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Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
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Journal Article
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
2014
Overview
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.
Publisher
Springer Netherlands,Springer,Springer Nature B.V
Subject
/ Computer science; control theory; systems
/ Data processing. List processing. Character string processing
/ Exact sciences and technology
/ Kernels
/ Knowledge bases (artificial intelligence)
/ Learning and adaptive systems
/ Mathematical Logic and Formal Languages
/ Mathematical Logic and Foundations
/ Mathematical logic, foundations, set theory
/ Memory organisation. Data processing
/ Proof theory and constructive mathematics
/ Proving
/ Sciences and techniques of general use
/ Software
