HOList: An Environment for Machine Learning of Higher Order Logic Theorem Proving

Kshitij Bansal, Sarah Loos, Markus Rabe, Christian Szegedy, Stewart Wilcox
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:454-463, 2019.

Abstract

We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an interesting challenge for deep learning. We provide an open-source framework based on the HOL Light theorem prover that can be used as a reinforcement learning environment. HOL Light comes with a broad coverage of basic mathematical theorems on calculus and the formal proof of the Kepler conjecture, from which we derive a challenging benchmark for automated reasoning approaches. We also present a deep reinforcement learning driven automated theorem prover, DeepHOL, that gives strong initial results on this benchmark.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-bansal19a, title = {{HOL}ist: An Environment for Machine Learning of Higher Order Logic Theorem Proving}, author = {Bansal, Kshitij and Loos, Sarah and Rabe, Markus and Szegedy, Christian and Wilcox, Stewart}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {454--463}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/bansal19a/bansal19a.pdf}, url = {https://proceedings.mlr.press/v97/bansal19a.html}, abstract = {We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an interesting challenge for deep learning. We provide an open-source framework based on the HOL Light theorem prover that can be used as a reinforcement learning environment. HOL Light comes with a broad coverage of basic mathematical theorems on calculus and the formal proof of the Kepler conjecture, from which we derive a challenging benchmark for automated reasoning approaches. We also present a deep reinforcement learning driven automated theorem prover, DeepHOL, that gives strong initial results on this benchmark.} }
Endnote
%0 Conference Paper %T HOList: An Environment for Machine Learning of Higher Order Logic Theorem Proving %A Kshitij Bansal %A Sarah Loos %A Markus Rabe %A Christian Szegedy %A Stewart Wilcox %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-bansal19a %I PMLR %P 454--463 %U https://proceedings.mlr.press/v97/bansal19a.html %V 97 %X We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an interesting challenge for deep learning. We provide an open-source framework based on the HOL Light theorem prover that can be used as a reinforcement learning environment. HOL Light comes with a broad coverage of basic mathematical theorems on calculus and the formal proof of the Kepler conjecture, from which we derive a challenging benchmark for automated reasoning approaches. We also present a deep reinforcement learning driven automated theorem prover, DeepHOL, that gives strong initial results on this benchmark.
APA
Bansal, K., Loos, S., Rabe, M., Szegedy, C. & Wilcox, S.. (2019). HOList: An Environment for Machine Learning of Higher Order Logic Theorem Proving. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:454-463 Available from https://proceedings.mlr.press/v97/bansal19a.html.

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