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partial ordering on (partialOrderingOn)

A BinaryRelation is a partial ordering on a SetOrClass only if the relation is reflexiveOn the SetOrClass, and it is both an AntisymmetricRelation, and a TransitiveRelation.

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

class
is instance of
  inheritable relation  
is instance of
  binary predicate  
is instance of
asymmetric relation
is instance of
is instance of
  partial ordering on  

Coordinate term(s)

back fn  cardinality fn  front fn  principal host fn  probability fn  skin fn  arc weight  attribute  authors  before or equal  causes  causes subclass  citizen  closed on  completely fills  connected  contains information  cooccur  copy  crosses  date  decreases likelihood  developmental form  disjoint  distributes  documentation  duration  earlier  editor  element  employs  equal  equivalence relation on  exploits  expressed in language  faces  family relation  fills  finishes  frequency  graph part  greater than  greater than or equal to  has purpose  has skill  holds during  holds obligation  holds right  hole  identity element  immediate instance  immediate subclass  in list  in scope of interest  increases likelihood  independent probability  inhabits  inhibits  initial list  instance  inverse  irreflexive on  larger  less than  less than or equal to  manner  material  measure  meets temporally  member  modal attribute  overlaps temporally  parent  partially fills  partly located  path length  penetrates  possesses  precondition  prevents  proper part  properly fills  property  publishes  range  range subclass  realization  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  surface  temporal part  time  total ordering on  trichotomizing on  uses  valence  version 

Type restrictions

partialOrderingOn(binary relation, set or class)

Axioms (2)

If relation is partial ordering on class, then relation is reflexive on class and relation is an instance of transitive relation and relation is an instance of antisymmetric relation. 
(=>
      (partialOrderingOn ?RELATION ?CLASS)
      (and
            (reflexiveOn ?RELATION ?CLASS)
            (instance ?RELATION TransitiveRelation)
            (instance ?RELATION AntisymmetricRelation)))
relation is total ordering on class if and only if relation is partial ordering on class and relation is trichotomizing on class. 
(<=>
      (totalOrderingOn ?RELATION ?CLASS)
      (and
            (partialOrderingOn ?RELATION ?CLASS)
            (trichotomizingOn ?RELATION ?CLASS)))