Re-using and combining multiple ontologies on the Web is bound to lead to inconsistencies between the combined vocabularies. Even many of the ontologies that are in use today turn out to be inconsistent once some of their implicit knowledge is made explicit. However, robust and efficient methods to deal with inconsistencies are lacking from current Semantic Web reasoning systems, which are typically based on classical logic. In earlier papers, we have proposed the use of syntactic relevance functions as a method for reasoning with inconsistent ontologies. In this paper, we extend that work to the use of semantic distances. We show how Google distances can be used to develop semantic relevance functions to reason with inconsistent ontologies. In essence we are using the implicit knowledge hidden in the Web for explicit reasoning purposes. We have implemented this approach as part of the PION reasoning system. We report on experiments with several realistic ontologies. The test results show that a mixed syntactic/semantic approach can significantly improve reasoning performance over the purely syntactic approach. Furthermore, our methods allow to trade-off computational cost for inferential completeness. Our experiment shows that we only have to give up a little quality to obtain a high performance gain.