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<Paper uid="J92-4004">
  <Title>Using Descriptions of Trees in a Tree Adjoining Grammar</Title>
  <Section position="8" start_page="514" end_page="515" type="concl">
    <SectionTitle>
6. Conclusions
</SectionTitle>
    <Paragraph position="0"> In this paper, we have embedded TAG in the unification framework in a manner consistent with the constraint-based approach used in this framework. Starting from first principles and taking the localization of dependencies within the elementary structures of a TAG grammar as the only basic principle, we have argued that the objects manipulated by such a grammar are not trees but descriptions of well-formed syntactic structures. From D-Theory, we have adopted the use of domination relation and use of identifiers to refer to nodes while describing such structures. Quasi-trees were introduced to depict pictorially partial descriptions of trees. The pairing of quasi-nodes (with domination link between them) was then used to explain the association of two feature structures with individual nodes in previous definition of Feature structure-based Tree Adjoining Grammars (FTAG). In fact, we also show that the formalism defined in Harbusch (1990) (where only one feature structure is associated with every node) turns out to be similar to the use of FTAG with an additional decision to merge every pair of quasi-nodes by default. We argue that such defaults lead to nonmonotonic behavior.</Paragraph>
    <Paragraph position="1"> One can now view FTAG as a generalization of TAG in that arbitrary categories (as used in GPSG) can label nodes, instead of just atomic symbols (nonterminals) as in TAG. In fact, by not insisting that a pair of quasi-nodes be labeled by the same category in FTAG, as was done in TAG, we argue that the &amp;quot;adjoining constraints&amp;quot; follow from the definition of adjunction and the labeling of quasi-nodes, thus making unnecessary the stipulations of SA and OA constraints. In addition, contrary to the assumptions made in current literature on TAG, we show that there are two possible interpretations of NA constraints, only one of which is a special case of SA constraint. We note that as the information associated with quasi-nodes grows during derivation, &amp;quot;adjoining constraints&amp;quot; get instantiated dynamically in an FTAG. We make use of this property in order to give examples to show how FTAG can give more succinct descriptions than TAG.</Paragraph>
    <Paragraph position="2"> We have given a logical formulation of FTAG. This builds on a similar treatment of FUG given by Rounds and Manaster-Ramer. We view this logical formulation as a description of those trees and associated feature structures that are built by CFG-based unification grammars. Unlike a CFG-based formalism that allows only for substitution operation, for an FTAG one has to depict adjunction in addition to substitution. Our treatment captures both these cases. We end by giving a presentation of the semantics that can be used to give the denotation of a grammar, i.e., in our case, the structures derived by a grammar.</Paragraph>
    <Paragraph position="3"> We have emphasized throughout the paper that we are only interested in the definition of the FlAG formalism. In particular, we have not been concerned with linguistic analyses. However, we have raised a few questions about the formalism that we believe can only be answered on linguistic grounds. In the context of the new interpretation, some of these include whether the linguistic uses of multi-component adjoining can be simulated as the adjoining operation; whether there is an essential need to divide the elementary structures of the grammar as initial and auxiliary structures; and whether the adjoining operation itself can be defined as a substitution  Computational Linguistics Volume 18, Number 4 operation, the apparent differences between these operations being derived on the basis of some more fundamental linguistic principles used in the design of the elementary structures of the grammar. Even if the answer is in the affirmative, we believe there is considerable advantage to be gained by deriving this operation in order that we can manipulate directly the elementary structures that localize various forms of the dependencies. As observed earlier, with the derivation of this operation (like the derivation of the elementary structures of the grammar), we can disregard (i.e., not reason with) the principles used (to derive them) during the derivation of more complex structures. Finally we have also shown that the new interpretation of the TAG formalism proposed here allows for the possibility of a more compact representation of a TAG grammar.</Paragraph>
  </Section>
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