Proving Theorems using Incremental Learning and Hindsight Experience Replay
This addresses the challenge of creating efficient, domain-specific theorem provers without relying on handcrafted heuristics or bootstrapping from traditional provers, representing a significant but incremental advance in automated reasoning.
The paper tackles the problem of automated theorem proving in first-order logic without equality by proposing an incremental learning algorithm with a learned clause-scoring function and hindsight experience replay, showing that trained provers can match or surpass state-of-the-art traditional provers on the TPTP dataset in terms of proof quantity and quality.
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either depend on these traditional provers to bootstrap themselves or fall short on reaching comparable performance. In this paper, we propose a general incremental learning algorithm for training domain specific provers for first-order logic without equality, based only on a basic given-clause algorithm, but using a learned clause-scoring function. Clauses are represented as graphs and presented to transformer networks with spectral features. To address the sparsity and the initial lack of training data as well as the lack of a natural curriculum, we adapt hindsight experience replay to theorem proving, so as to be able to learn even when no proof can be found. We show that provers trained this way can match and sometimes surpass state-of-the-art traditional provers on the TPTP dataset in terms of both quantity and quality of the proofs.