Class Irreflexive-Relation

Arity: 1
Documentation:
Relation R is irreflexive if if R(a,a) never holds.

Notes:

  • This is a change in definition. Used to mean (not reflexive).
  • Formerly: antireflexive-relation
Instance-Of: Class, Relation, Set
Subclass-Of: Binary-Relation, Relation, Set
Superclass-Of: Asymmetric-Relation


Slots:

Arity: 2

Implication Axioms for Irreflexive-Relation:

(=> (Irreflexive-Relation ?R) (Forall (?X) (Not (Holds ?R ?X ?X))))


Equivalence Axioms for Irreflexive-Relation:

(<=> (Irreflexive-Relation ?R)
     (And (Binary-Relation ?R) (Forall (?X) (Not (Holds ?R ?X ?X)))))


Implication Axioms mentioning Irreflexive-Relation:

(=> (Asymmetric-Relation ?R) (Irreflexive-Relation ?R))


Equivalence Axioms mentioning Irreflexive-Relation:

(<=> (Asymmetric-Relation ?R)
     (And (Antisymmetric-Relation ?R) (Irreflexive-Relation ?R)))