Proof-Pattern Recognition and Lemma Discovery in ACL2

Jonathan Heras, Ekaterina Komendantskaya, Moa Johansson, Ewen Maclean

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.
Original languageEnglish
Title of host publicationLogic for Programming, Artificial Intelligence, and Reasoning
Subtitle of host publication19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings
EditorsKen McMillan, Aart Middeldorp, Andrei Voronkov
PublisherSpringer
Pages389-406
Number of pages18
ISBN (Electronic)9783642452215
ISBN (Print)9783642452208
DOIs
Publication statusPublished - 2013
Event19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning - Stellenbosch, United Kingdom
Duration: 14 Dec 201319 Dec 2013

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
Volume8312
ISSN (Print)0302-9743

Conference

Conference19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Abbreviated titleLPAR 2013
CountryUnited Kingdom
CityStellenbosch
Period14/12/1319/12/13

Fingerprint

Pattern recognition
Learning systems
Statistics

Keywords

  • Theorem Proving
  • Statistical Machine-Learning
  • Pattern Recognition
  • Lemma Discovery
  • Analogy

Cite this

Heras, J., Komendantskaya, E., Johansson, M., & Maclean, E. (2013). Proof-Pattern Recognition and Lemma Discovery in ACL2. In K. McMillan, A. Middeldorp, & A. Voronkov (Eds.), Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings (pp. 389-406). (Lecture Notes in Computer Science; Vol. 8312). Springer. https://doi.org/10.1007/978-3-642-45221-5_27
Heras, Jonathan ; Komendantskaya, Ekaterina ; Johansson, Moa ; Maclean, Ewen. / Proof-Pattern Recognition and Lemma Discovery in ACL2. Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings. editor / Ken McMillan ; Aart Middeldorp ; Andrei Voronkov. Springer, 2013. pp. 389-406 (Lecture Notes in Computer Science).
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Heras, J, Komendantskaya, E, Johansson, M & Maclean, E 2013, Proof-Pattern Recognition and Lemma Discovery in ACL2. in K McMillan, A Middeldorp & A Voronkov (eds), Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings. Lecture Notes in Computer Science, vol. 8312, Springer, pp. 389-406, 19th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, Stellenbosch, United Kingdom, 14/12/13. https://doi.org/10.1007/978-3-642-45221-5_27

Proof-Pattern Recognition and Lemma Discovery in ACL2. / Heras, Jonathan; Komendantskaya, Ekaterina; Johansson, Moa; Maclean, Ewen.

Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings. ed. / Ken McMillan; Aart Middeldorp; Andrei Voronkov. Springer, 2013. p. 389-406 (Lecture Notes in Computer Science; Vol. 8312).

Research output: Chapter in Book/Report/Conference proceedingChapter

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AU - Maclean, Ewen

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N2 - We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.

AB - We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it.

KW - Theorem Proving

KW - Statistical Machine-Learning

KW - Pattern Recognition

KW - Lemma Discovery

KW - Analogy

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DO - 10.1007/978-3-642-45221-5_27

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T3 - Lecture Notes in Computer Science

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BT - Logic for Programming, Artificial Intelligence, and Reasoning

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Heras J, Komendantskaya E, Johansson M, Maclean E. Proof-Pattern Recognition and Lemma Discovery in ACL2. In McMillan K, Middeldorp A, Voronkov A, editors, Logic for Programming, Artificial Intelligence, and Reasoning: 19th International Conference, LPAR-19, Stellenbosch, South Africa, December 14-19, 2013. Proceedings. Springer. 2013. p. 389-406. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-642-45221-5_27