Class Symmetric-Relation

• Defined in ontology: Frame-ontology
• Source pathname: /tmp_mnt/vol/q/htw/cms/ontolingua/examples/ontolingua/../../all-ontologies/ontolingua/frame-ontology.lisp

Arity: 1

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

Instance-Of: Class, Relation, Set

Subclass-Of: Binary-Relation, Relation, Set

Superclass-Of: Equivalence-Relation

---

Slots:

Arity: 2

Implication Axioms for Symmetric-Relation:

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

Equivalence Axioms for Symmetric-Relation:

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

Implication Axioms mentioning Symmetric-Relation:

(=> (Equivalence-Relation ?R) (Symmetric-Relation ?R))

Equivalence Axioms mentioning Symmetric-Relation:

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