Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Details Premise Selection for Mathematics by Corpus Analysis and Kernel Methods Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

2011-08-17

arxiv.org/abs/1108.3446v2

Computer Science

Learning

26 pages

Scientific paper

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal 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 Vampire/SInE state-of-the-art system for automated reasoning in large theories.

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