I worked with toools such as KARMA, D2RQ, Virtuoso.. It seems that all of them give new ontologies from a database, but not mapping the instances in ontology to a database so its values can get updated.
The only way that I could follow to map a RDB to let's say a customized ontology is using Jena framework. I could simply read the data from RDB using JAVA and import my ontology afterwards. In the next step, I could create the OWL instances and the final RDF dump by making use of Jena library. This may help --> (http://jena.apache.org/documentation/ontology/)
ontology structures is normally not supported in relational database system schema, because it consists of related tables of data , i would rather think of another database schema to represent ontologies , so instead using relational database think about using network database schema or hierarchal database schema
1) To convert an ontology into a relational database (probably with some information loss) you must perform the mapping I described before.
2) However, an OWL ontology can be stored directly in a database with Jena libraries: SDB (any relational database with JDBC) or TDB (own NOSQL format).
https://jena.apache.org/documentation/sdb/
http://jena.apache.org/documentation/tdb/
Both libraries work. An ontology is stored as RDF triples. The performance of SDB is rather poor. To access information on a class with several relations/attributes , the library makes a bunch of small queries for triples. They consume much time.
TDB performs much better, probably it is memory mapped.
Maybe you can be interested in Ontology-based Data Management (OBDM) and specifically in Ontology-based Data Access (OBDA). OBDA is a new paradigm in which an ontology is used to provide a formal representation of the domain of interest and is used for accessing the data. Topically in OBDA we have a three-level architecture in which we find the ontology, the data sources, and the mapping between the two. Users access external data by querying the ontology, without possessing knowledge on how the data is organized and where it is stored.
Here you can find more information about this approach: