Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

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 lar...

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Bibliographic Details
Published in:Journal of automated reasoning Vol. 52; no. 2; pp. 191 - 213
Main Authors: Alama, Jesse, Heskes, Tom, Kühlwein, Daniel, Tsivtsivadze, Evgeni, Urban, Josef
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.02.2014
Springer
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Automated reasoning
Benchmarking
Computer Science
Computer science; control theory; systems
Construction
Data processing. List processing. Character string processing
Exact sciences and technology
Kernels
Knowledge bases (artificial intelligence)
Learning and adaptive systems
Logic and foundations
Mathematical analysis
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Mathematical logic, foundations, set theory
Mathematics
Memory organisation. Data processing
Proof theory and constructive mathematics
Proving
Sciences and techniques of general use
Software
Symbolic and Algebraic Manipulation
Automated reasoning in large theories
Premise selection
Automated theorem proving
Machine learning
Automated reasoning
Formal method
Knowledge base
Automatic proving
Kernel method
Theorem proving
Fine grain structure
Proof theory
Artificial intelligence
Formal verification
ISSN:0168-7433, 1573-0670
Online Access:Get full text
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Summary: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.
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ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-013-9286-5