FALCON: Sound and Complete Neural Semantic Entailment over ALC Ontologies

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. Symbolic approaches can guarantee sound and complete semantic entailment but are sensitive to inconsistency and missing information. To this end, we propose FALCON, a Fuzzy ALC Ontology Neural reasoner. FALCON uses fuzzy logic operators to generate single model structures for arbitrary ALC ontologies, and uses multiple model structures to compute semantic entailments. Theoretical results demonstrate that FALCON is guaranteed to be a sound and complete algorithm for computing semantic entailments over ALC ontologies. Experimental results show that FALCON enables not only approximate reasoning (reasoning over incomplete ontologies) and paraconsistent reasoning (reasoning over inconsistent ontologies), but also improves machine learning in the biomedical domain by incorporating background knowledge from ALC ontologies.