Textbox 1 The ontology expression.

An ontology can be defined as a tuple Ω = {X, R}, where X is the set of concepts or classes, and R is a set of relations.

L = Levels (О_h) = Total number of levels in the ontology hierarchy, 0 ≤ n ≤ L, where n⋲ Z⁺ and n = 0 represents the root node.

X_{n, j} = a model classifying О at a level n; where, j ⋲ {0, 1, …., |X_n|}

|X| = Number of instances classified as class X

E = Edge (X_{n, j}, X_{n−1, k}) = edge between node X_{n, j} and its parent node X_{n−1, k}

We have used the concept and represented our ontology with four tuples:

O = {X_a, R, I, A}

X_a: {X_a1, X_a2, …., X_an} represents “n” concepts or classes and each X_a.i. has a set of “j” attributes or properties A_i = {a₁, a₂,……., a_j} provided n, i, j ⋲ Z⁺.

R: A set of binary relations between the elements of X_a. It holds two subsets –

a. H: Inheritance relationship among concepts

b. S: Semantic relationship between concepts with a domain and range

I: Represents a knowledge base with set of object instances.

A: Represents a set of axioms to model O. A includes domain specific constraints to model an Ontology with X_a, R, and I.