Theorem-Grounded Execution Ontologies for Interpretable Machine Reasoning

Theorem-Grounded Execution Ontologies (TGEO) is a new framework introduced for modeling reasoning in large language models as an executable state-transition process. TGEO features five key components: theorem-grounded reasoning priors, executable ontologies, operator-mediated state transitions, predicate and contract-based validation, and architectural auditing. Its evaluation on theorem-intensive tasks shows that TGEO enhances interpretability, verifiability, and reproducibility in AI reasoning systems, addressing the challenges of latent reasoning processes in existing models.