The paper introduces a reference‑free proxy‑judge framework for autoformalization, separating correctness into grounding, statement faithfulness, coverage, and inference. It presents three theoretical results linking proxy error rates to pass‑but‑wrong rates, the impact of false rejections on refinement, and a decomposition of final pass rates. The framework is instantiated with eight proxies and evaluated on ProofNet, miniF2F, e‑SNLI, and ProntoQA, showing that the predictions hold and identifying failure routes.
arXiv:2610.17358v1 Announce Type: cross Abstract: Formal verification proves that a program satisfies its specification, but says nothing about whether the specification captures what the author mean...
The paper introduces GUARD, a neuro‑symbolic system that autoformalizes argumentative material by completing missing premises (guards) before formal verification. It uses large language models to generate candidate guards, Isabelle/HOL to verify them, and a contrastive test to ensure the proof depends on the original premises and does not over‑generalize. Experiments on Debatepedia and ARCT show that GUARD improves verified‑faithful scores by over 30 points and reduces leakage by about 20 points compared to prior LLM‑driven theorem proving methods.
arXiv:2607. 13069v1 Announce Type: new Abstract: Large language models produce chain-of-thought (CoT) reasoning that appears logically sound yet may not genuinely depend on its stated premises.
arXiv:2607. 12650v1 Announce Type: cross Abstract: Tool access alone does not make LLM empirical reasoning governable: accepted outputs need not descend from attested evidence, and accepted deductions need not hold up under formal scrutiny.
arXiv:2608. 15432v1 Announce Type: new Abstract: In formal verification, both the autoformalization of statements and automated proof search have been studied extensively.
arXiv:2609.21190v1 Announce Type: cross Abstract: Ensuring the correctness of LLM-generated code is a core challenge for modern software engineering. Benchmarks for agentic code generation check corr...
arXiv:2607. 01223v1 Announce Type: new Abstract: When should an AI system's answer be trusted?
arXiv:2608. 14221v1 Announce Type: new Abstract: Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4.
The paper presents a unified dataset of 350 Lean tasks to evaluate specification generation (SpecGen) for verifiable code, combining metrics of formal validity, reference similarity, equivalence, and behavioural adequacy. It highlights that restricting similarity measures to a subset of tasks can shift rankings, and shows that a perfect postcondition score can still miss critical input coverage, underscoring the need for separate feedback on input and output constraints.
arXiv:2607. 19407v1 Announce Type: new Abstract: Formal theorem proving has emerged as a frontier challenge for machine learning, yet the ecosystem is fragmented: proofs remain siloed across incompatible systems, limiting both training data for learning-based provers and the portability of verified results.
arXiv:2606. 29493v1 Announce Type: new Abstract: Benchmarks for LLM-assisted theorem proving in Lean are often treated as intrinsically reliable because every solved instance comes with a machine-checked proof.
The paper introduces a compiler-guided adaptive proof search framework for Lean 4 theorem proving, addressing the challenge of context-dependent proofs in real-world projects. It balances exploration and exploitation by generating diverse starting points via dual-model generation and resampling when stagnation occurs, while refining promising states using compiler-grounded pairwise comparison. Experiments on seven Lean 4 projects from miniCTX‑v2 demonstrate that the method improves average pass rates by 12.8 percentage points within a pass@32 budget and reduces LLM calls by 21.9 % compared to pass@k baselines.