<?xml version="1.0" standalone="yes"?>
<Paper uid="P99-1011">
  <Title>A Meta-Level Grammar: Redefining Synchronous TAG for Translation and Paraphrase</Title>
  <Section position="4" start_page="0" end_page="82" type="intro">
    <SectionTitle>
2 S-TAG and Machine Translation
</SectionTitle>
    <Paragraph position="0"> Synchronous TAG, the mapping between two Tree Adjoining Grammars, was first proposed by Shieber and Schabes (1990). An application proposed concurrently with the definition of S-TAG was that of machine translation, mapping between English and French (Abeill~ et al, 1990); work continues in the area, for example using S-TAG for English-Korean machine translation in a practical system (Palmer et al, 1998). In mapping between, say, English and French, there is a lexicalised TAG for each language (see XTAG, 1995, for an overview of such a grammar). Under the definition of TAG, a grammar contains elementary trees, rather than flat rules, which combine together via the operations of substitution and adjunction (composition operations) to form composite structures--derived trees--which will ultimately provide structural representations for an input string if this string is grammatical. An overview of TAGs is given in Joshi and Schabes (1996).</Paragraph>
    <Paragraph position="1"> The characteristics of TAGs make them better suited to describing natural language than Context Free Grammars (CFGs): CFGs are not adequate to describe the entire syntax of natural language (Shieber, 1985), while TAGs are able to provide structures for the constructions problematic for CFGs, and without a much greater generative capacity. Two particular chaxacteris- null tics of TAG that make it well suited to describing natural language are the extended domain of locality (EDL) and factoring recursion from the domain of dependencies (FRD). In TAG, for instance, information concerning dependencies is given in one tree (EDL): for example, in Figure 1,1 the information that the verb defeated has subject and object arguments is contained in the tree al. In a CFG, with rules of the form S --+ NP VP and VP --+ V NP, it is not possible to have information about both arguments in the same rule unless the VP node is lost. TAG keeps dependencies together, or local, no matter how far apart the corresponding lexicM items are. FRD means that recursive information--for example, a sequence of adjectives modifying the object noun of defeated--are factored out into separate trees, leaving dependencies together.</Paragraph>
    <Paragraph position="2"> A consequence of the TAG definition is that, unlike CFG, a TAG derived tree is not a record of its own derivation. In CFG, each tree given as a structural description to a string enables the rules applied to be recovered. In a TAG, this is not possible, so each derived tree has an associated derivation tree. If the trees in Figure 1 were composed to give a structural description for Garrad cunningly defeated the Sumerians, the derived tree and its corresponding deriva-</Paragraph>
    <Paragraph position="4"> tively, for Figure 1 tion tree would be as in Figure 2. 2 Weir (1988) terms the derived tree, and its component elementary trees, OBJECT-LEVEL TREES; the derivation tree is termed a META-LEVEL TREE, since it describes the object-level trees. The derivation trees are context free (Weir, 1988), that is, they can be expressed by a CFG; Weir showed that applying a TAG yield function to a context free derivation tree (that is, reading the labels off the tree, and substituting or adjoining the corresponding object-level trees as appropriate) will uniquely specify a TAG tree. Schabes and Shieber (1994) characterise this as a function 7) from derivation trees to derived trees.</Paragraph>
    <Paragraph position="5"> The idea behind S-TAG is to take two TAGs and link them in an appropriate way so that when substitution or adjunction occurs in a tree in one grammar, then a corresponding composition operation occurs in a tree in the other grammar. Because of the way TAG's EDL captures dependencies, it is not problematic to have translations more complex than word-for-word mappings (Abeill~ et al, 1990). For example, from the Abeill~ et al paper, handling argument swap, as in (1), is straightforward. These would be represented by tree pairs as in Figure 3.</Paragraph>
    <Paragraph position="6"> 2In derivation trees, addresses are given using the Gorn addressing scheme, although these are omitted in this paper where the composition operations are obvious.  b. Marie manque g Jean.</Paragraph>
    <Paragraph position="7"> In these tree pairs, a diacritic (\[-/7) represents a link between the trees, such that if a substitution or adjunction occurs at one end of the link, a corresponding operation must occur at the other end, which is situated in the other tree of the same tree pair. Thus if the tree for John in a7 is substituted at E\] in the left tree of a6, the tree for Jean must be substituted at \[-~ in the right tree. The diacritic E\] allows a sentential modifier for both trees (e.g. unfortunately / malheureusement).</Paragraph>
    <Paragraph position="8"> The original definition of S-TAG (Shieber and Schabes, 1990), however, had a greater generative capacity than that of its component TAG grammars: even though each component grammar could only generate Tree Adjoining Languages (TALs), an S-TAG pairing two TAG grammars could generate non-TALs. Hence, a redefinition was proposed (Shieber, 1994). Under this new definition, the mapping between grammars occurs at the meta level: there is an isomorphism between derivation trees, preserving structure at the meta level, which establishes the translation. For example, the deriva* tion trees for (1) using the elementary trees of Figure 3 is given in Figure 4; there is a clear isomorphism, with a bijection between nodes, and parent-child relationships preserved in the mapping.</Paragraph>
    <Paragraph position="9"> In translation, it is not always possible to have a bijection between nodes. Take, for example, (2).</Paragraph>
    <Paragraph position="10"> a\[misses\] a\[man.que ~\] s a\[John\] a\[Mary\] a\[Jean\] a\[Marie\] /  In English, hopefully would be represented by a single tree; in French, on esp~re que typically by two. Shieber (1994) proposed the idea of bounded subderivation to deal with such aberrant cases--treating the two nodes in the derivation tree representing on esp~re que as singular, and basing the isomorphism on this. This idea of bounded subderivation solves several difficulties with the isomorphism requirement, but not all. An example by Shieber demonstrates that translation involving clitics causes problems under this definition, as in (3). The partial derivation trees containing the clitic lui and its English parallel are as in Figure 5.</Paragraph>
    <Paragraph position="11">  (3) a. The doctor treats his teeth.</Paragraph>
    <Paragraph position="12"> b. Le docteur lui soigne les dents.</Paragraph>
    <Paragraph position="13">  A potentially unbounded amount of material intervening in the branches of the righthand tree means that an isomorphism between the trees cannot be established under Shieber's specification even with the modification of bounded subderivations. Shieber suggested that the isomorphism requirement may be overly stringent;</Paragraph>
    <Paragraph position="15"> but intuitively, it seems reasonable that what occurs in one grammar should be mirrored in the other in some way, and this reflected in the derivation history.</Paragraph>
    <Paragraph position="16"> Section 3 looks at representing syntactic paraphrase in S-TAG, where similar problems are encountered; in doing this, it can be seen more clearly than in translation that the difficulty is caused not by the isomorphism requirement itself but by the fact that the isomorphism does not exploit any of the structure inherent in the derivation trees.</Paragraph>
  </Section>
class="xml-element"></Paper>