Distributed Theorem Proving via Graph Neural Networks

Abstract

Automated theorem proving (ATP) is a cornerstone of artificial intelligence, aiming to mechanize mathematical reasoning. However, traditional ATP systems often struggle with scalability and efficiency, particularly for complex theorems. This paper proposes a novel approach utilizing Graph Neural Networks (GNNs) to address these limitations by transforming theorem proving into a distributed graph reasoning problem. We introduce a framework where logical statements are represented as graphs and a GNN is trained to perform parallel inference across multiple nodes in a distributed system. The core claim is that GNNs can significantly accelerate and scale ATP by enabling efficient parallel reasoning. The proposed method leverages the inherent graph representation capabilities of GNNs to capture relationships between logical components, facilitating automated deduction and inference. This approach offers a promising direction for future advancements in ATP, potentially leading to more robust and scalable automated reasoning systems. The effectiveness of this approach is demonstrated through theoretical analysis and conceptual design, outlining the key components and functionalities of the proposed system.