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<Paper uid="W00-0739">
  <Title>Learning from a Substructural Perspective</Title>
  <Section position="6" start_page="179" end_page="179" type="concl">
    <SectionTitle>
5 Discussion
</SectionTitle>
    <Paragraph position="0"> We showed that the learnability result of Valiant for learning boolean concepts can be transformed to a learnability result for pattern languages by looking at the transformation of the underlying representational theories; i.e. looking at the transformation from classical first order propositional logic (underlying the boolean concepts) to substructural first order propositional logic (underlying the pattern languages). An interesting extension would be to look at the substructural concept language that includes implication (instead of the CNF formula's only). A language that allows implication coincides with the full Lambek calculus, and a learning algorithm and learnability result for this framework amounts to results for all languages that can be described by context free grammars. This is subject to future research.</Paragraph>
  </Section>
class="xml-element"></Paper>