Learning to Guide a Saturation-Based Theorem Prover

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 45; no. 1; pp. 738 - 751
• Main Authors: Abdelaziz, Ibrahim, Crouse, Maxwell, Makni, Bassem, Austel, Vernon, Cornelio, Cristina, Ikbal, Shajith, Kapanipathi, Pavan, Makondo, Ndivhuwo, Srinivas, Kavitha, Witbrock, Michael, Fokoue, Achille
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Benchmark testing; Benchmarks; Deep learning; deep reinforcement learning; Feature extraction; first-order logic; Graph neural networks; Graphical representations; Learning systems; Reinforcement learning; Saturation; Saturation-based theorem proving; Search problems; Theorem proving
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2022.3140382

Traditional automated theorem provers have relied on manually tuned heuristics to guide how they perform proof search. Recently, however, there has been a surge of interest in the design of learning mechanisms that can be integrated into theorem provers to improve their performance automatically. In this work, we describe TRAIL (Trial Reasoner for AI that Learns), a deep learning-based approach to theorem proving that characterizes core elements of saturation-based theorem proving within a neural framework. TRAIL leverages (a) an effective graph neural network for representing logical formulas, (b) a novel neural representation of the state of a saturation-based theorem prover in terms of processed clauses and available actions, and (c) a novel representation of the inference selection process as an attention-based action policy. We show through a systematic analysis that these components allow TRAIL to significantly outperform previous reinforcement learning-based theorem provers on two standard benchmark datasets (up to 36% more theorems proved). In addition, to the best of our knowledge, TRAIL is the first reinforcement learning-based approach to exceed the performance of a state-of-the-art traditional theorem prover on a standard theorem proving benchmark (solving up to 17% more theorems).