
## 5.2 Concepts Of Another Ontologies

 Some Virtual Modeling of Complex Systems concepts:
Virtual; Virtual Model, digital description of the object, the classical example of virtual model; Virtual function, virtual class. Modeling; System; Complexity.

 The model and design of a virtual school are given by (Glazunov and Borovik, 2009).

 Some ontologies of the course Introduction to String Theory have presented in
(Glazunov, 2008a, 2008b)
 **6 FORMALIZATION OF ONTOLOGY**
The formalization of steps (i) - (iv) from (a) carry out our considerations to 
(v) Axioms, Postulates;
(vi) Rules of Inference;
(vii) Confirmation (Verification); 
(viii) Induction (Uncertainty, Statistics, Probabilistic Rules). 

 Gruber and Olsen (Gruber, 1993) gave the ontology for physical quantities, units of measure and algebra for engineering models. We will use it for presentation of elements of ontology of charges and fields from the problem domain Electromagnetism. The SI unit of quantity of electric charge is the coulomb. The charge of an electron is approximately 1.602 x 10 19 COULOMB. 

(defobject COULOMB (basic-unit COULOMB))
(defobject NEWTON (basic-unit NEWTON))
 The electric field is a vector field with SI units of newtons per coulomb (NEWTON
COULOMB 1
). 

(defobject NEWTON / COULOMB
 (= NEWTON / COULOMB
 (unit* newton (unit^ coulomb -1))))
 Next step of the formalization is given by the following postulate: Ontology as well as investigative method (that also may be treated as an ontology) may be represented as graphs (simple graphs, multigraphs, pseudographs). We will call the graph the ontology graph. 

## 7 Ontologies And Category Theory 7.1 Graphs And Categories

Recall definitions and basic facts about graphs and categories. Let Ens be the category of sets, V, E its objects. A graph G = (V, E, s, t) consists of sets V, E and pair of functions s, t:
E V. The functions s and t are called source and target and elements of *V and E* are called vertices and arrows. A morphism 