Non-strict partial order

Set

context $X$
definiendum $ \le\ \in\ \mathrm{it} $

The relation $\le$ is an order relation if it's in the intersection of all reflexive, all anti-symmetric and all transitive relation. Hence

context $ \le\ \in\ \mathrm{Rel}(X) $
$ x,y,z \in X $
postulate $ x \le x $
postulate $ x\le y\ \land\ y\le x \implies (x=y) $
postulate $ x \le y\ \land\ y \le z \Leftrightarrow x\le z $

Here we use infix notation: $x\le y\ \equiv\ \le(x,y)$.

Discussion

Reference

Wikipedia: Order theory, Poset

Parents

Subset of

Reflexive relation, Anti-symmetric relation, Transitive relation

Equivalent to

Poset