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.
Abstract (translated)
背景：神经符号方法通过逻辑约束增强神经网络分类器的可靠性，但它们缺乏对本体论的原生支持。 目标：我们的目标是开发一种神经符号方法，能够可靠地输出与形式化了特定领域知识的描述逻辑本体相一致的预测结果。 方法：我们将一个描述逻辑本体编码为电路——这是一种前馈可微计算图，支持查询和转换的可执行操作。我们证明该电路可用于（i）生成捕获本体语义的合成数据集；（ii）在GPU上高效地进行演绎推理；（iii）实现神经符号模型，其预测结果与本体中定义的知识大致一致或可以证明的一致。 结果：使用电路生成的合成数据集在定性上准确地捕捉到本体的语义，并且对机器学习分类器（包括神经网络）构成了挑战。此外，我们还展示了将本体编译为电路是进行可扩展演绎推理的一种有前景的方法，在运行时间方面比现有的推理器快了三个数量级。最后，我们将我们的神经符号分类器与神经网络基准进行了比较，证明它们可以可靠地生成一致的预测结果，并保持了竞争性甚至优于基准的表现。 结论：通过将描述逻辑本体编译为电路，我们实现了深度学习和知识表示领域之间的更紧密集成。我们展示了单一电路表示可用于解决多种与实际应用密切相关且具有挑战性的任务。
URL
https://arxiv.org/abs/2601.14894
