To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits
Nicolas Lazzari, Valentina Presutti, Antonio Vergari

TL;DR
This paper introduces a method to compile Description Logic ontologies into circuits, enabling scalable reasoning and neuro-symbolic classification that is consistent with domain knowledge, improving over traditional neural network approaches.
Contribution
We develop a novel approach to encode ontologies as circuits, facilitating efficient reasoning and neuro-symbolic predictions aligned with formal domain knowledge.
Findings
Synthetic datasets capture ontology semantics and challenge ML classifiers.
Circuit compilation enables reasoning up to 1000x faster than existing reasoners.
Neuro-symbolic classifiers maintain or improve performance while ensuring knowledge consistency.
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…
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Taxonomy
TopicsAdvanced Graph Neural Networks · Explainable Artificial Intelligence (XAI) · Topic Modeling
