Automated Theorem Proving in Intuitionistic Propositional Logic by Deep Reinforcement Learning
This work addresses the challenge of limited data in automated theorem proving for researchers in logic and AI, though it is incremental as it builds on existing reinforcement learning methods.
The authors tackled automated theorem proving in intuitionistic propositional logic by developing a deep reinforcement learning algorithm with data augmentation and a compact graph representation, achieving 84% success on a benchmark compared to 52% for a baseline prover.
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in intuitionistic propositional logic. The most significant challenge in the application of deep learning to the ATP is the absence of large, public theorem database. We, however, overcame this issue by applying a novel data augmentation procedure at each iteration of the reinforcement learning. We also improve the efficiency of the algorithm by representing the syntactic structure of formulas by a novel compact graph representation. Using the large volume of augmented data, we train highly accurate graph neural networks that approximate the value function for the set of the syntactic structures of formulas. Our method is also cost-efficient in terms of computational time. We will show that our prover outperforms Coq's $\texttt{tauto}$ tactic, a prover based on human-engineered heuristics. Within the specified time limit, our prover solved 84% of the theorems in a benchmark library, while $\texttt{tauto}$ was able to solve only 52%.