A partially ordered set (poset) is a
relational structure<P, ≤> where
≤ is a binary relation that is reflexive, antisymmetric and transitive, i.e. satisfies
x≤x,
x≤y and y≤x⇒x=y, and
x≤y and y≤z⇒x≤z.
A strict partially ordered set (strict poset) is a
relational structure<P, < > where
< is a binary relation that is irreflexive, and transitive, i.e. satisfies
¬x < x and
x < y and y < z⇒x < z.