Alex Shkotin STATEMENT:

ONTOLOGY=FORMAL_THEORY+FINITE_MODEL

Maxima: "Ontology" is a mirage made by great DL logics in the minds of experts of Expert Systems and WWW.

But ontology, unlike Expert System knowledge, must be presented to public/customer as a text for a universal processor like Protege+Hermit or Jena if you prefer batch mode

{:-)

Till now the main idea is that

Ontology is a formal text keeping together elements of Formal Theory and Finite Model in a form suitable for Reasoner - usually DL one. A Reasoner can check automatically consistency, perform classification and do other great reasoning services.

To clarify term "engineer's models (aka axiom sets)" let's look at a situation like this: we have

a) a formal theory (some axioms and definitions) for particular application area like "air vehicle model-based design" mentioned by Henson Graves, see [1].

b) a finite model of theory (a) keeping a particular engineer's model in a DB.

If we need to reason about this (b) model under (a) axioms we convert axioms of formal theory to axioms of OWL-DL and we convert model itself to OWL-DL axioms and this latter set is known as "engineer's models (aka axiom sets)".

The point is that when we work with the finite model itself we need another kind of language (not OWL) to perform "engineering" task: for ex. how many wings do this aircraft have?

And we need a language to handle these models.

These models are finite as they have a finite number of elements. They use numbers but a finite number of them each.

The famous example of a finite model is a graph as still a math object but very useful for modeling. DB is not a math object, unfortunately. If we add a label possibility to graph we should describe it rigorously, and then we may get RDF.

One of the first examples of using the graph as a model is Seven Bridges of Königsberg[2].

[1] Air Vehicle Model-Based Design and Simulation Pilot, by Henson Graves, Stephen Guest, Jeff Vermette, Yvonne Bijan, Harold Banks, Greg Whitehead, Bill Ison. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.638.8184

[2] Seven Bridges of Königsberg. https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg