Class ANTISYMMETRIC-RELATION

• Defined in theory: Frame-ontology
• Source code: frame-ontology.lisp

Slots on this class:

Documentation:

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.

Instance-Of: Class

Subclass-Of: Binary-relation

Superclass-Of: Asymmetric-relation

Implication Axioms:

(=> (And (Holds ?R ?X ?Y) (Holds ?R ?Y ?X)) (= ?X ?Y))

Equivalence Axioms:

(<=> (Antisymmetric-Relation ?R)
     (And (Binary-Relation ?R)
          (=> (And (Holds ?R ?X ?Y) (Holds ?R ?Y ?X)) (= ?X ?Y))))

Axioms:

(Binary-Relation ?R)

Other Related Axioms:

(<=> (Antisymmetric-Relation ?R)
     (And (Binary-Relation ?R)
          (=> (And (Holds ?R ?X ?Y) (Holds ?R ?Y ?X)) (= ?X ?Y))))

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

Notes:

• See-Also: asymmetric-relation