<?xml version="1.0" standalone="yes"?>
<Paper uid="E93-1034">
  <Title>Tuples, Discontinuity, and Gapping in Categorial Grammar*</Title>
  <Section position="8" start_page="294" end_page="294" type="concl">
    <SectionTitle>
8 Conclusion
</SectionTitle>
    <Paragraph position="0"> When \[Moortgat, 1988\] introduced discontinuity operators for categorial grammar, he noted that ordered sequent calculus was an inadequate medium for the representation of a full logic. In \[Moortgat, 1991b\] the LDS formalism was invoked, but as we have seen, the LDS format alone is not enough. The present paper has argued that a different view is required on the model theory of discontinuity than that suggested by interpretation in just a semigroup algebra. This view is provided by adding to the algebra of interpretation the tuple operation of \[Solias, 1992\]. Not only does this clear up some vagueness with respect to existential and universal formulations, it also admits of a full labelled logic. This has brought us to a stage where it is appropriate to address such issues as completeness and Cut-elimination.</Paragraph>
  </Section>
class="xml-element"></Paper>