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<Paper uid="E89-1014">
  <Title>A logical treatment of semi-free word order and bounded discontinuous constituency</Title>
  <Section position="6" start_page="0" end_page="0" type="concl">
    <SectionTitle>
7. Conclusion
</SectionTitle>
    <Paragraph position="0"> There are several comments to make here. First, the specific logic presented here is not important in itself. There are undoubtedly much better ways of formalising the same ideas. In particular, the semantics of the logic is unduly complicated compared to the simple intuitions about linguistic structure whose expression it is designed to allow.</Paragraph>
    <Paragraph position="1"> Specifically, a logic which uses partially ordered intensional sets instead of sequences is simpler and intuitively more desirable. However, this approach also has its drawbacks. What is significant is the illustration that syntactic structure and a treatment of nonconfigurational word order can be treated within a single logical framework.</Paragraph>
    <Paragraph position="2"> Second, the semantics is complicated a great deal by the reconstruction of intensional structures within classical set theory. A typed language which simply distinguishes atomic tokens from types and the use of intensional nonweUfounded set theory would give a far cleaner semantics.</Paragraph>
    <Paragraph position="3"> axiomatisation is still in work. This is largely due to the complexity of the semantics of set and sequence descriptions and the belief that there should be an adequate logic with a simpler (algebraic) semantics and consequently a simpler proof theory. We simply note here that we believe that a Henkin style completeness proof can be given for the logic (or an equivalent one).</Paragraph>
  </Section>
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