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<Paper uid="C04-1026">
  <Title>A Relational Syntax-Semantics Interface Based on Dependency Grammar</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> A key assumption of traditional syntax-semantics interfaces, starting with (Montague, 1974), is that the mapping from syntax to semantics is functional, i. e. that once we know the syntactic structure of a sentence, we can deterministically compute its semantics. null Unfortunately, this assumption is typically not justified. Ambiguities such as of quantifier scope or pronominal reference are genuine semantic ambiguities; that is, even a syntactically unambiguous sentence can have multiple semantic readings. Conversely, a common situation in natural language generation is that one semantic representation can be verbalised in multiple ways. This means that the relation between syntax and semantics is not functional at all, but rather a true m-to-n relation.</Paragraph>
    <Paragraph position="1"> There is a variety of approaches in the literature on syntax-semantics interfaces for coping with this situation, but none of them is completely satisfactory. One way is to recast semantic ambiguity as syntactic ambiguity by compiling semantic distinctions into the syntax (Montague, 1974; Steedman, 1999; Moortgat, 2002). This restores functionality, but comes at the price of an artificial blow-up of syntactic ambiguity. A second approach is to assume a non-deterministic mapping from syntax to semantics as in generative grammar (Chomsky, 1965), but it is not always obvious how to reverse the relation, e. g. for generation. For LFG, the operation of functional uncertaintainty allows for a restricted form of relationality (Kaplan and Maxwell III, 1988). Finally, underspecification (Egg et al., 2001; Gupta and Lamping, 1998; Copestake et al., 2004) introduces a new level of representation, which can be computed functionally from a syntactic analysis and encapsulates semantic ambiguity in a way that supports the enumeration of all semantic readings by need.</Paragraph>
    <Paragraph position="2"> In this paper, we introduce a completely relational syntax-semantics interface, building upon the underspecification approach. We assume a set of linguistic dimensions, such as (syntactic) immediate dominance and predicate-argument structure; a grammatical analysis is a tuple with one component for each dimension, and a grammar describes a set of such tuples. While we make no a priori functionality assumptions about the relation of the linguistic dimensions, functional mappings can be obtained as a special case. We formalise our syntax-semantics interface using Extensible Dependency Grammar (XDG), a new grammar formalism which generalises earlier work on Topological Dependency Grammar (Duchier and Debusmann, 2001).</Paragraph>
    <Paragraph position="3"> The relational syntax-semantics interface is supported by a parser for XDG based on constraint programming. The crucial feature of this parser is that it supports the concurrent flow of possibly partial information between any two dimensions: once additional information becomes available on one dimension, it can be propagated to any other dimension.</Paragraph>
    <Paragraph position="4"> Grammaticality conditions and preferences (e. g. selectional restrictions) can be specified on their natural level of representation, and inferences on each dimension can help reduce ambiguity on the others. This generalises the idea of underspecification, which aims to represent and reduce ambiguity through inferences on a single dimension only.</Paragraph>
    <Paragraph position="5"> The structure of this paper is as follows: in Section 2, we give the general ideas behind XDG, its formal definition, and an overview of the constraint-based parser. In Section 3, we present the relational syntax-semantics interface, and go through examples that illustrate its operation. Section 4 shows how the semantics side of our syntax-semantics interface can be precisely related to mainstream semantics research. We summarise our results and point to further work in Section 5.</Paragraph>
  </Section>
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