Definition Grounding in Theory-Level Auto-formalization

arXiv cs.AIOctober 15, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2610.19223v1 Announce Type: new Abstract: LLM-based auto-formalization systems can now generate formally verified Lean code at unprecedented rates. However, a formalization advances mathematical research only when further mathematical results can be built on it, especially when its definitions and helper lemmas are general enough to be imported and used idiomatically. We propose definition grounding, where definition formalizations are continuously judged and revised, as a method to ensure formalization quality. We find that agents formalizing definitions from textbook text often produce definitions that later statements cannot use, and only 25%-50% of their definition sets are compati

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