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<Paper uid="P98-1088">
  <Title>Memoisation for Glue Language Deduction and Categorial Parsing</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> The multiplicative fragment of linear logic, which includes just the linear implication (o-) and multiplicative ((r)) operators, has found a number of applications within linguistics and computational linguistics. Firstly, it can be used in combination with some system of labelling (after the 'labelled deduction' methodology of (Gabbay, 1996)) as a general method for formulating various categorial grammar systems. Linear deduction methods provide a common basis for parsing categorial systems formulated in this way. Secondly, the multiplicative fragment forms the core of the system used in work by Dalrymple and colleagues for handling the semantics of LFG derivations, providing a 'glue language' for assembling the meanings of sentences from those of words and phrases.</Paragraph>
    <Paragraph position="1"> Although there are a number of deduction methods for multiplicative linear logic, there is a notable absence of tabular methods, which, like chart parsing for CFGs, avoid redundant computation. Hepple (1996) presents a compilation method which allows for tabular deduction for implicational linear logic (i.e. the fragment with only o--). This paper develops that method to cover the fragment that includes the multiplicative. The use of this method for the applications mentioned above is discussed.</Paragraph>
  </Section>
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