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<Paper uid="E99-1009">
  <Title>Geometry of Lexico-Syntactic Interaction</Title>
  <Section position="1" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
Abstract
</SectionTitle>
    <Paragraph position="0"> Interaction of lexical and derivational semantics---for example substitution and lambda conversion--- is typically a part of the on-line interpretation process. Proof-nets are to categorial grammar what phrase markers are to phrase structure grammar: unique graphical structures underlying equivalence classes of sequential syntactic derivations; but the role of proof-nets is deeper since they integrate also semantics. In this paper we show how interaction of lexical and derivational semantics at the lexico-syntactic interface can be precomputed as a process of off-line lexical compilation comprising Cut elimination in partial proof-nets.</Paragraph>
    <Paragraph position="1"> Introduction Consider the paraphrase: following examples of  (1) a.</Paragraph>
    <Paragraph position="2"> b.</Paragraph>
    <Paragraph position="3"> C.</Paragraph>
    <Paragraph position="4"> Frodo lives in Bag End.</Paragraph>
    <Paragraph position="5"> Frodo inhabits Bag End.</Paragraph>
    <Paragraph position="6"> ((in b) (live\])) (2) a.</Paragraph>
    <Paragraph position="7"> b.</Paragraph>
    <Paragraph position="8"> C.</Paragraph>
    <Paragraph position="9">  John tries to find Mary.</Paragraph>
    <Paragraph position="10"> John seeks Mary.</Paragraph>
    <Paragraph position="11"> ((try (find rn ) ) j) Typically, for at least (lb) and (2b) the normalised semantic forms result from a process of substitution and lambda conversion subsequent to or simultaneous with syntactic derivation. We show how such interaction of lexical and derivational semantics at the lexico-syntactic interface can be precomputed as a process of off-line lexical compilation comprising Cut elimination in partial proof-nets.</Paragraph>
    <Paragraph position="12"> For accessibility, we devote in the initial sections a considerable proportion of space to an introduction to categorial grammar oriented towards proof-nets; see also Morrill (1994), Moortgat (1996) and Carpenter (1997).</Paragraph>
  </Section>
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