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)

entity

abstract

relation

binary relation

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)

if rel is an instance of intransitive relation,
then for all inst1,inst2,inst3 holds: if rel(inst1,inst2) holds and rel(inst2,inst3) holds, then rel(inst1,inst3) doesn't hold

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