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<Paper uid="P03-1045">
  <Title>k-valued Non-Associative Lambek Categorial Grammars are not Learnable from Strings</Title>
  <Section position="1" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
Abstract
</SectionTitle>
    <Paragraph position="0"> This paper is concerned with learning categorial grammars in Gold's model. In contrast to k-valued classical categorial grammars, k-valued Lambek grammars are not learnable from strings. This result was shown for several variants but the question was left open for the weakest one, the non-associative variant NL.</Paragraph>
    <Paragraph position="1"> We show that the class of rigid and k-valued NL grammars is unlearnable from strings, for each k; this result is obtained by a specific construction of a limit point in the considered class, that does not use product operator.</Paragraph>
    <Paragraph position="2"> Another interest of our construction is that it provides limit points for the whole hierarchy of Lambek grammars, including the recent pregroup grammars.</Paragraph>
    <Paragraph position="3"> Such a result aims at clarifying the possible directions for future learning algorithms: it expresses the difficulty of learning categorial grammars from strings and the need for an adequate structure on examples. null</Paragraph>
  </Section>
class="xml-element"></Paper>