Abstract
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic. The clause selection heuristics in such systems are, however, often evaluating clauses in isolation, ignoring other clauses. This has changed recently by equipping the E/ENIGMA system with a graph neural network (GNN) that chooses the next given clause based on its evaluation in the context of previously selected clauses. In this work, we describe several algorithms and experiments with ENIGMA, advancing the idea of contextual evaluation based on learning important components of the graph of clauses.
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Notes
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The publication of this large evaluation is in preparation.
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Another popular way how to generalize k-means (and assign a point to more than one cluster) is to use Gaussian mixture models.
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Details are at https://github.com/ai4reason/ATP_Proofs.
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On a server with 36 hyperthreading Intel(R) Xeon(R) Gold 6140 CPU @ 2.30 GHz cores, 755 GB of memory, and 4 NVIDIA GeForce GTX 1080 Ti GPUs.
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Acknowledgments
Supported by the ERC Consolidator grant AI4REASON no. 649043 (JJ, JU), by the Czech project AI & Reasoning CZ.02.1.01/0.0/0.0/15_003/0000466 and the European Regional Development Fund (KC, JU), by the ERC Starting grant SMART no. 714034 (JJ, MO), and by the Czech MEYS under the ERC CZ project POSTMAN no. LL1902 (JJ).
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Chvalovský, K., Jakubův, J., Olšák, M., Urban, J. (2021). Learning Theorem Proving Components. In: Das, A., Negri, S. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2021. Lecture Notes in Computer Science(), vol 12842. Springer, Cham. https://doi.org/10.1007/978-3-030-86059-2_16
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