  Inconsistency handling is an important issue in knowledge management.
Especially in ontology engineering, logical inconsistencies may occur during
ontology construction. A natural way to reason with an inconsistent ontology is
to utilize the maximal consistent subsets of the ontology. However, previous
studies on selecting maximum consistent subsets have rarely considered the
semantics of the axioms, which may result in irrational inference. In this
paper, we propose a novel approach to reasoning with inconsistent ontologies in
description logics based on the embeddings of axioms. We first give a method
for turning axioms into distributed semantic vectors to compute the semantic
connections between the axioms. We then define an embedding-based method for
selecting the maximum consistent subsets and use it to define an
inconsistency-tolerant inference relation. We show the rationality of our
inference relation by considering some logical properties. Finally, we conduct
experiments on several ontologies to evaluate the reasoning power of our
inference relation. The experimental results show that our embedding-based
method can outperform existing inconsistency-tolerant reasoning methods based
on maximal consistent subsets.
