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Presenting Proofs in a Human-Oriented Way

  • Helmut Horacek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1632)

Abstract

Presenting machine-generated proofs in terms adequate to the needs of a human audience is a serious challenge. One salient property of mathematical proofs as typically found in textbooks is that lines of reasoning are expressed in a rather condensed form by leaving out elementary and easily inferable, but logically necessary inference steps, while explaining involved ones in more detail. To date, automated proof presentation techniques are not able to deal with this issue in an adequate manner. Addressing this problem in a principled way, we describe an approach that successively enhances a logically self-contained proof at the assertion level through communicatively justified modifications of the original line of reasoning. These enhancements include expansion of involved theorem applications, omission of trivial justifications, compactification of intermediate inference steps, and broadening the scope of justifications to support focused argumentation, as in chains of inequations. Through incorporating these measurements, many proofs are presented in a shorter and better understandable fashion than in previous approaches.

Keywords

Mathematical Proof Argumentation Structure Modus Tollens Inference Step Proof Presentation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Helmut Horacek
    • 1
  1. 1.Universität des Saarlandes FB 14 InformatikSaarbrückenGermany

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