用形式化验证技术构建可机器检查的专利分析框架，确保推理过程正确无误。
Formally Verified Patent Analysis via Dependent Type Theory: Machine-Checkable Certificates from a Hybrid AI + Lean 4 Pipeline
- 将专利权利要求编码为图结构，匹配度用已验证的完全格表示
- 通过依赖类型理论证明关键算法正确性，覆盖核心逻辑完全机验
- 适合需要高可靠性专利分析的法律与企业研发团队
我们提出一种结合AI与Lean 4的混合式专利分析形式化验证框架。核心算法1b在固定匹配分后可完全机器验证。自由实施、权利要求解释敏感性、跨权利要求一致性及等同原则分析均在规格层形式化，并生成内核可检的候选证书。现有方法依赖人工专家（慢且不可扩展）或机器学习/NLP（概率性、不透明、非组合）。据我们所知，这是首个基于依赖类型理论的交互式定理证明应用于知识产权分析的框架。权利要求以图结构编码于Lean 4，匹配强度为已验证完全格元素，置信度通过经证明的单调函数沿依赖关系传播。五个知识产权用例（专利-产品映射、自由实施、权利要求解释敏感性、跨权利要求一致性、等同原则）通过六个算法实现。结构引理、覆盖率生成器及闭路身份覆盖 = W_cov 在Lean 4中被机器验证。其余高层定理仅提供非正式证明草图，其证明生成函数采用架构缓解策略（信任度外的生成器，输出经内核检查且无sorry项，轴心公理经审计）。保证条件性：仅保证下游计算的数学正确性，不保证机器学习得分本身的准确性。合成内存模块权利要求案例展示加权覆盖率与构造敏感性分析。与已判决案件的验证为未来工作。
原文摘要 · Abstract (English)
We present a formally verified framework for patent analysis as a hybrid AI + Lean 4 pipeline. The DAG-coverage core (Algorithm 1b) is fully machine-verified once bounded match scores are fixed. Freedom-to-operate, claim-construction sensitivity, cross-claim consistency, and doctrine-of-equivalents analyses are formalized at the specification level with kernel-checked candidate certificates. Existing patent-analysis approaches rely on manual expert analysis (slow, non-scalable) or ML/NLP methods (probabilistic, opaque, non-compositional). To our knowledge, this is the first framework that applies interactive theorem proving based on dependent type theory to intellectual property analysis. Claims are encoded as DAGs in Lean 4, match strengths as elements of a verified complete lattice, and confidence scores propagate through dependencies via proven-correct monotone functions. We formalize five IP use cases (patent-to-product mapping, freedom-to-operate, claim construction sensitivity, cross-claim consistency, doctrine of equivalents) via six algorithms. Structural lemmas, the coverage-core generator, and the closed-path identity coverage = W_cov are machine-verified in Lean 4. Higher-level theorems for the other use cases remain informal proof sketches, and their proof-generation functions are architecturally mitigated (untrusted generators whose outputs are kernel-checked and sorry-free axiom-audited). Guarantees are conditional on the ML layer: they certify mathematical correctness of computations downstream of ML scores, not the accuracy of the scores themselves. A case study on a synthetic memory-module claim demonstrates weighted coverage and construction-sensitivity analysis. Validation against adjudicated cases is future work.
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