The semantic web aims at enabling the web to understand and answer the requests from people and machines. It relies on several standards for representing and reasoning about web contents. Among them, the Web Ontology Language (OWL) is used to define ontologies, i.e. knowledge bases, and is formalized with description logics. In this paper, we demonstrate how dynamic taxonomies and their benefits can be transposed to browse OWL DL ontologies. We only assume the ontology has an assertional part, i.e. defines objects and not only concepts. The existence of relations between objects in OWL leads us to define new navigation modes for crossing these relations. A prototype, ODALISQUE, has been developed on top of well-known tools for the semantic web.