Ontology-Guided Neuro-Symbolic Inference: Grounding Language Models with Mathematical Domain Knowledge

Language models exhibit fundamental limitations---hallucination, brittleness, and lack of formal grounding---that are particularly problematic in high-stakes specialist fields requiring verifiable reasoning. I investigate whether formal domain ontologies can enhance language model reliability through retrieval-augmented generation. Using mathematics as proof of concept, I implement a neuro-symbolic pipeline leveraging the OpenMath ontology with hybrid retrieval and cross-encoder reranking to inject relevant definitions into model prompts. Evaluation on the MATH benchmark with three open-source models reveals that ontology-guided context improves performance when retrieval quality is high, but irrelevant context actively degrades it---highlighting both the promise and challenges of neuro-symbolic approaches.