Many ontologies, i.e., Description Logic (DL) knowledge bases, have been developed to provide rich knowledge about various domains, and a lot of them are based on ALC, i.e., a prototypical and expressive DL, or its extensions. The main task that explores ALC ontologies is to compute semantic entailment. We developed FALCON, a Fuzzy ALC Ontology Neural reasoner, which uses fuzzy logic operators to generate model structures for arbitrary ALC ontologies, and uses multiple model structures to compute faithful semantic entailments. Theoretical results show that FALCON faithfully approximates semantic entailment over ALC ontologies and therefore endows neural networks with world models and the ability to reason over them. Experimental results show that FALCON enables approximate reasoning, paraconsistent reasoning (reasoning with inconsistencies), and improves machine learning in the biomedical domain by incorporating knowledge expressed in ALC.

翻译：许多本体（即描述逻辑（DL）知识库）已被开发用于提供各领域的丰富知识，其中大量本体基于ALC（一种具有原型性与表达力的描述逻辑）或其扩展。探索ALC本体的核心任务是计算语义蕴含。我们提出了FALCON（一种模糊ALC本体神经推理器），通过模糊逻辑算子为任意ALC本体生成模型结构，并利用多重模型结构计算可信语义蕴含。理论结果表明，FALCON能忠实逼近ALC本体上的语义蕴含，从而赋予神经网络世界模型及其推理能力。实验结果表明，FALCON支持近似推理、超协调推理（处理不一致的推理），并通过整合ALC表达的知识，提升了生物医学领域的机器学习性能。