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intransitive relation (IntransitiveRelation)

A BinaryRelation rel is intransitive only if (rel inst1 inst2) and (rel inst2 inst3) imply not (rel inst1 inst3), for all inst1, inst2, and inst3.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

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

Instance(s)

immediate instance  immediate subclass  member  penetrates  element  meets temporally  parent 

Coordinate term(s)

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

Axioms (1)

(=>
      (instance ?REL IntransitiveRelation)
      (forall
            (?INST1 ?INST2 ?INST3)
            (=>
                  (and
                        (holds ?REL ?INST1 ?INST2)
                        (holds ?REL ?INST2 ?INST3))
                  (not
                        (holds ?REL ?INST1 ?INST3)))))