Distance function

Definition
Given a set of ontological entities $$O$$, a distance function is a dissimilarity function $$\delta:O\times O \longrightarrow \mathbb{R}^+$$ that holds the following properties:
 * Identity of indiscernibles $$\forall x,y \in O, \delta(x,y)= 0$$ if and only if $$x=y$$
 * Simmetry: $$\forall x,y \in O, \delta(x,y) = \delta(y,x)$$
 * Subadditivity (triangle inequality): $$\forall x,y,z \in O, \delta(x,y)+\delta(y,z)\geq \delta(x,z)$$