Learning-assisted theorem proving with millions of lemmas.
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| Title: | Learning-assisted theorem proving with millions of lemmas. |
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| Authors: | Kaliszyk, Cezary1 cezary.kaliszyk@uibk.ac.at, Urban, Josef2 josef.urban@gmail.com |
| Source: | Journal of Symbolic Computation. Jul2015, Vol. 69, p109-128. 20p. |
| Subjects: | Machine learning, Mathematics theorems, Mathematical analysis, Estimation theory, Mathematicians |
| Abstract: | Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck . [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Symbolic Computation is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 100413312 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Learning-assisted theorem proving with millions of lemmas. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kaliszyk%2C+Cezary%22">Kaliszyk, Cezary</searchLink><relatesTo>1</relatesTo><i> cezary.kaliszyk@uibk.ac.at</i><br /><searchLink fieldCode="AR" term="%22Urban%2C+Josef%22">Urban, Josef</searchLink><relatesTo>2</relatesTo><i> josef.urban@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Symbolic+Computation%22">Journal of Symbolic Computation</searchLink>. Jul2015, Vol. 69, p109-128. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+theorems%22">Mathematics theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Estimation+theory%22">Estimation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematicians%22">Mathematicians</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck . [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Symbolic Computation is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jsc.2014.09.032 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 109 Subjects: – SubjectFull: Machine learning Type: general – SubjectFull: Mathematics theorems Type: general – SubjectFull: Mathematical analysis Type: general – SubjectFull: Estimation theory Type: general – SubjectFull: Mathematicians Type: general Titles: – TitleFull: Learning-assisted theorem proving with millions of lemmas. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kaliszyk, Cezary – PersonEntity: Name: NameFull: Urban, Josef IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 07477171 Numbering: – Type: volume Value: 69 Titles: – TitleFull: Journal of Symbolic Computation Type: main |
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