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<Paper uid="W06-1602">
  <Title>Sydney, July 2006. c(c)2006 Association for Computational Linguistics An Empirical Approach to the Interpretation of Superlatives</Title>
  <Section position="4" start_page="0" end_page="10" type="intro">
    <SectionTitle>
2 Syntax and Semantics of Superlatives
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="0" end_page="9" type="sub_section">
      <SectionTitle>
2.1 Surface Forms
</SectionTitle>
      <Paragraph position="0"> In English, superlative adjectives appear in a large variety of syntactic and morphological forms.</Paragraph>
      <Paragraph position="1"> One-syllable adjectives and some two-syllable adjectivesaredirectlyinflectedwiththesuffix&amp;quot;-est&amp;quot;. null Somewordsoftwosyllablesandallwordsofthree or more syllables are instead introduced by &amp;quot;most&amp;quot; (or &amp;quot;least&amp;quot;). Superlatives can be modified by ordinals, cardinals or adverbs, such as intensifiers or modals, and are normally preceeded by the definite article or a possessive. The examples below illustrate the wide variety and uses of superlative adjectives.</Paragraph>
      <Paragraph position="2">  the tallest woman AS Roma's quickest player the Big Board's most respected floor traders France's third-largest chemical group the most-recent wave of friendly takeovers the two largest competitors the the southern-most tip of England its lowest possible prices Superlative adjectives can manifest themselves in predicative (&amp;quot;Mia is the tallest.&amp;quot;) or attributive form (&amp;quot;the tallest woman&amp;quot;). Furthermore, there are superlative adverbs, such as &amp;quot;most recently&amp;quot;, and idiomatic usages.</Paragraph>
    </Section>
    <Section position="2" start_page="9" end_page="9" type="sub_section">
      <SectionTitle>
2.2 The Comparison Set
</SectionTitle>
      <Paragraph position="0"> It is well known that superlatives can be analysed in terms of comparative constructions (Szabolcsi, 1986; Alshawi, 1992; Gawron, 1995; Heim, 1999; Farkas and Kiss, 2000). Accordingly, &amp;quot;the oldest character&amp;quot; can be interpreted as the character such that there is no older character, in the given context. Therefore, a correct semantic interpretation of the superlative depends on the correct characterisation of the comparison set. The comparison set denotes the set of entities that are compared to each other with respect to a certain dimension (see Section 2.3). In &amp;quot;the oldest character in the book&amp;quot;, the members of the comparison set are characters in the book, and the dimension of comparison is age.</Paragraph>
      <Paragraph position="1"> The computation of the comparison set is complicated by complex syntactic structure involving the superlative. The presence of possessives for example, as in &amp;quot;AS Roma's quickest player&amp;quot;, extends the comparison set to players of AS Roma.</Paragraph>
      <Paragraph position="2"> Prepositional phrases (PPs), gerunds, and relative clauses introduce additional complexity. PPs that are attached to the head noun of the superlative are part of the comparison set -- those that modify the entire NP are not. Similarly, restrictive relative clause are included in the comparison set, non-restrictive aren't.</Paragraph>
      <Paragraph position="3"> We illustrate this complexity in the following examples, taken from the Wall Street Journal, where the comparison set is underlined: The oldest designer got to work on the dashboard, she recalls. (WSJ02) A spokesman for Borden Inc., the nation's largestmilk producer, concedesGoyamaybeon to something. (WSJ02) Right now, the largest loan the FHA can insure in high-cost housing markets is $101,250.</Paragraph>
      <Paragraph position="4"> (WSJ03) With newspapers being the largest single component of solid waste in our landfills ...</Paragraph>
      <Paragraph position="5"> (WSJ02) ... questions being raised by what generally are considered the most complex arms-control talks ever attempted. (WSJ02) Besides syntactic ambiguities, the determination of the comparison set can be further complicated by semantic ambiguities. Some occurrences of superlatives licence a so-called &amp;quot;comparitive&amp;quot; reading, as in the following example discussed in the formal semantics literature (Heim, 1999; Szabolcsi, 1986): John climbed the highest mountain.</Paragraph>
      <Paragraph position="6"> Here, in the standard interpretion, the mountain referred to is the highest available in the context. However, another interpretation might arise inasituationwhereseveralpeopleclimbedseveral mountains, and John climbed a mountain higher than anyone else did, but not necessarily the highest of all mountains in the context. Our corpus study reveals that these readings are rare, although they tend to be more frequent in questions than in newspaper texts.</Paragraph>
    </Section>
    <Section position="3" start_page="9" end_page="9" type="sub_section">
      <SectionTitle>
2.3 Dimension
</SectionTitle>
      <Paragraph position="0"> Part of the task of semantically interpretating superlative adjectives is the selection of the dimension on which entities are compared. In &amp;quot;the  highestmountain&amp;quot;wecomparemountainswithrespect to the dimension height, in &amp;quot;the best paper&amp;quot; we compare papers with respect to the dimension quality, and so on. A well-known problem is that some adjectives can be ambiguous or vague in choosing their dimension. Detecting the appropriate dimension is not covered in this paper, but is orthogonal to the analysis we provide.</Paragraph>
    </Section>
    <Section position="4" start_page="9" end_page="10" type="sub_section">
      <SectionTitle>
2.4 Superlatives and Entailment
</SectionTitle>
      <Paragraph position="0"> Superlatives exhibit a non-trivial semantics. Some examples of textual entailment make this very evident. Consider the contrasts in the following entailment tests with indefinite and universally quantified noun phrases: I bought a blue car |=I bought a car I bought a car negationslash|=I bought a blue car I bought every blue car negationslash|=I bought every car I bought every car |=I bought every blue car  Observe that the directions of entailments are mirrorred. Now consider a similar test with superlatives, where the entailments fail in both directions: null I bought the cheapest blue car negationslash|=I bought the cheapest car I bought the cheapest car negationslash|=I bought the cheapest blue car. These entailment tests underline the point that the meaning of superlatives is rather complicated, and that a shallow semantic representation, say lx.[cheapest(x) [?] car(x)] for &amp;quot;cheapest car&amp;quot;, simply won't suffice. A semantic represention capturing the meaning of a superlative requires a more sophisticated analysis. In particular, it is important to explicitly represent the comparison set of a superlative. In &amp;quot;the cheapest car&amp;quot;, the comparison set is formed by the set of cars, whereas in &amp;quot;the cheapest blue car&amp;quot;, the comparison set is the set of blue cars. Semantically, we can represent &amp;quot;cheapest blue car&amp;quot; as follows, where the comparison set is made explicit in the antecedent of the conditional:</Paragraph>
      <Paragraph position="2"> blue car is cheaper than any other blue car. A meaning representation like this will logically predict the correct entailment relations for superlatives. null</Paragraph>
    </Section>
  </Section>
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