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<Paper uid="J91-3002">
  <Title>Chinese Number-Names, Tree Adjoining Languages, and Mild Context-Sensitivity</Title>
  <Section position="9" start_page="295" end_page="296" type="concl">
    <SectionTitle>
7. Conclusions
</SectionTitle>
    <Paragraph position="0"> * We have shown that, when viewed as a formal language, the number-name system of Chinese is neither a single- nor a multiple-component Tree Adjoining Language, due to its strung-together number-names of indefinite length. As a consequence, it cannot be generated by any Linear Context-Free Rewriting System, including Context-Free Grammars, Head Grammars, Linear Indexed Grammars, or Combinatory Categorial Grammars. It appears also not to be Mildly Context-Sensitive at all, notwithstanding its  recognition in linear time. Our formal results relate directly either to the syntax proper of Chinese or to the interface between that natural language, the most widely natively spoken one, and the mathematical component of the human cognitive endowment.</Paragraph>
    <Paragraph position="1"> Similar results hold, most likely, for other natural languages, perhaps even for English. Consequently, it may be the case that Zwicky (1963) did expound after all, at least in spirit if not in letter, the first valid argument that English is non-context-free. On a practical side, then, our study may help Geoff Pullum untangle himself from his odd/even dates dilemma. On a more theoretical side, we have discovered something quite interesting about the nature of human language and its relationship to numeral systems.</Paragraph>
  </Section>
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