A relation R on a set S is reflexive if every element is related to itself: for all a ∈ S, aRa holds.
Reflexivity is one of the three defining properties of a partial order (along with transitivity and antisymmetry) and one of the two defining properties of a preorder (along with transitivity).
Reflexivity says: every element is at least as good as itself, every point is accessible from itself, every object has an identity morphism. In a poset viewed as a category, reflexivity corresponds to the existence of identity morphisms: the morphism a → a witnesses that a ≤ a.
In modal logic, reflexivity of the accessibility relation validates the T axiom: □φ → φ. If every world accesses itself, then what is necessary is true — if φ holds at all accessible worlds and the current world is accessible from itself, then φ holds at the current world. The modality j in the semiotic universe is extensive (a ≤ j(a)), which is the order-theoretic expression of reflexivity for the corresponding accessibility structure.