Similarity function

Definition
Given a set of ontological entities $$O$$, a similarity function is a function $$\sigma:O\times O \longrightarrow \mathbb{R}^+$$ that associates to every pair of entities of $$O$$, a real number that express the resemblance between the entities, and such that holds the following properties:
 * Non-negativity: $$\forall x,y \in O, \sigma(x,y)\geq 0$$
 * Maximality: $$\forall x,y \in O, \sigma(x,x)\geq \sigma(x,y)$$

Some authors add to this list this other property:
 * Simmetry: $$\forall x,y\in O, \sigma(x,y) = \sigma(y,x)$$

In the same way, it is possible to define the dual concept of dissimiarity function as a function $$\delta:O\times O \longrightarrow \mathbb{R}^+$$, that express the difference between two entities, with the following properties:
 * Non-negativity $$\forall x,y \in O, \sigma(x,y)\geq 0 $$
 * Minimality: $$\forall x\in O, \delta(x,x)= 0$$

A (dis)similarity function is normalized if their range is the real interval $$[0,1]$$.