Ontology

If you have done this before, an example would help.

Here is an article that explains about ontology databases:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3230227/

I don't think QuickBase has any substantial features to accommodate "ontology modeling". In fact, the general idea of "the semantic web" is considered a failure:

Three reasons why the Semantic Web has failed
https://gigaom.com/2013/11/03/three-reasons-why-the-semantic-web-has-failed/

Moreover, if you could be more specific about what you want to accomplish I am pretty confident we could find a solution within the native capabilities of QuickBase or using script.

A colleague of mine explained to me the use of a database that utilized ontology modelling to make query and post more flexible and information was more readily intuited from the data. The data structure was not readily available and is most likely considered proprietary to the service provider and so I was seeking an understanding of how ontology modelling could achieve these outcomes.

This is one of those situations where the intention was to learn more by viewing and interpreting any existing examples (preferably in Quick Base).

And here is an example of a post on the web negating a post on the web negating a post on the web...
http://fogbeam.com/blog/fogbeam/entry/dominiek-ter-heide-is-dead?blogger=http://fogbeam.blogspot.com/2013/11/dominiek-ter-heide-is-dead-wrong.html