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<Paper uid="E95-1032">
  <Title>Ellipsis and Quantification: A Substitutional Approach</Title>
  <Section position="3" start_page="0" end_page="229" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Dalrymple, Shieber and Pereira (1991) (henceforth, DSP) give an equational treatment of ellipsis via higher-order unification which, amongst other things, provides an insightful analysis of the interactions between ellipsis and quantification. But it suffers a number of drawbacks, especially when viewed from a computational perspective.</Paragraph>
    <Paragraph position="1"> First, the precise order in which quantifiers are scoped and ellipses resolved determines the final interpretation of elliptical sentences. It is hard to see how DSP's analysis could be implemented within a system employing a pipelined architecture that, say, separates quantifier scoping out from other reference resolution operations--this would seem to preclude the generation of some legitimate readings. Yet many systems, for good practical reasons, employ this kind of architecture.</Paragraph>
    <Paragraph position="2"> Second, without additional constraints, DSP slightly overgenerate readings for sentences like (1) 3ohn revised his paper before the teacher did, and so did Bill.</Paragraph>
    <Paragraph position="3"> Kehler (1993a) has convincingly argued that this problem arises because DSP do not distinguish between merely co-referential and co-indexed (in his terminology, role-linked) expressions.</Paragraph>
    <Paragraph position="4"> Third, though perhaps less importantly, higher-order unification going beyond second-order matching is required for resolving ellipses involving quarttification. This increases the computational complexity of the ellipsis resolution task.</Paragraph>
    <Paragraph position="5"> This paper presents a treatment of ellipsis which avoids these difficulties, while having essentially the same coverage as DSP. The treatment is easily implementable, and forms the basis of the ellipsis resolution component currently used within the Core Language Engine (Alshawi et al., 1992).</Paragraph>
    <Paragraph position="6"> Ellipsis interpretations are represented as simple sets of substitutions on semantic representations of the antecedent. The substitutions can be built up in an order-independent way (i.e. before, after or during scoping), and without recourse to higher-order unification. The treatment is similar to the discourse copying analysis of (Kehler, 1993a), and to the substitutional treatment suggested by Kamp within Discourse Representation Theory, described in (Gawron and Peters, 1990). However, we extend the notion of strict and sloppy identity to deal with more than just pronouns. In doing so, we readily deal with phenomena like scope parallelism.</Paragraph>
    <Paragraph position="7"> While the treatment of ellipsis is hopefully of some value in its own right, a more general conclusion can be drawn concerning the requirements for a computational theory of semantics. Briefly, the standard view within formal semantics, which DSP inherit, identifies semantic interpretation with composition: interpretation is the process of taking the meanings of various constituents and composing them together to form the meaning of the whole.</Paragraph>
    <Paragraph position="8"> This makes semantic interpretation a highly order-dependent affair; e.g. the order in which a functor is composed with its arguments can substantially affect the resulting meaning. This is reflected in the order-sensitive interleaving of scope and ellipsis resolution in DSP's account. In addition, composition is only sensitive to the meanings of its components.</Paragraph>
    <Paragraph position="9"> Typically there is a many-one mapping from compositions onto meanings. So, for example, whether two terms with identical meanings are merely co-referential or are co-indexed is the kind of information that may get lost: the difference amounts to two ways of composing the same meaning.</Paragraph>
    <Paragraph position="10"> The alternative proposed here is to view seman- null tic interpretation as a process of building a (possibly partial) description of the intended semantic composition; i.e. (partial) descriptions of what the meanings of various constituents are, and how they should be composed together: While the order in which composition operations are performed can radically affect the outcome, the order in which descriptions are built up is unimportant. In the case of ellipsis, this extra layer of descriptive indirection permits an equational treatment of ellipsis that (i) is order-independent, (ii) can take account compositional distinctions that do not result in meaning differences, and also (iii) does not require the use of higher-order unification for dealing with quantitiers.</Paragraph>
    <Paragraph position="11"> The paper is organised as follows. Section 2 describes the substitutional treatment of ellipsis by way of a few examples presented in a simplified version of Quasi Logical Form (QLF) (Alshawi and Crouch, 1992; Alshawi et el., 1992). Section 3 gives the semantics for the notation, and argues that QLF is best understood as providing descriptions of semantic compositions. Section 4 raises some open questions concerning the determination of parallelism between ellipsis and antecedent, and other issues. Section 5 concludes.</Paragraph>
  </Section>
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