishability. Expressions of the form 'The (n) large \[CN\]' are infelicitous when the smallest element of the designated set S (named x) and the largest CN smaller than all elements of S (named y) are perceptually indistinguishable. null C2. Natural Grouping. Expressions of the form 'The (n) large \[CN\]' are better avoided when the difference in size between x and y is 'comparativeh small. One way of making this precise is by requiring that the difference hetween x and C3.</Paragraph>
      <Paragraph position="3"> y cannot be smaller than that between either x or y and one of their neighbouring elements.</Paragraph>
      <Paragraph position="4"> Consider, for. example,.: a domain .consisting .of mice that are lcm, lcm, 2cm, 7cm, 9cm and 9cm large; then C2 predicts that the only felicitous use of 'the large mice' refers to the largest three of the group.</Paragraph>
      <Paragraph position="5"> Minimality. Otherwise, preference is given to the absolute form. This implies that when objects of only two sizes are present, and the differ-Salient (strict): ence is perceptually distinguishable, the absoml (2em);,m~.(Scm) ................ .~ * : .,~.~Ante~formds~pr.eferEedover:t~hes~perta'~iv~fovm. Salient (relaxed): (For example, in a domain where there are two ml (2cm), m2 (5cm), m3 (7cm); sizes of pills, we are much more likely to speak of 'the large pills' than of 'the largest pills'.) In languages in which the superlative form is morphologically more complex than the absolute form, constraint C3 can be argued to follow from general Gricean principles (Grice 1975)).</Paragraph>
      <Paragraph position="6"> As for the presence/absence of the numeral, we conjecture that the disambiguating numeral (as in 'the n large mice' or 'the n largest mice') can be omitted under two types of circumstances: (1) when any ambiguity resulting from different values of n is likely to be inconsequential (see Van Deemter and Peters (1996) for various perspectives); (2) when the domain allows only one 'natural grouping' (in the sense of C2). Before and until a more accurate version of the notion of a natural grouping is available (perhaps using fuzzy logic as in Zimmermann 1985), generators could be forbidden to omit the numeral, except in the case of a definite description in the singular.</Paragraph>
    </Section>
    <Section position="3" start_page="182" end_page="183" type="sub_section">
      <SectionTitle>
Appendix: A Supporting Experiment
</SectionTitle>
      <Paragraph position="0"> Human subjects were asked to judge the correctness of an utterance in a variety of situations. The experiment was set up to make plausible that, in a situation in which only perceptual context-dependence (see section 1) is relevant, expressions of the form 'the n. large CN' can be used whenever certain simple conditions are fullfilled. Note that this (0) direction of the hypothesis is most directly relevant to the design of a generator, since we expect a generator to avoid mistakes rather than ahvays use an expression whenever it is legitimate.</Paragraph>
      <Paragraph position="1"> Hypothesis (=&gt;): In a situation in which the domain D represents the set of perceptually relevant objects, an expression of the form 'the n large CN' (where n 2 2 1), can be used to refer to a set S of cardinality n if all objects in D - S are smaller than anv of the n..</Paragraph>
      <Paragraph position="2">  The experiment explores whether 'the n large CN' can refer to the n largest objects in the domain, whether or not this set of objects is held together by spatial position or other factors. Subjects were presented with 26 different situations, in each of which they had to say whether the sentence The two high numbers appear in brackets would constitute a correct utterance. The literal text of our question was: Suppose you want to inform a hearer *.which numbers:.,irr~'a:,gi~ren.list:,appeav inbrackets*, where the hearer knows what the numbers are, but not which of them appear in brackets. For example, the hearer knows that the list is 1 2 1 7 7 1 1 3 1.</Paragraph>
      <Paragraph position="3"> You, as a speaker, know that only the two occurrences of the number 7 appear in brackets: 1 2 1 (7) (7) 1 1 3 1. Our question to you is: Would it be *correct* to convey this information by saying &amp;quot;The two high numbers appear in brackets&amp;quot;? (...).</Paragraph>
      <Paragraph position="4"> All subjects were shown the 26 situations in the same, arbitrary, order. Each situation presented to the subjects contained a list of nine numbers. In 24 cases, the lists had the following form: lllxyzlll, where each of x, y, z equalled either 6 or 9, and where there were always two numbers among x, y, z that appear in brackets. In 16 out of 24 cases, the two bracketed positions are right next to each other, allowing us to test whether spatial contiguity' plays any role. Subjects were presented with two additional situations, namely 1 1 1 (6) 1 (7) 1 1 1 and 1 1 1 (7) 1 (6) 1 1 1 in which, unlike the other 24 situations, the two largest numbers are not equally large, to make sure that the descriptions do not require the elements in their denotation to be similar in that respect. Our questions were presented via email to 30 third-year psychology/cognitive science students at the University of Durham. UK. all of whom were native speakers of English and ten of which responded.</Paragraph>
      <Paragraph position="5"> Results: Eight subjects responded in exact conformance with the analysis of section 2.1, marking all and only those five sequences in which the highest 2 numbers appeared in brackets. Only two subjects deviated slightly from this analysis: one of the two (subject 9) described all the expected situations as 'correct' plus the two cases in which two contiguous 6-es appeared in brackets: the other subject (subject 10) appears to have made a typing err~n, confusing two subsequent situations in the experiment? All other responses of subjects 9 and 10 were as predicted. This means: tha t all .sub.jects except subject 10 were consistent with our '=#' hypothesis. The experiment suggests that the converse of the hypothesis might also be true, in which it is claimed that expressions of the form 'the n large CN' cannot be employed to refer to the set S unless S consists of the n largest objects in D: Hypothesis (.C/=): In a situation in which the domain D represents the set of percept_..: .......... ~ ~.t.ually: relevmtt, ob_jects&gt;a~:-expressionof t~he. form 'the n large CN' (where n _&gt; 1), can only be used to refer to a set S of cardinality n if all objects in D - S are smaller than any of the n.</Paragraph>
      <Paragraph position="6"> Again disregarding subject 10, eight out of nine subjects act in accordance with Hypothesis .C/=, while only one appears to follow a somewhat more liberal rule. Given these findings, it appears to be safe to build a generator that implements both hypotheses, since none of our subjects would be likely to disagree with any of the descriptions generated by it.</Paragraph>
      <Paragraph position="7"> This experiment has evident limitations. In particular, it has no bearing on the pragmatic constraints suggested in section 5.2, which might be tested in a follow-up experiment.</Paragraph>
    </Section>
  </Section>
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