Class SYMMETRIC-RELATION

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

Slots on this class:

Documentation:

Relation R is symmetric if R(x,y) implies R(y,x).

Instance-Of: Class

Subclass-Of: Binary-relation

Superclass-Of: Equivalence-relation

Implication Axioms:

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

Equivalence Axioms:

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

Axioms:

(Binary-Relation ?R)

Other Related Axioms:

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

(<=> (Equivalence-Relation ?R)
     (And (Reflexive-Relation ?R)
          (Symmetric-Relation ?R)
          (Transitive-Relation ?R)))