A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving

Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment in automated theorem proving remains a challenge. In this paper we introduce TRAIL, a system that applies deep reinforcement learning to saturation-based theorem proving. TRAIL leverages (a) a novel neural representation of the state of a theorem prover and (b) a novel characterization of the inference selection process in terms of an attention-based action policy. We show through systematic analysis that these mechanisms allow TRAIL to significantly outperform previous reinforcementlearning-based theorem provers on two benchmark datasets for first-order logic automated theorem proving (proving around 15% more theorems).

Authors

• Maxwell Crouse
• Ibrahim Abdelaziz
• Bassem Makni
• Spencer Whitehead
• Cristina Cornelio
• Pavan Kapanipathi
• Kavitha Srinivas IBM Research
• Veronika Thost
• Michael Witbrock NAOInstitute, University of Auckland, New Zealand School of Computer Science, University of Auckland, New Zealand
• Achille Fokoue

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