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symmetric relation (SymmetricRelation)

A BinaryRelation rel is symmetric just in case (rel inst1 inst2) imples (rel inst2 inst1), for all inst1 and inst2.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

[tree]
entity
is subclass of
  abstract  
is subclass of
  relation  
is subclass of
  binary relation  
is subclass of
  symmetric relation  

Instance(s)

disjoint  independent probability  overlaps temporally  connected  meets spatially  overlaps spatially  overlaps partially  sibling  connected engineering components 

Subclass(es)

equivalence relation 

Coordinate term(s)

antisymmetric relation  binary predicate  intransitive relation  irreflexive relation  reflexive relation  transitive relation  trichotomizing relation  unary function 

Related WordNet synsets

See more related synsets on a separate page.

Axioms (2)

(=>
      (instance ?REL SymmetricRelation)
      (forall
            (?INST1 ?INST2)
            (=>
                  (holds ?REL ?INST1 ?INST2)
                  (holds ?REL ?INST2 ?INST1))))
If relation is equivalence relation on class, then relation is an instance of transitive relation and relation is an instance of symmetric relation and relation is reflexive on class. 
(=>
      (equivalenceRelationOn ?RELATION ?CLASS)
      (and
            (instance ?RELATION TransitiveRelation)
            (instance ?RELATION SymmetricRelation)
            (reflexiveOn ?RELATION ?CLASS)))