Theory-Level Autoformalization Aims for Unified Formal Knowledge Bases

Marcus J. Min, Mike He, Zhaoyu Li, Zixuan Yi, Sharad Malik, Aarti Gupta, Xujie Si, Osbert Bastani· July 16, 2026 View original

Summary

This position paper advocates for "theory-level autoformalization," moving beyond individual statement translation to formalizing complete mathematical theories as structured libraries. It discusses the significance, challenges, and future directions for building unified formal knowledge bases.

Autoformalization, the process of translating natural language into machine-verifiable formal languages, has traditionally focused on individual statements. However, true mathematical formalization involves entire theories, comprising interconnected axioms, definitions, and lemmas, which must be established before theorems can even be stated. This paper argues for a shift towards "theory-level autoformalization." This paradigm shift entails formalizing complete theories as structured libraries, capturing all their inherent inter-dependencies. The authors highlight the profound significance of this approach, contrasting it with alternative views and identifying key open challenges in achieving such comprehensive formalization. They propose three promising avenues for future research and development in this domain, aiming to build unified and machine-verifiable formal knowledge bases that can support advanced AI reasoning and proof verification.

Why it matters

Professionals in AI research, formal verification, and knowledge representation can benefit from a theory-level approach to autoformalization, enabling the creation of more robust, verifiable, and interconnected AI knowledge systems.

How to implement this in your domain

  1. 1Explore existing autoformalization tools and their limitations regarding theory-level representation.
  2. 2Contribute to or adopt research efforts focused on formalizing complete theories rather than isolated statements.
  3. 3Investigate methods for representing and managing inter-dependencies within formal knowledge bases.
  4. 4Develop AI systems capable of reasoning over structured formal libraries for proof verification or knowledge discovery.
  5. 5Collaborate with mathematicians and logicians to define and validate formal theory structures.

Who benefits

AcademiaSoftware DevelopmentAI ResearchLegalTech

Key takeaways

  • Autoformalization should move from isolated statements to complete theories.
  • Theory-level autoformalization creates structured, machine-verifiable knowledge bases.
  • This approach captures inter-dependencies between axioms, definitions, and lemmas.
  • It is crucial for advanced AI reasoning and formal proof verification.

Original post by Marcus J. Min, Mike He, Zhaoyu Li, Zixuan Yi, Sharad Malik, Aarti Gupta, Xujie Si, Osbert Bastani

"arXiv:2607.13292v1 Announce Type: new Abstract: Autoformalization translates informal natural language into formal, machine-verifiable languages. While most work focuses on individual statements, real formalization efforts are inherently theory-level: they require an entire web o…"

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Originally posted by Marcus J. Min, Mike He, Zhaoyu Li, Zixuan Yi, Sharad Malik, Aarti Gupta, Xujie Si, Osbert Bastani on X · view source

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