I haven't read the article, but logical truth is always "just" axiomatic. You can relate it to empirical reality using e.g. correspondence theory, induction, authoritative texts and other relating methods (ontologies).

An ontology, on the other hand, is the study of what is or in sum what reality is, when understood from the viewpoint of the author. That's its raison d'être.

Perhaps this is relevant? I stopped reading these articles because I'm too rusty.