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<Paper uid="C00-2091">
  <Title>Generation, Lambek Calculus, Montague's Semantics and Semantic Proof Nets</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> From the type logical grmnmars point of view, the parametric part of the language analysis is the lexicon, and the constant one is the logical rules. This should of course hold both for parsing and generation, hence we can consider the reversibility properties of such grammars. And a relevant problem is to compare the complexity of the two cases.</Paragraph>
    <Paragraph position="1"> For Lambek calculus (Lambek, 1958), the parsing complexity is still an open problem. But the question arises to know how to generate in this framework, and how d(~cult (on the computational side) it is. (Merenciano and Morrill, 1997) answered with a labelled deductive system guided with A-term unification. But a drawback of this latter mechanism consists in its algorithmic undecidability (from second order unification).</Paragraph>
    <Paragraph position="2"> Relying on the linear logic (Girard, 1987) (which provides a powerful framework to express Lambek calculus, specially with proof nets for the latter (Roorda, 1991; Lamarche and Retor6, 1996)), this paper wants to adress the problem of finding the way we can associate given lexical entries to fit a given semantic expression and generate a syntactically correct expression (for the moment, we do not care to the choice of the lexical items). For this purpose, we express our problem as a proof search one in (multiplicative) linear logic which is decidable.</Paragraph>
    <Paragraph position="3"> Moreover, we characterize the semantic recipes of lexical items that provide a polynomial solution for the syntactic realization process. Then we give an example of this process.</Paragraph>
  </Section>
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