Intelligent Proof Assistance for Dynamic Fault Tree Analysis: A Multi-Model Approach for Tactic Generation and Proof Synthesis in HOL4

Abstract

This research proposes a framework providing proof automation for the Dynamic Fault Tree (DFT) analysis performed in the interactive theorem prover HOL4. Empowering both seasoned experts and novices alike, this framework uses the capabilities of deep learning models, including a Transformer-based architecture and a Convolutional Neural Network (CNN), to overcome the complexities associated with crafting intricate tactics and the manual proofs developed in HOL4. By employing an innovative multi-model approach, the system seamlessly guides users through the proof generation process, starting from a user-provided theorem or goal. Leveraging the strengths of the Transformer model, the system intelligently generates a preliminary tactic based on the given input. Building upon this initial step, the system deftly constructs the entire proof, employing the Transformer model’s proficiency in handling lengthy sequences. The ingenious combination of the CNN and Transformer models enables the seamless integration of goal-directed theorem proving and automated proof synthesis. The proposed approach marks a significant milestone in enhancing the accessibility and usability of DFT analysis available in HOL4, revolutionizing the landscape of formal DFT analysis. The AI-driven approach pioneered in this work not only fosters efficiency and understanding but also ensures an unmatched user experience within the DFT analysis community