Article
#1020
Issue
MathAI 2026 Selected Papers
Special Issue
Received
30 Apr 2026
Accepted
15 May 2026
Published
22 May 2026
Explainable AI for Mathematics: Proofs as Code with Knowledge Graph and Domain Ontology Support
MathAI 2026 Selected Papers
Special Issue
Mathematics & AI
2026, 1(2), 17
CC BY 4.0
Open access. This article is licensed under a
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knowledge graph
explainable AI
neural theorem proving
domain ontology
mathlib dependency graph
Lean 4
graph RAG
Abstract
We investigate whether structured knowledge retrieval from a mathematical library's dependency graph can improve neural theorem proving at inference time while maintaining explainability of the retrieved context. Through a controlled ablation study on the miniF2F-Test benchmark (197~tasks, 8~non-chain-of-thought modes, $K{=}8$ attempts per mode), we find that graph-based retrieval augmentation significantly improves proof generation on hard problems -- those where the base model's parametric knowledge is insufficient -- while having no measurable effect on problems the model already solves reliably. On 109~hard tasks, the best graph-augmented mode nearly triples the baseline success rate (pass@1: $3.56\% \to 10.42\%$, $+6.8$~percentage points, $p{=}0.001$, Wilcoxon signed-rank test). Deterministic pattern-based graph entry points outperform LLM-generated ones ($11\times$ faster, higher accuracy). The retrieved graph context is fully traceable: each hint maps to a specific edge in the Mathlib dependency graph, enabling the user to verify \emph{why} particular lemmas were suggested. The approach is training-free, composable with any base prover, and adds negligible computational overhead.
Cite this article
Khalov A.; Ataeva, O.; Tuchkova, N. Explainable AI for Mathematics: Proofs as Code with Knowledge Graph and Domain Ontology Support. Mathematics & AI 2026, 1(2), 17. https://doi.org/10.66693/mathai.1020
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