arXiv:2606.25363cs.IRcs.AI2026-06被引 2

构建跨正式与非正式数学的定理依赖图谱,实现知识无缝连接。

TheoremGraph: Bridging Formal and Informal Mathematics

论文配图:TheoremGraph: Bridging Formal and Informal Mathematics
图 1 · 摘自论文原文
  • 融合arXiv论文与Lean形式化库,构建统一定理依赖图谱。
  • 从1170万定理环境提取1.83亿条依赖关系,匹配准确率达87%。
  • 适合数学搜索、溯源与推理增强,支持开放接口使用。

数学知识围绕命题及其依赖关系组织,但呈现不均衡:非正式论文仅在文档层面引用,而形式化库记录细粒度依赖,覆盖范围小。我们提出TheoremGraph,一个统一的命题级依赖图谱,涵盖非正式与形式化数学。在非正式侧,解析1170万条定理类环境,恢复1.83亿条候选有向依赖,每条标注来源以便用户权衡覆盖与精度。在形式化侧,发布LeanGraph,基于Lean 4的提取器生成38.8105万个声明节点和1130万条带类型边,覆盖25个Lean项目。通过嵌入生成的自然语言口号至共享语义空间,将跨论文及跨正式/非正式命题关联起来;LLM判别器确认47,952个匹配项,余弦相似度≥0.8时接受率从48%升至87%(≥0.9时)。在形式概念检索中,我们的命名+签名表示结合图扩展,召回率@10达0.775,接近LeanSearch v2的0.780,且无需语言模型重排。数据集、提取器、HTTP API与MCP接口已开放,支持数学搜索、溯源与检索增强推理,详见theoremsearch.com与huggingface.co/datasets/uw-math-ai/theorem-matching。

原文摘要 · Abstract (English)

Mathematical knowledge is organized around statements and their dependencies, but this structure is exposed unevenly: informal papers cite mostly at the document level, while formal libraries record fine-grained dependencies over a much smaller body of mathematics. We introduce TheoremGraph, a unified statement-level dependency graph spanning both informal and formal mathematics. On the informal side, we parse 11.7M theorem-like environments from mathematics arXiv and recover 18.3M candidate directed dependencies, each labeled by the extractor that proposed it so downstream users can trade coverage for precision. On the formal side, we release LeanGraph, a Lean 4 elaborator-level extractor producing 388,105 declaration nodes and 11.3M typed edges across 25 Lean projects. We bridge the two graphs by embedding generated natural-language slogans into a shared semantic space, linking related statements across papers and across the informal/formal divide; an LLM judge affirms 47,952 such matches above a 0.8 cosine floor, with the judge-acceptance rate rising from 48% across the floor to 87% in the >=0.9 tier. On formal concept retrieval, our name-and-signature representation with graph expansion comes within 0.5pp of LeanSearch v2's reranked Recall@10 (0.775 vs. 0.780) without an LM reranker. We release the dataset, extractors, HTTP API, and MCP interface as infrastructure for mathematical search, attribution, and retrieval-augmented reasoning, available at theoremsearch.com and huggingface.co/datasets/uw-math-ai/theorem-matching.

数学知识图谱形式化证明定理检索语义链接

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。