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<Paper uid="P02-1010">
  <Title>Ellipsis Resolution with Underspecified Scope</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Explicit computation of all scope configurations is apt to slow down an NLP system considerably.</Paragraph>
    <Paragraph position="1"> Therefore, underspecification of scope ambiguities is an important prerequisite for efficient processing.</Paragraph>
    <Paragraph position="2"> Many tasks, like ellipsis resolution or anaphora resolution, are arguably best performed on a representation with fixed scope order. An underspecification formalism should support execution of these tasks.</Paragraph>
    <Paragraph position="3"> This paper aims to upgrade an existing underspecification formalism for scope ambiguities, Under-specified Discourse Representation Theory (UDRT) (Reyle, 1993), so that both ellipsis and anaphora resolution can work on the underspecified structures.</Paragraph>
    <Paragraph position="4"> a1 Many thanks for discussion and motivation are due to the colleagues in Saarbrucken.</Paragraph>
    <Paragraph position="5"> Several proposals have been made in the literature on how to integrate scope underspecification and ellipsis resolution in a single formalism, e.g. Quasi-Logical Forms (QLF) (Crouch, 1995) and the Constraint Language for Lambda Structures (CLLS) (Egg et al., 2001). That work has primarily aimed at devising methods to untangle quantifier scoping and ellipsis resolution which often interact closely (see Section 6). To this end, description languages have been modelled in which the disambiguation steps of a derivation need not be executed but rather can be explicitly recorded as constraints on the final structure. Constraints are only evaluated when the underspecified representation is finally interpreted. In contrast, UDRT aims at providing a representation formalism that supports interpretation processes such as theorem proving and anaphora resolution. Understood in this sense, underspecification often obviates the need for complete disambiguation. Another consequence is, however, that the strategy of postponing disambiguation steps is in some cases insufficient. A case in point is the phenomenon dubbed Missing Antecedents by Grinder and Postal (1971), illustrated in sentence (1): One of the pronoun's antecedents is overt, the other is supplied by ellipsis resolution.</Paragraph>
    <Paragraph position="6"> (1) Harry sank a destroyera2 and so did Bill and theya2a4a3 a5 both went down with all hands. (Grinder and Postal, 1971, 279) Most approaches to ellipsis and anaphora resolution, e.g. (Asher, 1993; Crouch, 1995; Egg et al., 2001), can readily derive the reading. But consider: (2) Harry sometimes reads a book about a seabattle and so does Bill. They borrow those books from the library.</Paragraph>
    <Paragraph position="7"> Computational Linguistics (ACL), Philadelphia, July 2002, pp. 72-79. Proceedings of the 40th Annual Meeting of the Association for Example (2) still retains five readings (Are there two or even more books? are there one, two, or more than two sea-battles?). An underspecified representation should not be committed to any of these readings, but it should specify that &amp;quot;a book&amp;quot; has narrow scope with respect to the conjunction. Furthermore, an approach to underspecification and ellipsis resolution should make clear why this representation is to be constructed for the discourse (2). While QLF fails the first requirement (a single representation),  CLLS fails the second (triggers for construction).</Paragraph>
    <Paragraph position="8"> (3) * A destroyera2 went down in some battle and a  cruiser did too. Harry sank both destroyersa2a4a3 a5 .</Paragraph>
    <Paragraph position="9"> The discourse in (3) is not well-formed. But none of the approaches mentioned can ascertain this fact without complete scope resolution (or ad-hoc restrictions). null The paper is organized as follows. Section 2 gives a short introduction to UDRT. Section 3 formulates the general setup of ellipsis resolution assumed in the rest of the paper. Section 4 presents a proposal to deal with scope parallelism in an underspecified representation. Section 5 shows how ellipsis can be treated if it is contained in its antecedent. Section 6 describes a way to model the interaction of ellipsis resolution and scope resolution in an underspecified structure. In section 7 strict and sloppy identity is discussed. Section 8 concludes.</Paragraph>
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