<?xml version="1.0" standalone="yes"?>
<Paper uid="P92-1022">
  <Title>An Alternative Conception of Tree-Adjoining Derivation*</Title>
  <Section position="2" start_page="0" end_page="167" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> In a context-free grammar, the derivation of a string in the rewriting sense can be captured in a single canonical tree structure that abstracts all possible derivation orders. As it turns out, this derivation tree also corresponds exactly to the hierarchical structure that the derivation imposes on the str!ng, the derived tree structure of the string.</Paragraph>
    <Paragraph position="1"> The formalism of tree-adjoining grammars (TAG), on the other hand, decouples these two notions of derivation tree and derived tree. Intuitively, the derivation tree is a more finely grained structure *The authors are listed in alphabetical order. The first author was supported in part by DARPA Grant N001490-31863, ARO Grant DAAL03-S9-C-0031 and NSF Grant IRI90-16592. The second author was supported in part by Presidential Young Investigator award IRI-91-57996 from the National Science Foundation. The authors wish to thank Aravind Joshi for his support of the research, and Aravind Joshi, Anthony Kroeh, Fernando Pereira, and K. Vijay-Shanker for their helpful discussions of the issues involved. We are indebted to David Yarowsky for aid in the design of the experiment mentioned in footnote 5 and for its execution.</Paragraph>
    <Paragraph position="2">  than the derived tree, and as such can serve as a substrate on which to pursue further analysis of the string. This intuitive possibility is made manifest in several ways. Fine-grained syntactic analysis can be pursued by imposing on the derivation tree further combinatoriM constraints, for instance, selective adjoining constraints or equational constraints over feature structures. Statistical analysis can be explored through the specification of derivational probabilities as formalized in stochastic tree-adjoining grammars. Semantic analysis can be overlaid through the synchronous derivations of two TAGs.</Paragraph>
    <Paragraph position="3"> All of these methods rely on the derivation tree as the source of the important primitive relationships among trees. The decoupling of derivation trees from derived trees thus makes possible a more flexible ability to pursue these types of analyses. At the same time, the exact definition of derivation becomes of paramount importance. In this paper, we argue that previous definitions of tree-adjoining derivation have not taken full advantage of this decoupling, and are not as appropriate as they might be for the kind of further analysis that tree-adjoining analyses could make possible. In particular, the standard definition of derivation, due to Vijay-Shanker (1987), requires that elementary trees be adjoined at distinct nodes in elementary trees. However, in certain cases, especially cases characterized as linguistic modification, it is more appropriate to allow multiple adjunctions at a single node.</Paragraph>
    <Paragraph position="4"> In this paper, we propose a redefinition of TAG derivation along these lines, whereby multiple auxiliary trees of modification can be adjoined at a single node, whereas only a single auxiliary tree of predication can. The redefinition constitutes a new definition of derivation for TAG that we will refer to as extended derivation. In order for such a redefinition to be serviceable, however, it is necessary that it be both precise and operational. In service of the former, we provide a rigorous specification of our proposal in terms of a compilation of TAGs into corresponding linear indexed grammars (LIG) that makes the derivation structure explicit. With respect to the latter, we show how the generated LIG can drive a parsing algorithm that recovers, either implicitly or explicitly, the extended derivations of the string.</Paragraph>
    <Paragraph position="5"> The paper is organized as follows. First, we review Vijay-Shanker's standard definition of TAG derivation, and introduce the motivation for extended derivations. Then, we present the extended notion of derivation informally, and formalize it through the compilation of TAGs to LIGs. The original compilation provided by Vijay-Shanker and Weir and our variant for extended derivations are both decribed. Finally, we briefly mention a parsing algorithm for TAG that recovers extended derivations either implicitly or explicitly, and discuss some issues surrounding it. Space limitations preclude us from presenting the algorithm itself, but a full description is given elsewhere (Schabes and Shieber, 1992).</Paragraph>
  </Section>
class="xml-element"></Paper>