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<Paper uid="J91-3003">
  <Title>The Generative Power of Categorial Grammars and Head-Driven Phrase Structure Grammars with Lexical Rules</Title>
  <Section position="7" start_page="310" end_page="311" type="concl">
    <SectionTitle>
7. Conclusion
</SectionTitle>
    <Paragraph position="0"> The system presented here for lexical rules in a simplified form of categorial grammar with only one head-complement rule scheme has proven to generate arbitrary recursively enumerable languages. The inevitable conclusion is that if we want a natural and effectively decidable lexical rule system for categorial grammars or head-driven  Computational Linguistics Volume 17, Number 3 phrase structure grammars, then we must place restrictions on the system given here or look to state lexical rules at completely different levels of representation which themselves provide the restrictiveness desired, such as in terms of some finite set of thematic roles and grammatical relations, as is done in Lexical Function Grammar (LFG) (see Bresnan 1982; Levin 1987; Bresnan and Kanerva 1989). The common assumption that lexical rules can perform arbitrary operations on subcategorization lists based on obliqueness is simply not restrictive enough to yield an effective recognition algorithm.</Paragraph>
  </Section>
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