Explainable AI for Mathematics: Proofs as Code with Knowledge Graph and Domain Ontology Support

Andrey Khalov, Olga Ataeva, Natalia Tuchkova

Abstract:

Neural theorem-proving systems can generate formal proofs, but they of-
ten behave as a ”black box”. It is unclear which pieces of mathematical
knowledge led to success or failure. We present SciLibRU, an infrastructure
that materializes Lean 4’s Mathlib as an ontology-typed knowledge graph
(tens of millions of RDF facts) and links mathematical entities to multi-
modal representations (code, natural-language text, formulae, and related
artifacts) under a shared identifier space. Building on this graph, we en-
able transparent proof support. Using candidate hints that are retrieved via
graph navigation and/or semantic search, and each suggestion is explicitly
traceable to concrete Mathlib dependency edges. That makes the evidence
chain inspectable by humans. Experiments on miniF2F-Test show that
graph-based augmentation substantially improves success on harder prob-
lems while remaining training-free and composable with any base prover.