Alex Shkotin STATEMENT:
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 .
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.
 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
 Seven Bridges of Königsberg. https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg
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1. Correct Use of Axiom sets in engineering modeling. The semantics of a descriptive model (axiom set) is defined by its interpretative semantics. The use of inference to reason about the things described by the model has to correlate to the inference semantics for inference to be valid. While the descriptive model axiom sets are finitely presented, engineering is interested in physical interpretations not just data base interpretations. When a customer takes delivery of an aircraft an initial step is to verify that all of the equipment specified for the aircraft is actually delivered. For used aircraft counterfeit parts are a significant recognized problem. The corresponding engineering model of a physical aircraft is an interpretation of the model in the modeling formalism. The use of interpretations to define the semantics of a model is a form of conditional realism in the sense that reality is defined by the interpretations. For a model there is no presupposition that there exists an interpretation or that there in only one unique interpretation of a model. Often models are contradictory and have no interpretations. Engineering models generally have multiple interpretations. When we build a model for a type of aircraft there is no guarantee that all interpretations of the model have the same number of wings. Generally a lot of work is needed to produce a model whose interpretations are constrained to be what the model developer intended.
2. Description Logic is insufficient for the engineering object language. An object language of a formalism suitable for engineering cannot be represented in Description Logic (DL) as DL does not have function symbols (papers of Motik and Horrocks establish this). Function symbols are needed to represent axiom sets common in engineering.
3. Meta Logic. The meta logic is the language in which models and interpretations are defined. The meta logic has meta categories types. To represent engineering models and their interpretations the meta logic need meta-categories for types and sets (see General Formal Ontology) that are sufficiently defined so that the properties of interpretations needed can be defined and used formally.
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