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<Paper uid="C04-1028">
  <Title>Generalizing Dimensionality in Combinatory Categorial Grammar</Title>
  <Section position="6" start_page="0" end_page="0" type="concl">
    <SectionTitle>
5 Conclusions
</SectionTitle>
    <Paragraph position="0"> In this paper, we generalize the traditional Saussurian sign in CCG with an n-dimensional linguistic sign. The dimensions in the generalized linguistic sign can be related through indexation. Indexation places constraints on signs by requiring that co-indexed material is unifiable, on a per-dimension basis. Consequently, we do not need to overload the syntactic category with information from different dimensions.</Paragraph>
    <Paragraph position="1"> The resulting sign structure resembles the signs found in constraint-based grammar formalisms.</Paragraph>
    <Paragraph position="2"> There is, however, an important difference. Information at various dimensions can be related through co-indexation, but dimensions cannot be directly  referenced. As analysis remains driven only by inference over categories, only those constraints triggered by indexation on the categories are imposed. We do not allow for re-entrancy.</Paragraph>
    <Paragraph position="3"> It is possible to conceive of a scenario in which the various levels can contribute toward determining the well-formedness of an expression. For example, we may wish to evaluate the current information structure against a discourse model, and reject the analysis if we find it is unsatisfiable. If such a move is made, then the complexity will be bounded by the complexity of the dimension for which it is most difficult to determine satisfiability.</Paragraph>
  </Section>
class="xml-element"></Paper>