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<Paper uid="P00-1057">
  <Title>Multi-Component TAG and Notions of Formal Power</Title>
  <Section position="6" start_page="6" end_page="6" type="evalu">
    <SectionTitle>
5 Discussion
</SectionTitle>
    <Paragraph position="0"> Our version of MCTAG follows other work in incorporating dependency into a constituency-based approach to modeling natural language. One such early integration involved work by Gaifman #281965#29, which showed that projective dependency grammars could be represented by CFGs. However, it is known that there are common phenomena which require non-projective dependency grammars, so looking only at projective desuch connection.</Paragraph>
    <Paragraph position="1">  Against tradition, we forbid root adjunction, because adjunction at the foot ensures that a bottom-up traversal of the derived tree will encounter elementary trees in the same order as they appear in a bottom-up traversal of the derivation tree, simplifying the calculation of derivations.</Paragraph>
    <Paragraph position="2">  pendency grammars is inadequate. Following the observation of TAG derivations' similarity to dependency relations, other formalisms have also looked at relating dependency and constituency approaches to grammar formalisms.</Paragraph>
    <Paragraph position="3"> A more recent instance is D-Tree Substitution Grammars #28DSG#29 #28Rambow et al., 1995#29, where the derivations are also interpreted as dependency relations. Thought of in the terms of this paper, there is a clear parallel with R-MCTAG, with a local set ultimately representing dependencies having some yield function applied to it; the idea of non-immediate dominance also appears in both formalisms. The di#0Berence between the two is in the kinds of languages that they are able to describe: DSG is both less and more restrictive than R-MCTAG. DSG can generate the language count-k for some arbitrary k #28that is, fa  it extremely powerful, whereas R-MCTAG can only generate count-4. However, DSG cannot generate the copy language #28that is, fww j w 2 #06  g with #06 some terminal alphabet#29, whereas R-MCTAG can; this may be problematic for a formalism modeling natural language, given the key role of the copy language in demonstrating that natural language is not context-free #28Shieber, 1985#29. R-MCTAGisthusa moreconstrainedrelaxation of the notion of immediate dominance in favor of non-immediate dominance than is the case for DSG.</Paragraph>
    <Paragraph position="4"> Another formalism of particular interest here is the Segmented Adjoining Grammar of #28Kulick, 2000#29. This generalization of TAGis characterized by an extension of the adjoining operation, motivated by evidence in scrambling, clitic climbing and subject-to-subject raising. Most interestingly, this extension to TAG, proposed on empirical grounds, is de#0Cned by a composition operation with constrained non-immediate dominance links that looks quite similar to the formalism described in this paper, which began from formal considerationsand was then appliedto data. This con#0Duence suggests that the ideas described here concerning combining dependency and constituency might be reaching towards some deeper connection.</Paragraph>
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