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<Paper uid="J94-1004">
  <Title>An Alternative Conception of Tree-Adjoining Derivation</Title>
  <Section position="2" start_page="0" end_page="0" type="abstr">
    <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.</Paragraph>
    <Paragraph position="1"> As it turns out, this derivation tree also corresponds exactly to the hierarchical structure that the derivation imposes on the string, the derived tree structure of the string. 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 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 combinatorial 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="2"> 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.</Paragraph>
    <Paragraph position="3"> 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, attributable to Vijay-Shanker (1987),  * Cambridge, MA 02139 t Division of Applied Sciences, Cambridge, MA 02138 (~) 1994 Association for Computational Linguistics  Computational Linguistics Volume 20, Number 1 requires that auxiliary 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. 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 formal definition of extended derivation using a new approach to representing derivations as equivalence classes of ordered derivation trees. With respect to the latter, we provide a method of compilation of TAGs into corresponding linear indexed grammars (LIG), which makes the derivation structure explicit; and 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 and its formal definition. The original compilation of TAGs to LIGs provided by Vijay-Shanker and Weir and our variant for extended derivations are both described. Finally, we discuss a parsing algorithm for TAG that operates by a variant of Earley parsing on the corresponding LIG. The set of extended derivations can subsequently be recovered from the set of Earley items generated by the algorithm. The resultant algorithm is further modified so as to build an explicit derivation tree incrementally as parsing proceeds; this modification, which is a novel result in its own right, allows the parsing algorithm to be used by systems that require incremental processing with respect to tree-adjoining grammars.</Paragraph>
  </Section>
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