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Journal of Automated Reasoning

, Volume 52, Issue 2, pp 191–213 | Cite as

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

  • Jesse Alama
  • Tom Heskes
  • Daniel Kühlwein
  • Evgeni Tsivtsivadze
  • Josef UrbanEmail author
Article

Abstract

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. This work develops learning-based premise selection in two ways. First, a fine-grained dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed, extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50 % improvement on the benchmark over the state-of-the-art Vampire/SInE system for automated reasoning in large theories.

Keywords

Automated reasoning in large theories Machine learning Premise selection Automated theorem proving 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Jesse Alama
    • 1
  • Tom Heskes
    • 2
  • Daniel Kühlwein
    • 2
  • Evgeni Tsivtsivadze
    • 2
  • Josef Urban
    • 2
    Email author
  1. 1.Center for Artificial IntelligenceNew University of LisbonLisbonPortugal
  2. 2.Intelligent Systems, Institute for Computing and Information SciencesRadboud UniversityNijmegenNetherlands

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