Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

  • Authors:

  • Jesse Alama;Tom Heskes;Daniel Kühlwein;Evgeni Tsivtsivadze;Josef Urban

  • Affiliations:

  • Center for Artificial Intelligence, New University of Lisbon, Lisbon, Portugal 1099085;Intelligent Systems, Institute for Computing and Information Sciences, Radboud University, Nijmegen, Netherlands;Intelligent Systems, Institute for Computing and Information Sciences, Radboud University, Nijmegen, Netherlands;Intelligent Systems, Institute for Computing and Information Sciences, Radboud University, Nijmegen, Netherlands;Intelligent Systems, Institute for Computing and Information Sciences, Radboud University, Nijmegen, Netherlands

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 2014

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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.