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<Paper uid="P03-1047">
  <Title>Bridging the Gap Between Underspecification Formalisms: Minimal Recursion Semantics as Dominance Constraints</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> In the past few years there has been considerable activity in the development of formalisms for underspecified semantics (Alshawi and Crouch, 1992; Reyle, 1993; Bos, 1996; Copestake et al., 1999; Egg et al., 2001). The common idea is to delay the enumeration of all readings for as long as possible. Instead, they work with a compact underspecified representation; readings are enumerated from this representation by need.</Paragraph>
    <Paragraph position="1"> Minimal Recursion Semantics (MRS) (Copestake et al., 1999) is the standard formalism for semantic underspecification used in large-scale HPSG grammars (Pollard and Sag, 1994; Copestake and Flickinger, ). Despite this clear relevance, the most obvious questions about MRS are still open:  1. Is it possible to enumerate the readings of MRS structures efficiently? No algorithm has been published so far. Existing implementations seem to be practical, even though the problem whether an MRS has a reading is NP-complete (Althaus et al., 2003, Theorem 10.1).</Paragraph>
    <Paragraph position="2"> 2. What is the precise relationship to other un- null derspecification formalism? Are all of them the same, or else, what are the differences? We distinguish the sublanguages of MRS nets and normal dominance nets, and show that they can be intertranslated. This translation answers the first question: existing constraint solvers for normal dominance constraints can be used to enumerate the readings of MRS nets in low polynomial time.</Paragraph>
    <Paragraph position="3"> The translation also answers the second question restricted to pure scope underspecification. It shows the equivalence of a large fragment of MRSs and a corresponding fragment of normal dominance constraints, which in turn is equivalent to a large fragment of Hole Semantics (Bos, 1996) as proven in (Koller et al., 2003). Additional underspecified treatments of ellipsis or reinterpretation, however, are available for extensions of dominance constraint only (CLLS, the constraint language for lambda structures (Egg et al., 2001)).</Paragraph>
    <Paragraph position="4"> Our results are subject to a new proof technique which reduces reasoning about MRS structures to reasoning about weakly normal dominance constraints (Bodirsky et al., 2003). The previous proof techniques for normal dominance constraints (Koller et al., 2003) do not apply.</Paragraph>
  </Section>
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