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A Neurally-Guided, Parallel Theorem Prover

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Book cover Frontiers of Combining Systems (FroCoS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11715))

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Abstract

We present a prototype of a neurally-guided automatic theorem prover for first-order logic with equality. The prototype uses a neural network trained on previous proof search attempts to evaluate subgoals based directly on their structure, and hence bias proof search toward success. An existing first-order theorem prover is employed to dispatch easy subgoals and prune branches which cannot be solved. Exploration of the search space is asynchronous with respect to both the evaluation network and the existing prover, allowing for efficient batched neural network execution and for natural parallelism within the prover. Evaluation on the MPTP dataset shows that the prover can improve with learning.

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Notes

  1. 1.

    Learning to Reason with Neural Architectures. Lerna is also the lair of the mythical many-headed beast Hydra. Source code available at https://github.com/MichaelRawson/lerna.

  2. 2.

    https://github.com/JUrban/deepmath/blob/master/M2k_list.

  3. 3.

    NVIDIA® GeForce® GT 730.

  4. 4.

    Intel® Core™ i7-6700 CPU @ 3.40 GHz, 16 GB RAM.

  5. 5.

    https://rusty1s.github.io/pytorch_geometric/build/html/modules/nn.html.

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Acknowledgements

The authors wish to thank Josef Urban and his group in ČVUT, Prague for their help and encouragement with early iterations of this work, and for supplying the Mizar dataset used in this paper.

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Authors and Affiliations

  1. University of Manchester, Manchester, UK

    Michael Rawson & Giles Reger

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  1. Michael Rawson
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  2. Giles Reger
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Correspondence to Michael Rawson .

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Editors and Affiliations

  1. CNRS, University of Toulouse, Toulouse, France

    Andreas Herzig

  2. Middlesex University London, London, UK

    Andrei Popescu

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Rawson, M., Reger, G. (2019). A Neurally-Guided, Parallel Theorem Prover. In: Herzig, A., Popescu, A. (eds) Frontiers of Combining Systems. FroCoS 2019. Lecture Notes in Computer Science(), vol 11715. Springer, Cham. https://doi.org/10.1007/978-3-030-29007-8_3

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  • DOI: https://doi.org/10.1007/978-3-030-29007-8_3

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