OBO is an ontology language that has often been used for modeling ontologies in the life sciences. Its definition is relatively informal, so, in this paper, we provide a clear specification for OBO syntax and semantics via a mapping to OWL. This mapping also allows us to apply existing Semantic Web tools and techniques to OBO. We show that Semantic Web reasoners can be used to efficiently reason with OBO ontologies. Furthermore, we show that grounding the OBO language in formal semantics is useful for the ontology development process: using an OWL reasoner, we detected a likely modeling error in one OBO ontology.