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Methods of Lemma Extraction in Natural Deduction Proofs
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  • Open Access
  • Published: 04 November 2012

Methods of Lemma Extraction in Natural Deduction Proofs

  • Karol Pąk1 

Journal of Automated Reasoning volume 50, pages 217–228 (2013)Cite this article

  • 789 Accesses

  • 22 Citations

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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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Authors and Affiliations

  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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  • Received: 06 December 2011

  • Accepted: 10 October 2012

  • Published: 04 November 2012

  • Issue Date: February 2013

  • DOI: https://doi.org/10.1007/s10817-012-9267-0

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Keywords

  • Lemma
  • Extraction
  • Natural
  • Deduction
  • Legibility
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