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<Paper uid="C94-1083">
  <Title>CATEGORIAL GRAMMAR AND DISCOURSE REPRESENTATION THEORY</Title>
  <Section position="3" start_page="508" end_page="508" type="intro">
    <SectionTitle>
1. FROM ENGLISII TO LAMBEK PROOFS
</SectionTitle>
    <Paragraph position="0"> I shall assume familiarity with I~tmbck's calculus and rehearse only its most elementary features.</Paragraph>
    <Paragraph position="1"> Starting with it set of basic categoric.v, which for tile purposes of this paper will be {txt, s, n, cn} (for texts, sentences, names and common nouns), we define it category to be either a basic category or anything of one of the forms a / b or b \ a, where a and b are categories. A sequent is an expression 7&amp;quot; l- c, where T is a not&gt;empty finite sequence of categories (the antecedent) and c (the succedent) is a category. A sequent is provable if it can be proved with the help of the following  An example of a proof in this calculus is given in fig. 1, where it is shown that (s / (n \ s)) / on, cn, (n \ s) / n, ((s / n) \s) / cn, cn }- s is a provable sequent. If the categories in the antecedent of this sequent are assigned to the words 'a', 'man', 'adores', 'It' and 'woman' respectively, wc Call interpret the derivability of tile given sequent ,'is saying that these words, in this order, belong to the category s.</Paragraph>
  </Section>
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