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International Conference on Logic for Programming Artificial Intelligence and Reasoning

LPAR 2013: Logic for Programming, Artificial Intelligence, and Reasoning pp 503–517Cite as

Lemma Mining over HOL Light

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8312)

Abstract

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of all lemmas in the core HOL Light library, adding thousands of the best lemmas to the pool of named statements that can be re-used in later proofs. The usefulness of the new lemmas is then evaluated by comparing the performance of automated proving of the core HOL Light theorems with and without such added lemmas.

Keywords

  • Automate Reasoning
  • Eigenvector Centrality
  • Large Theory
  • Automate Prove
  • Inference Graph

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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  • DOI: 10.1007/978-3-642-45221-5_34
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Author information

Authors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk & Josef Urban

  2. Radboud University, Nijmegen, 6525 HP, Netherlands

    Cezary Kaliszyk & Josef Urban

Authors
  1. Cezary Kaliszyk
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  2. Josef Urban
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Editor information

Editors and Affiliations

  1. Microsoft Research, Redmond, WA, USA

    Ken McMillan

  2. University of Innsbruck, Austria

    Aart Middeldorp

  3. University of Manchester, UK

    Andrei Voronkov

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Kaliszyk, C., Urban, J. (2013). Lemma Mining over HOL Light . In: McMillan, K., Middeldorp, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2013. Lecture Notes in Computer Science, vol 8312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45221-5_34

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  • DOI: https://doi.org/10.1007/978-3-642-45221-5_34

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