Learning to Guide a Saturation-Based Theorem Prover

Abstract

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 introduce TRAIL, 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 problems).

A Graph Neural Network Reasoner for Game Description Language

“…Beyond the two mentioned earlier, many other researchers have applied graph neural networks to the logical domain (Thost and Chen 2021;Abdelaziz et al 2021;Glorot et al 2019;Paliwal et al 2020;Crouse et al 2019;Olšák, Kaliszyk, and Urban 2019). Most work in the logical domain focus on tasks such as entailment and automated theorem proving, which typically uses much smaller graphs as the logical formulae consist of fewer clauses than an entire GDL game description.…”