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<Paper uid="P97-1069">
  <Title>Generative Power of CCGs with Generalized Type-Raised Categories</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> The class of Combinatory Categorial Grammars (CCG-Std) was proved to be weakly equivalent to Linear Index Grammars and Tree Adjoining Grammars (Joshi, Vijay-Shanker, and Weir, 1991; Vijay-Shanker and Weir, 1994).</Paragraph>
    <Paragraph position="1"> But CCG-Std cannot handle the generalization of type raising that has been used in accounting for various linguistic phenomena including: coordination and extraction (Steedman, 1985; Dowty, 1988; Steedman, 1996), prosody (Prevost and Steedman, 1993), and quantifier scope (Park, 1995). Intuitively, all of these phenomena call for a non-traditional, more flexible notion of constituency capable of representing surface structures including &amp;quot;(Subj V) (Obj)&amp;quot; in English. Although lexical type raising involving variables can be introduced to derive such a constituent? unconstrained use of variables can increase the power. For example, a grammar involving (T\z)/(T\v) can generate a language A&amp;quot;B&amp;quot;C&amp;quot;D&amp;quot;E&amp;quot; which CCG-Std cannot (Hoffman, 1993).</Paragraph>
    <Paragraph position="2"> This paper argues that there is a class of grammars which allows the use of linguistically-motivated form of type raising involving variables while it is still weakly equivalent to CCG-Std. A class of grammars, CCG-GTRC, is introduced in the next section as an extension to CCG-Std. Then we show that CCG-GTRC can actually be simulated by a CCG-Std, proving the equivalence.</Paragraph>
    <Paragraph position="3"> degThanks to Mark Steedman, Beryl Hoffman, Anoop Sarkar, and the reviewers. The research was supported in part by NSF Grant Nos. IRI95-04372, STC-SBR-8920230, ARPA Grant No. N66001-94-C6043, and ARID Grant No. DAAH04-94G0426. null IOur lexieal rules to introduce type raising are non-recursive and thus do not suffer from the problem of the overgeneration discussed in (Carpenter, 1991).</Paragraph>
  </Section>
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