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inverse (inverse)

The inverse of a BinaryRelation is a relation in which all the tuples of the original relation are reversed. In other words, one BinaryRelation is the inverse of another if they are equivalent when their arguments are swapped.

Ontology

SUMO / STRUCTURAL-ONTOLOGY

Class(es)

class
is instance of
  inheritable relation  
is instance of
  binary predicate  
is instance of
  inverse  

Coordinate term(s)

arc weight  authors  before or equal  causes  causes subclass  citizen  closed on  connected  contains information  cooccur  copy  date  decreases likelihood  developmental form  disjoint  distributes  documentation  duration  earlier  editor  element  employs  equal  equivalence relation on  exploits  expressed in language  faces  family relation  finishes  frequency  graph part  greater than  greater than or equal to  has purpose  has skill  holds during  holds obligation  holds right  hole  identity element  in list  in scope of interest  increases likelihood  independent probability  inhabits  inhibits  initial list  instance  irreflexive on  larger  less than  less than or equal to  material  measure  meets temporally  modal attribute  overlaps temporally  parent  partial ordering on  partly located  path length  possesses  precondition  prevents  property  publishes  range  range subclass  refers  reflexive on  related internal concept  sibling  smaller  starts  sub attribute  sub collection  sub graph  sub list  sub process  sub proposition  subclass  subrelation  subsumes content class  subsumes content instance  successor attribute  successor attribute closure  temporal part  time  total ordering on  trichotomizing on  uses  valence  version 

Type restrictions

inverse(binary relation, binary relation)

Related WordNet synsets

conversely
with the terms of the relation reversed; "conversely, not all women are mothers"
conversely pertains to noun...  
See more related synsets on a separate page.

Axioms (7)

If rel1 is an inverse of rel2, then for all inst1,inst2 holds: rel1(inst1,inst2) holds if and only if rel2(inst2,inst1) holds. 
(=>
      (inverse ?REL1 ?REL2)
      (forall
            (?INST1 ?INST2)
            (<=>
                  (holds ?REL1 ?INST1 ?INST2)
                  (holds ?REL2 ?INST2 ?INST1))))
greater than is an inverse of less than. 
(inverse greaterThan lessThan)
greater than or equal to is an inverse of less than or equal to. 
(inverse greaterThanOrEqualTo lessThanOrEqualTo)
arc cosine fn is an inverse of cosine fn. 
(inverse ArcCosineFn CosineFn)
arc sine fn is an inverse of sine fn. 
(inverse ArcSineFn SineFn)
arc tangent fn is an inverse of tangent fn. 
(inverse ArcTangentFn TangentFn)
smaller is an inverse of larger. 
(inverse smaller larger)