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): $\forall x,y,z \in O, \delta(x,y)+\delta(y,z)\geq \delta(x,z)$