Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuits

Details

Neuro-symbolic learning over formal ontologies has faced a hard constraint: either embed the ontology in a continuous space (losing classical entailment), or restrict to the Horn fragment EL++, which has a single canonical model. Baobab removes this restriction by compiling full OWL 2 DL (SROIQ) ontologies into Sentential Decision Diagrams (SDDs). The compilation saturates a propositional core under a consequence-based calculus, then handles remaining SROIQ features — nominals, number restrictions, role axioms — over the active domain. The SDD's weighted model count trains a perception network under partial supervision. On an MNIST-coupled task exercising every SROIQ feature, a CNN learns to read digits connected by a successor relation and recovers latent ontological concepts. Critically, the paper identifies and mitigates reasoning shortcuts — when multiple ontology-consistent solutions exist, standard approaches collapse onto one and become overconfident. Baobab's Bayes-optimal posterior calculation using the circuit's enumerated completions outperforms alternatives. Soundness is machine-checked in Lean 4. Code is publicly available. Relevant for teams building learning systems under complex biomedical or Semantic Web ontological constraints — this approach enables learning without relaxing the formal logic.