Relation R is an antisymmetric-relation if for distinct x and y, R(x,y) implies not R(y,x). In other words, for all x,y, R(x,y) and R(y,x) => x=y. R(x,x) is still possible.Notes:
- See-Also: asymmetric-relation
(=> (Antisymmetric-Relation ?R) (=> (And (Holds ?R ?X ?Y) (Holds ?R ?Y ?X)) (= ?X ?Y)))
(<=> (Antisymmetric-Relation ?R) (And (Binary-Relation ?R) (=> (And (Holds ?R ?X ?Y) (Holds ?R ?Y ?X)) (= ?X ?Y))))
(=> (Asymmetric-Relation ?R) (Antisymmetric-Relation ?R)) (=> (Partial-Order-Relation ?R) (Antisymmetric-Relation ?R))
(<=> (Asymmetric-Relation ?R) (And (Antisymmetric-Relation ?R) (Irreflexive-Relation ?R))) (<=> (Partial-Order-Relation ?R) (And (Reflexive-Relation ?R) (Antisymmetric-Relation ?R) (Transitive-Relation ?R)))