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Methods of Lemma Extraction in Natural Deduction Proofs

Journal of Automated Reasoning volume 50, pages217–228(2013)Cite this article

Abstract

The existing examples of natural deduction proofs, either declarative or procedural, indicate that often the legibility of proof scripts is of secondary importance to the authors. As soon as the computer accepts the proof script, many authors do not work on improving the parts that could be shortened and do not avoid repetitions of technical sub-deductions, which often could be replaced by a single lemma. This article presents selected properties of reasoning passages that may be used to determine if a reasoning passage can be extracted from a proof script, transformed into a lemma and replaced by a reference to the newly created lemma. Additionally, we present methods for improving the legibility of the reasoning that remains after the extraction of the lemmas.

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  1. Institute of Informatics, University of Białystok, Białystok, Poland

    Karol Pąk

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  1. Karol Pąk
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Correspondence to Karol Pąk.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Pąk, K. Methods of Lemma Extraction in Natural Deduction Proofs. J Autom Reasoning 50, 217–228 (2013). https://doi.org/10.1007/s10817-012-9267-0

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Keywords

  • Lemma
  • Extraction
  • Natural
  • Deduction
  • Legibility