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<Paper uid="C96-1073">
  <Title>Focus and Higher-Order Unification</Title>
  <Section position="2" start_page="0" end_page="430" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> In this paper, we argue that Higher Order Unification (HOU) provides a linguistically adequate tool for modeling the semantics of focus. Building up on (Pulman, 1995), we develop a unification-based analysis of focus which we show favourably compares with two prominent theories of focus,</Paragraph>
    <Section position="1" start_page="0" end_page="430" type="sub_section">
      <SectionTitle>
Rooth's Alternative Semantics and Krifka's Struc-
</SectionTitle>
      <Paragraph position="0"> tured Meanings theory. For data which is generally viewed as a test-bed for focus theory (utterances with multiple focus operators and second occurrence expressions), we show that contrary to Rooth's and Krifka's theories, the HOU treatment yields a transparent analysis while avoiding under- and over-generation.</Paragraph>
      <Paragraph position="1"> Focus is a much debated notion. In this paper, we assume a simplifed version of Jackendoff's definition: a focus is the semantic value of a prosoditally prominent element. We take the identification of prosodically prominent elements as given. To set the stage for this paper, we will briefly review the folklore, i.e. the main issues of focus theory. It is commonly agreed that focus triggers the formation of an additional semantic value which we will call the Focus Semantic Value (FSV). The name and definition of the FSV varies from author to author: Jackendoff (Jackendoff, 1972) calls it the presuppositional set, Rooth (Rooth, 1992) the Alternative Sct and Krifka (Krifka, 1992) the Ground. In this paper, we assume a definition of the FSV which is in essence Rooth's Alternative set, that is, tile set of semantic objects obtained by making an appropriate substitution in the focus position. For instance, the FSV of (la) is defined as (lb), the set of properties of the form like-lug y where y is an individual (in what follows, focus is indica~ted using upper-case; we also follow Montague's convention that for any type % D~ is the set of objects of type r and wff~ is the set of wits of type r).</Paragraph>
      <Paragraph position="2">  (1) a. Jon only likes MARY b. lyc  It is also usuMly agreed that certain linguistic elements associate with focus in that the meaning of the utterance containing these elements varies depending on the choice of focus. For instance in (2a-b), the focus operator only associates with focus so that the difference in focus between (2a) and (2b) induces a difference in meaning between the two utterances: in a world where aon introduced Paul to Mary and Sarah, and no other introduction takes place, (2a) is necessarily  false whilst (2b) is true.</Paragraph>
      <Paragraph position="3"> (2) a. Jon only int,vduced Paul to MARY b. .Ion only intr'od,tced PAUL to Mary To model this &amp;quot;association with focus&amp;quot; phenomenon, the semantics of associating-elements (e.g. focus operators, qttantifieational adverbs) is made contingent on the FSV which itself, wtries with the choice of focus. The following example illustrates this. Suppose that the meaning of o'nlg is determined by the following rule:</Paragraph>
      <Paragraph position="5"> where NP', VP' represent the meaning of NP and VP respectively, and t, kS'V stands for the focus semantic value of the VP. As we have seen above, the FSV of (la) is (lb), hence by the above semantic for only, the semantics of (1 a) is:</Paragraph>
      <Paragraph position="7"> Intuitively, the only property of the form likeing y that holds of Jon is the property of like ing Mary.</Paragraph>
    </Section>
  </Section>
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