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Totalordnungsrelation (TotalOrderingRelation)

A BinaryRelation is a TotalOrderingRelation if it is a PartialOrderingRelation and a TrichotomizingRelation.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

[tree]

is subclass of

abstrakter Gegenstand

is subclass of

Relation

is subclass of

zweiwertige Relation

is subclass of

transitive Relation
is subclass of

is subclass of

[tree]

is subclass of

abstrakter Gegenstand

is subclass of

Relation

is subclass of

zweiwertige Relation

is subclass of

antisymmetrische Relation
is subclass of

is subclass of

[tree]

is subclass of

abstrakter Gegenstand

is subclass of

Relation

is subclass of

zweiwertige Relation

is subclass of

reflexive Relation
is subclass of

is subclass of

is subclass of

Halbordnungsrelation
is subclass of

is subclass of

[tree]

is subclass of

abstrakter Gegenstand

is subclass of

Relation

is subclass of

zweiwertige Relation

is subclass of

trichotomizierende Relation
is subclass of

is subclass of

is subclass of

Totalordnungsrelation

Axioms (1)

Wenn rel ist ein fall von Totalordnungsrelation , dann für jeden inst1,inst2 gilt: rel(inst1,inst2) gilt oder rel(inst2,inst1) gilt .

(=>
      (instance ?REL TotalOrderingRelation)
      (forall
            (?INST1 ?INST2)
            (or
                  (holds ?REL ?INST1 ?INST2)
                  (holds ?REL ?INST2 ?INST1))))