A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving
This work addresses the problem of reducing manual heuristic tuning in automated theorem proving for researchers and practitioners in logic and AI, representing an incremental advance over prior reinforcement learning approaches.
The paper tackles the challenge of automating theorem proving in first-order logic by introducing TRAIL, a system that uses deep reinforcement learning with a novel neural state representation and attention-based action policy, resulting in a 15% improvement in proving theorems on benchmark datasets compared to previous reinforcement-learning-based methods.
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 reinforcement-learning-based theorem provers on two benchmark datasets for first-order logic automated theorem proving (proving around 15% more theorems).