Mapping between ontologies and relational databases is a necessity in realising the Semantic-Web vision. Most of the work concerning this topic has either (1) extracted OWL schemas using a limited range of OWL modelling constructs from relational schemas, or (2) extracted relational schemas from OWL schemas, that represent the OWL schemas as much as possible. By contrast, we propose a general framework that maps between relational databases and schemas expressed in OWL 2. In particular, we regard the transformation from databases to ontologies as being a two-phase process. Firstly, to convert the relational schemas into OWL schemas, and then to enrich the OWL schemas with highly expressive axioms, based on analysing the schemas and the data in the databases. Testing our data analysis heuristics on a number of databases, show that they produce OWL schemas, that include more semantic information than found in their respective relational schemas.