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<Paper uid="C88-2147">
  <Title>Feature Structures Based Tree Adjoining Grammars 1</Title>
  <Section position="2" start_page="0" end_page="714" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Tree Adjoining Grammars (TAG) were first introduced by Joshi, Levy, and Takalmshi \[Joshi et al. 1975\]. The first study of this system, from the point of view of its formal properties and linguistic applicability, was carried out by Joshi in \[Joshi 1985\]. TAG's have been used in providing linguistic analyses; a detailed study of the linguistic relevance was done by Kroch and Joshi in \[Kroch et al. 1985\].</Paragraph>
    <Paragraph position="1"> In this paper, we show lmw TAG's can be embedded in a feature structure based framework. Feature structure based Tree Adjoining Grammars (FTAG) are introduced in Section 2, and is f611owed by a comparsion of the descriptive capacity of FTAG and TAG. A restricted version of FTAG is proposed and some possible linguistic stipulations are considered. In Section 3, we introduce a calculus, which is an extension of the logical calculus of Rounds and Kasper \[Rounds et al. 1986, Kasper et al. 1986\] allowing A-abstraction and application, in order to describe the structures used in FTAG's. Finally, in Section 4, we summarize the work presented in this paper.</Paragraph>
    <Section position="1" start_page="0" end_page="714" type="sub_section">
      <SectionTitle>
1.1 Introduction to Tree Adjoining Grammars
</SectionTitle>
      <Paragraph position="0"> Tree Adjoining Grammars (TAG), unlike other grammatical systems used in computational linguistics, is a tree rewriting system. Unlike the string rewriting formalisms which writes recursion into the rules that generate the phrase structure, a TAG factors reeursion and dependencies into a finite set of elementary trees. The elementary trees in a TAG correspond to minimal linguistic structures that localize the dependencies such as agreement, subcategorization, and filler-gap. There are two kinds of elenrentary trees: the initial trees and auxiliary trees. The initial trees roughly (Figure 1) correspond to simple sentences. Thus, the root of an initial trce is labelled by the symbol S. They are required to have a frontier made up of terminals.</Paragraph>
      <Paragraph position="1"> The auxiliary trees (Figure 2) correspond roughly to minimal recursive constructions. Thus, if the root of an auxiliary tree is labelled by a nonterminal symbol, X, then there is a node (called the foot node) in the frontier of this tree which is labelled by X. The rest of the nodes in the frontier are labelled by terminal symbols.</Paragraph>
      <Paragraph position="2">  We will now define the operation of adjunction. Let 7 be a tree with a node labelled by X. Let fl be an auxiliary tree, whose root and foot node are also labelled by X. Then, adjoining/3 at the node labelled by  show tl~e result of adjoining the auxiliary tree fll at the subject NP node of the initial tree al.</Paragraph>
      <Paragraph position="3"> So far, the only restriction we have placed on the set of auxiliary trees that can be adjoined at a node is that the label of the node must be the same as the label of tile root (and the foot) node of the auxiliary tree. Fm'ther restriction on this set of auxiliary trees is done by enumerating with each node the subset of anxiliary trees which can be adjoined at that node. This specification of a set of auxiliary trees, which can be adjoined at a node, is called the Selective Adjoining (SA) constraints. In tim case where we specify the empty set, we say that the node has a Nail Adjoining (NA) constraint:~. It is possible to insist that adjunction is mandatory at a node. In such a case, wc say that the node has an Obligatory Adjoining (OA) constraint.</Paragraph>
      <Paragraph position="4"> A more detailed description of TAG's and their linguistic relevance may be found in \[Kroeh et al. 1985\].</Paragraph>
    </Section>
    <Section position="2" start_page="714" end_page="714" type="sub_section">
      <SectionTitle>
1.2 Feature Structure Based Grammatical Systems
</SectionTitle>
      <Paragraph position="0"> Several different approaches to natural language granunars have developed the notion of feature structures to describe linguistic objects. In order to capture certain linguistic phenomena such as agreement, subcategorization, cte., a number of. recent grammatical systems have added, on top of a CFG skclcton, a feature based informatioual element. Example or&amp;quot; sncb systems (see \[Shieber 1985a\]) include Generalized Phrase Structure Grammars (GPSG), Lexical functional Grammars (LFG), and tIead-driven Phrase Structure Grammars (IIPSG). A feature structure (as given below) is essentially a set of attribute-value pairs where values may be atomic ~*ymbols or another feature structure.</Paragraph>
      <Paragraph position="2"> Tim notation of the co-indexing box (\[\] in this example) is used to express the f;~ct that the values of two subfeatures are the stone. Feature structures with co-indexing boxes have also been called reentrant feature structures in the literature.</Paragraph>
      <Paragraph position="3"> We can define a partial ordering, E, on a set of feature structures using tbe notion of subsnmption (carries less in/ormalion or is more general). Unification of two feat,re structures (if it is defined) corresponds to the feature ~;tructure that has all the information contained in the original two feal;nre structures and nothing more. We will not describe feature structur,~s any fnrther (see \[Shieber 1985a\] for more details on featurc structures and an introduction to the unification based approach to grammars).</Paragraph>
    </Section>
  </Section>
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