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

arXiv: https://arxiv.org/abs/2608.17741 · HTML: https://mlsanity.com/paper/2608.17741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 44 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 23 of 23)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [OWL2Vec*: Embedding of OWL Ontologies](https://mlsanity.com/paper/2009.14654/) (2020)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [On the Independence Assumption in Neurosymbolic Learning](https://mlsanity.com/paper/2404.08458/) (2024)
- [Neurosymbolic Diffusion Models](https://mlsanity.com/paper/2505.13138/) (2025)
- [Extending Consequence-Based Reasoning to SRIQ](https://mlsanity.com/paper/1602.04498/) (2016)
- [To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits](https://mlsanity.com/paper/2601.14894/) (2026)
- [Consequence-based Reasoning for Description Logics with Disjunction, Inverse Roles, Number Restrictions, and Nominals](https://mlsanity.com/paper/1805.01396/) (2018)
- [Neurosymbolic Reasoning Shortcuts under the Independence Assumption](https://mlsanity.com/paper/2507.11357/) (2025)

## Abstract (arXiv)

OWL 2 DL ontologies, grounded in the description logic SROIQ, express large knowledge bases in biomedicine and the Semantic Web. Neuro-symbolic (NeSy) learners over description logics either embed the ontology in a continuous space, abandoning classical entailment, or restrict to the Horn fragment EL++, which has a single canonical model. We present Baobab, which compiles a SROIQ ontology with a finite ABox into a Sentential Decision Diagram (SDD): it saturates a propositional core under a consequence-based calculus and instantiates the remaining SROIQ features (nominals, number restrictions, and the role axioms) over the active domain. The SDD's evidence-conditioned weighted model count then trains a perception network to recognize real images under partial ABox supervision: on an ontology that exercises every distinctive SROIQ feature, a CNN learns to read MNIST digits coupled by a successor relation and recovers latent ontology concepts that an independent perception leaves at chance. When the supervision admits several ontology-consistent completions, an independent perception collapses onto one, a reasoning shortcut: we show that a mixture indexed by the query's justifications can represent the calibrated posterior no independent perception can, and that seeding it from the circuit's enumerated completions attains the Bayes-optimal posterior on a real-image MNIST task where single-WMC and learned mixtures (the BEARS-ensemble hypothesis class) do not: to our knowledge the first to characterize and mitigate reasoning shortcuts in a non-Horn description logic. Soundness of the compiler and the representation result are machine-checked in Lean 4. Code is available at https://github.com/bio-ontology-research-group/baobab.