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<Paper uid="W06-1521">
  <Title>Parsing TAG with Abstract Categorial Grammar</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> The algorithm we present is a specialization to TAGs of a more general one dedicated to second order Abstract Categorial Grammars (ACGs) (de Groote, 2001). Our aim is to give here an informal presentation of tools that can be used to design efficient parsing algorithms for formalisms more expressive than TAG. Therefore, we only give a representation of TAGs with linear l-terms together with simple derivation rules; we do not give in complete details the technical relation with ACGs.</Paragraph>
    <Paragraph position="1"> For some more information about ACGs and their relation to TAGs, one may read (de Groote, 2001) and (de Groote, 2002).</Paragraph>
    <Paragraph position="2"> The advantage of using ACG is that they are defined with very few primitives, but can encode many formalisms. Thus they are well suited to study from a general perspective a full class of formalisms. In particular, a special class of ACGs (second order ACGs) embeds LCFRS (de Groote and Pogodalla, 2004), i.e. mildly context sensitive languages. Therefore, the study of second order ACGs leads to insights on mildly context sensitive languages. Having a general framework to describe parsing algorithms for mildly context sensitive languages may give some help to transfer some interesting parsing technique from one formalism to another. It can be, for example, a good mean to obtain prefix-valid algorithms, LC algorithms, LR algorithms. . . for the full class of mildly context sensitive languages.</Paragraph>
    <Paragraph position="3"> The class of languages described by second order ACGs is wider than mildly context sensitive languages. They can encode tree languages, and more generally languages of linear l-terms. As Montague style semantics (Montague, 1974) is based on l-calculus, being able to parse linear l-term is a first step towards generation algorithms seen as parsing algorithm. Furthermore, since this parsing algorithm is a generalization of algorithms `a la Earley for CFGs and TAGs, the more general algorithm that can be used for generation (when semantic formulae are linear) can be considered as efficient.</Paragraph>
    <Paragraph position="4"> The paper is organized as follows: section two gives basic defintions and tools concerning the linear l-calculus. Section three explains how the indices usually used by parsers are represented for the linear l-calculus. Section four gives a rough explaination of the encoding of TAGs within a compiled representation of second order ACGs.</Paragraph>
    <Paragraph position="5"> Section five explains the parsing algorithm and we conclude with section six.</Paragraph>
  </Section>
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