To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits

2026-01-21

AI Summary

This work addresses the challenge that existing neuro-symbolic approaches struggle to natively support description logic ontologies, often yielding classifier outputs inconsistent with domain knowledge. To bridge this gap, the paper presents the first method to uniformly compile description logic ontologies into differentiable probabilistic circuits, enabling tight integration of neural networks with symbolic knowledge. The proposed framework supports semantically consistent synthetic data generation, GPU-accelerated inference, and the construction of consistency-aware neuro-symbolic classifiers. Experimental results demonstrate that the generated data faithfully reflect ontological semantics while posing meaningful challenges; inference achieves up to three orders of magnitude speedup over existing systems; and the resulting classifiers maintain competitive predictive performance while significantly improving semantic consistency.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Background: Neuro-symbolic methods enhance the reliability of neural network classifiers through logical constraints, but they lack native support for ontologies. Objectives: We aim to develop a neuro-symbolic method that reliably outputs predictions consistent with a Description Logic ontology that formalizes domain-specific knowledge. Methods: We encode a Description Logic ontology as a circuit, a feed-forward differentiable computational graph that supports tractable execution of queries and transformations. We show that the circuit can be used to (i) generate synthetic datasets that capture the semantics of the ontology; (ii) efficiently perform deductive reasoning on a GPU; (iii) implement neuro-symbolic models whose predictions are approximately or provably consistent with the knowledge defined in the ontology. Results We show that the synthetic dataset generated using the circuit qualitatively captures the semantics of the ontology while being challenging for Machine Learning classifiers, including neural networks. Moreover, we show that compiling the ontology into a circuit is a promising approach for scalable deductive reasoning, with runtimes up to three orders of magnitude faster than available reasoners. Finally, we show that our neuro-symbolic classifiers reliably produce consistent predictions when compared to neural network baselines, maintaining competitive performances or even outperforming them. Conclusions By compiling Description Logic ontologies into circuits, we obtain a tighter integration between the Deep Learning and Knowledge Representation fields. We show that a single circuit representation can be used to tackle different challenging tasks closely related to real-world applications.

Problem

• Neuro-symbolic classification
• Description Logic
• Ontology consistency
• Knowledge representation
• Neural network reliability

Innovation

• Neuro-symbolic AI
• Description Logic
• Probabilistic Circuits
• Ontology Compilation
• Differentiable Reasoning