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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Veröffentlicht in:	Journal of automated reasoning Jg. 52; H. 2; S. 191 - 213
Hauptverfasser:	Alama, Jesse, Heskes, Tom, Kühlwein, Daniel, Tsivtsivadze, Evgeni, Urban, Josef
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Dordrecht Springer Netherlands 01.02.2014 Springer Springer Nature B.V
Schlagworte:	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
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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.
AbstractList	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.[PUBLICATION 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. 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.
Author	Alama, Jesse Heskes, Tom Urban, Josef Kühlwein, Daniel Tsivtsivadze, Evgeni
Author_xml	– sequence: 1 givenname: Jesse surname: Alama fullname: Alama, Jesse organization: Center for Artificial Intelligence, New University of Lisbon – sequence: 2 givenname: Tom surname: Heskes fullname: Heskes, Tom organization: Intelligent Systems, Institute for Computing and Information Sciences, Radboud University – sequence: 3 givenname: Daniel surname: Kühlwein fullname: Kühlwein, Daniel organization: Intelligent Systems, Institute for Computing and Information Sciences, Radboud University – sequence: 4 givenname: Evgeni surname: Tsivtsivadze fullname: Tsivtsivadze, Evgeni organization: Intelligent Systems, Institute for Computing and Information Sciences, Radboud University – sequence: 5 givenname: Josef surname: Urban fullname: Urban, Josef email: Josef.Urban@gmail.com organization: Intelligent Systems, Institute for Computing and Information Sciences, Radboud University
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Cites_doi	10.1162/neco.1991.3.4.461 10.1007/978-3-540-71070-7_37 10.1007/978-3-540-78800-3_24 10.1007/3-540-45949-9 10.1007/978-3-642-15582-6_30 10.1007/978-3-642-02959-2_10 10.1007/11542384_3 10.1007/978-3-642-31374-5_1 10.4064/fm-32-1-176-783 10.1007/s10107-010-0420-4 10.1007/978-3-642-22673-1_10 10.1007/978-3-540-74591-4_18 10.1007/3-540-44581-1_27 10.1090/S0002-9947-1950-0051437-7 10.1017/CBO9780511581007 10.1007/BF00247436 10.1007/978-3-642-28717-6_6 10.1007/s10817-007-9085-y 10.1007/978-3-642-24364-6_2 10.1017/CBO9780511809682 10.1007/s10817-004-6245-1 10.1007/BFb0031814 10.1007/978-3-642-22438-6_23 10.1007/s10817-012-9269-y 10.1007/978-3-662-07964-5
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Keywords	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
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SubjectTerms	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
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Title	Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
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