Select language: english | cesky | deutsch | italiano | simplified chinese | traditional chinese | hindi
Concept:
English word:
Home

trichotomizing relation (TrichotomizingRelation)

A BinaryRelation rel is a TrichotomizingRelation just in case all ordered pairs consisting of distinct individuals are elements of rel.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

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

Subclass(es)

total ordering relation 

Coordinate term(s)

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

Axioms (1)

If rel is an instance of trichotomizing relation, then for all inst1,inst2 holds: rel(inst1,inst2) holds or inst1 is equal to inst2 or rel(inst2,inst1) holds. 
(=>
      (instance ?REL TrichotomizingRelation)
      (forall
            (?INST1 ?INST2)
            (or
                  (holds ?REL ?INST1 ?INST2)
                  (equal ?INST1 ?INST2)
                  (holds ?REL ?INST2 ?INST1))))