Formal Verification of Proofs from Automated Theorem Provers for Higher-Order Logic

2026-09-21

AI Summary

研究解决了自动定理证明器生成证明的验证问题，通过在Dedukti框架下开发一种通用方法来编码规则和证明步骤，并应用于高阶逻辑EP演算。

Abstract

We identify common challenges and requirements for verifying proofs from automated theorem provers in the Dedukti logical framework and develop a general methodology for deriving encodings of calculus rules and proof steps, including clausification. We then apply this methodology to the EP calculus for higher-order logic and integrate it into the automated theorem prover Leo-III. The resulting prototype reconstructs about 80% of generated proof steps automatically, making Leo-III the first higher-order automated theorem prover to support independently checkable proof reconstruction and providing a basis for cross-system reuse. The implementation uncovered several bugs in Leo-III.

Problem

• Formal Verification
• Automated Theorem Provers
• Higher-Order Logic
• Dedukti

Innovation

• formal verification
• automated theorem provers
• higher-order logic
• proof reconstruction