efined model theory suitable for logical inference.

Conceptually, at least, an ontology is closed under logical inference.
For me, this is an ideal, and I have the idea of a family of ontologies
that are the result of n-applications of inferencing rules.
I expect this is a rather well understood idea, but in case it is original,
I mean that if a proposition is true and there is an inference rule
that states the truth of some other proposition is implied by the truth
of the first proposition, that the 1-app