Presenting Proofs with Adapted Granularity

  • Marvin Schiller
  • Christoph Benzmüller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5803)


When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of detail (also called granularity). Often these presentations are neither intended nor suitable for human use. A challenge therefore is to develop user- and goal-adaptive proof presentation techniques that obey common mathematical practice. We present a flexible and adaptive approach to proof presentation based on classification. Expert knowledge for the classification task can be hand-authored or extracted from annotated proof examples via machine learning techniques. The obtained models are employed for the automated generation of further proofs at an adapted level of granularity.


Adaptive proof presentation proof tutoring automated reasoning machine learning granularity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Marvin Schiller
    • 1
  • Christoph Benzmüller
    • 2
  1. 1.German Research Center for Artificial Intelligence (DFKI)BremenGermany
  2. 2.International University in GermanyBruchsalGermany

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