## Definition Edit

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 $[0,1]$.