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<Paper uid="P99-1012">
  <Title>Preserving Semantic Dependencies in Synchronous Tree Adjoining Grammar*</Title>
  <Section position="4" start_page="88" end_page="89" type="intro">
    <SectionTitle>
2 Overview
</SectionTitle>
    <Paragraph position="0"> Our solution is to retain ISTAG, but move the isomorphism restriction from the derivation structure to the predicate-argument attachment structure described in (Joshi and Vijay-Shanker, 1999).</Paragraph>
    <Paragraph position="1"> This structure represents the composition of semantic predicates for lexicalized elementary trees, each of which contains a 'predicate' variable associated with the situation or entity that the predicate introduces, and a set of 'argument' variables associated with the foot node and substitution sites in the original elementary tree. The predicates are composed by identifying the predicate variable in one predicate with an argument variable in another, so that the two variables refer to the same situation or entity.</Paragraph>
    <Paragraph position="2"> Composition proceeds from the bottom up on the derivation tree, with adjuncts traversed in order from the lowest to the highest adjunction site in each elementary tree, in much the same way that a parser produces a derivation. Whenever an initial tree is substituted, its predicate variable is identified in the composed structure with an argument variable of the tree it substitutes into. Whenever an auxiliary tree is adjoined, the predicate variable of the tree it adjoins into is identified in the composed structure with one of its own argument variables. In cases of adjunction, an auxiliary tree's semantics can also specify which variable will become the predicate variable of the composed structure for use in subsequent adjunctions at higher adjunction sites: a modifier auxiliary will return the host tree's original predicate variable, and a predicative auxiliary will return its own predicate variable. 2 Since the traversal must 2See (Schabes and Shieber, 1994) for definitions of modifier and predicative auxiliaries.</Paragraph>
    <Paragraph position="3">  proceed from the bottom up, the attachment of predicates to arguments is neither destructive nor underspecified at any stage in the interpretation. null For example, assume the initial tree a:fly has a predicate variable s\], representing the situation of something flying, and an argument variable xl, representing the thing that is flying; and assume the predicative auxiliary tree/31 :beable-to has a predicate variable s2, representing the situation of something being possible, and an argument variable s3, representing the thing that is possible. If fll is now adjoined into a, the composed structure would have sl identified with s3 (since the situation of flying is the thing that is possible), and s2 as an over-all predicate variable, so if another tree later adjoins into this composed structure rooted on a, it will predicate over s2 (the situation that flying is possible) rather than over a's original predicate variable sl (the situation of flying by itself). Note that Joshi and Vijay-Shanker do not require the predicate and modifier distinctions, because they can explicitly specify the fates of any number of predicate variables in a tree's semantic representation. For simplicity, we will limit our discussion to only the two possibilities of predicative and modifier auxiliaries, using one predicate variable per tree.</Paragraph>
    <Paragraph position="4"> If we represent each such predicate-argument attachment as an arc in a directed graph, we can view the predicate-argument attachment structure of a derivation as a dependency graph, in much the same way as Candito and Kahane interpret the original derivation trees (Candito and Kahane, 1998a). More importantly, we can see that this definition predicts the predicate-argument dependencies for sentences (1) and (2) to be isomorphic:</Paragraph>
    <Paragraph position="6"> even though their derivation trees are not.</Paragraph>
    <Paragraph position="7"> This is because the predicative auxiliary for &amp;capaz-de returns its predicate variable to the host tree for subsequent adjunctions, so the auxiliary tree for g-pressuposto-que can attach it as one of its arguments, just as if it had adjoined directly to the auxiliary, as supposed-to does in English.</Paragraph>
    <Paragraph position="8"> It is also important to note that Joshi and Vijay-Shanker's definition of TAG compositional semantics differs from that of Shieber  and Schabes (Shieber and Schabes, 1990) using Synchronous TAG, in that the former preserves the scope ordering of predicative adjunctions, which may be permuted in the latter, altering the meaning of the sentence. 3 It is precisely this scope-preserving property we hope to exploit in our formulation of a dependency-based isomorphic synchronous TAG in the next two sections. However, as Joshi and Vijay-Shanker suggest, the proper treatment of synchronous translation to logical form may require a multi-component Synchronous TAG analysis in order to handle quantifiers, which is beyond the scope of this paper. For this reason, we will focus on examples in machine translation.</Paragraph>
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