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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > PartialOrderingRelation > TotalOrderingRelation
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TotalOrderingRelation comparison table
Subject documentation is a kind of have axiom
PartialOrderingRelationA BinaryRelation is a partial ordering if it is a ReflexiveRelation, an AntisymmetricRelation, and a TransitiveRelationTransitiveRelation
(=>
    (instance ?REL TransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
       (=>
          (and
             (holds ?REL ?INST1 ?INST2)
             (holds ?REL ?INST2 ?INST3))
          (holds ?REL ?INST1 ?INST3))))
TrichotomizingRelationA BinaryRelation ?REL is a TrichotomizingRelation just in case all ordered pairs consisting of distinct individuals are elements of ?RELBinaryRelation
(=>
    (instance ?REL TrichotomizingRelation)
    (forall (?INST1 ?INST2)
       (or
          (holds ?REL ?INST1 ?INST2) 
          (equal ?INST1 ?INST2) 
          (holds ?REL ?INST2 ?INST1))))
TotalOrderingRelation"A BinaryRelation is a TotalOrderingRelation if it is a PartialOrderingRelation and a TrichotomizingRelationTrichotomizingRelation
(=>
    (instance ?REL TotalOrderingRelation)
    (forall (?INST1 ?INST2)
       (or
          (holds ?REL ?INST1 ?INST2)
          (holds ?REL ?INST2 ?INST1))))

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