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<Paper uid="C04-1181">
  <Title>Interpreting Vague Utterances in Context</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Modeling context and its effects on interpretation may once have seemed to call for an open-ended investigation of people's knowledge of the common-sense world (Hobbs et al., 1993). But research on the semantics of practical dialogue (Allen et al., 2001) now approaches dimensions of context systematically, through increasingly lightweight, factored models. The evolving state of real-world activity proceeds predictably according to background plans and principles of coordination (Rich et al., 2001). The status of the dialogue itself is defined by circumscribed obligations to ground prior utterances, follow up open issues, and advance real-world negotiation (Larsson and Traum, 2000). Finally, the evolving state of the linguistic context is a direct outgrowth of the linguistic forms interlocutors use and the linguistic relationships among successive utterances (Ginzburg and Cooper, 2001; Asher and Lascarides, 2003). These compatible models combine directly to characterize an aggregate information state that provides a general background for interpretation (Bunt, 2000).</Paragraph>
    <Paragraph position="1"> We argue in this paper that such integrated models enable systems to calculate useful, fine-grained utterance interpretations from radically underspecified semantic forms. We focus in particular on vague scalar predicates like small or long. These predicates typify qualitative linguistic expression of quantitative information, and are thus both challenging and commonplace. Building on a multidimensional treatment of dialogue context, we develop and implement a theoretically-motivated model of vagueness which is unique in treating vague predicates as genuinely vague and genuinely context-sensitive, yet amenable to general processes of contextual and interpretive inference.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
1.1 Semantic insights
</SectionTitle>
      <Paragraph position="0"> We pursue our argument in the context of an implemented drawing application, FIGLET, which allows users to give English instructions to draw a caricature of an expressive face. Figure 1 shows a representative interaction with FIGLET; the user gives the successive instructions in (1):  (1) a. Make two small circles.</Paragraph>
      <Paragraph position="1"> b. Draw a long line underneath.</Paragraph>
      <Paragraph position="2">  Like Di Eugenio and Webber (1996), we emphasize that understanding such instructions requires contextual inference combining linguistic, task and domain knowledge. For example, consider the response to (1a) of placing circles so as to form the eyes of a new face. To recognize the possibility of drawing eyes exploits knowledge of the ongoing drawing task. To put the eyes where they belong in the upper part of the new face exploits domain knowledge. The response to (1b) adds the linguistic context as another ingredient. To identify where the line goes, the user uses the objects mentioned recently in the interaction as the understood spatial landmark for underneath. Figure 1 highlights the importance of using multidimensional representations of dialogue context in understanding instructions for quantitative domains.</Paragraph>
      <Paragraph position="3"> We leverage this background context in our computational approach to vagueness. We model a vague utterance like draw a long line as though it meant draw a line with, you know, length.Inthis approach, vague predicates are completely underspecified; linguistic knowledge says nothing about how long something long is. Instead, vague language explicitly draws on the background knowl-Initial blank figure state. After the user utters (1a): Make two small circles.</Paragraph>
      <Paragraph position="4"> After the user utters (1b): Draw a long line underneath.</Paragraph>
      <Paragraph position="5">  edge already being applied in utterance interpretation. The user's motivation in using long is to differentiate an intended interpretation, here an intended action, from alternative possibilities in context. Background knowledge already sets out the relevant ways to draw a line; drawing a long line means singling out some of them by the length of that new line. This model recalls dynamic theories of vague scalar predicates, such as the semantics of Kyburg and Morreau (2000), Barker (2002), or Kennedy (2003), but it is exactly implemented in FIGLET. The implementation capitalizes on the richness of current models of context to recover content for the you know of vagueness.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
1.2 Overview
</SectionTitle>
      <Paragraph position="0"> In Section 2, we motivate approaches to the semantics of vague scalar predicates that associate them with a presupposed standard of comparison. We illustrate how context can be understood to supply possible standards, and how pragmatic reasoning from utterances allows interlocutors to infer them.</Paragraph>
      <Paragraph position="1"> In Section 3, we establish a bridge to the general treatment of practical dialogue, by showing how multiple dimensions of context generally contribute to recognizing possible interpretations for under-specified utterances. Section 4 builds on Sections 2 and3toshowhowFIGLET exploits a rich model of utterance context to respond cooperatively to vague utterances like (1a) and (1b), while Section 5 details FIGLET's actual implementation. We conclude in Section 6 by suggesting further challenges that vagueness still poses for computational semantics.</Paragraph>
    </Section>
  </Section>
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