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<Paper uid="P04-1004">
  <Title>Analysis of Mixed Natural and Symbolic Language Input in Mathematical Dialogs</Title>
  <Section position="6" start_page="0" end_page="0" type="concl">
    <SectionTitle>
6 Conclusions and Further Work
</SectionTitle>
    <Paragraph position="0"> Based on experimentally collected tutorial dialogs on mathematical proofs, we argued for the use of deep syntactic and semantic analysis. We presented an approach that uses multimodal CCG with hybrid logic dependency semantics, treating natural and symbolic language on a par, thus enabling uniform analysis of inputs with varying degree of formal content verbalization.</Paragraph>
    <Paragraph position="1"> A preliminary evaluation of the mathematical expression parser showed a reasonable result. We are incrementally extending the implementation of the deep analysis components, which will be evaluated as part of the next Wizard-of-Oz experiment.</Paragraph>
    <Paragraph position="2"> One of the issues to be addressed in this context is the treatment of ill-formed input. On the one hand, the system can initiate a correction subdialog in such cases. On the other hand, it is not desirable to go into syntactic details and distract the student from the main tutoring goal. We therefore need to handle some degree of ill-formed input.</Paragraph>
    <Paragraph position="3"> Another question is which parts of mathematical expressions should have explicit semantic representation. We feel that this choice should be motivated empirically, by systematic occurrence of natural language references to parts of mathematical expressions (e.g., &amp;quot;the left/right side&amp;quot;, &amp;quot;the parenthesis&amp;quot;, and &amp;quot;the inner parenthesis&amp;quot;) and by the syntactic contexts in which they occur (e.g., the partitioning a40 [x][a27 A]a41 seems well motivated in &amp;quot;B contains no xa27 A&amp;quot;; [x a27 ] is a constituent in &amp;quot;x a27 of complement of B.&amp;quot;) We also plan to investigate the interaction of modal verbs with the argumentative structure of the proof. For instance, the necessity modality is compatible with asserting a necessary conclusion or a prerequisite condition (e.g., &amp;quot;A und B muessen disjunkt sein.&amp;quot; [A and B must be disjoint.]). This introduces an ambiguity that needs to be resolved by the domain reasoner.</Paragraph>
  </Section>
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