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<Paper uid="P99-1007">
  <Title>Unifying Parallels</Title>
  <Section position="3" start_page="0" end_page="49" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> (Dalrymple et al., 1991; Shieber et al., 1996) (henceforth DSP) present a treatment of VP-ellipsis which can be sketched as follows. An elliptical construction involves two phrases (usually clauses) which are in some sense structurally parallel. Whereas the first clause (we refer to it as the source) is semantically complete, the second (or target) clause is missing semantic material which can be recovered from the source.</Paragraph>
    <Paragraph position="1"> Formally the analysis consists of two components: the representation of the overall discourse (i.e. source and target clauses) and an equation which permits recovering the missing semantics.</Paragraph>
    <Paragraph position="3"> S is the semantic representation of the source, $1,..., Sn and T1,... ,Tn are the semantic representations of the parallel elements in the source and target respectively and R represents the relation to be recovered. The equation is solved using Higher-Order Unification (HOU): Given any solvable equation M = N, HOU yields a substitution of terms for free variables that makes M and N equal in the theory of a/~v-identity.</Paragraph>
    <Paragraph position="4"> The following example illustrates the workings of this analysis: (1) Jon likes Sarah and Peter does too.</Paragraph>
    <Paragraph position="5"> In this case the semantic representation and the equation associated with the overall discourse ar e: Equation R(j) = like(j,s) For this equation, HOU yields the substitution1: {R x.like(x,s)} and as a result, the resolved semantics of the target is: Ax.like(x, s)(p) - like(p, s) The DSP approach has become very influential in computational linguistics for two main reasons. First, it accounts for a wide range of observations concerning the interaction of VPellipsis, quantification and anaphora. Second, it bases semantic construction on a tool, HOU, which is both theoretically and computationally attractive. Theoretically, HOU is well-defined and well-understood - this permits a clear understanding of both the limitations and the predictions of the approach. Computationally, it has both a declarative and a procedural interpretation - this supports both transparency and implementation.</Paragraph>
    <Paragraph position="6"> 1As (Dalrymple et al., 1991) themselves observe, HOU also yields other, linguistically invalid, solutions. For a proposal on how to solve this over-generation problem, see (Gardent and Kohlhase, 1996b; Gardent et al., 1999).</Paragraph>
    <Paragraph position="7">  In this paper, I start (section 2) by clarifying the relationship between DSP's proposal and the semantic representation of discourse anaphors. In section 3 and 4, I then show that the HOU-treatment of ellipsis naturally extends  to provide: * A treatment of the interaction between parallelism and focus and * A general account of sloppy identity  Section 6 concludes and compares the approach with related work.</Paragraph>
  </Section>
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