Class Total-Order-Relation

• Defined in ontology: Frame-ontology
• Source pathname: /tmp_mnt/vol/q/htw/cms/ontolingua/examples/ontolingua/../../all-ontologies/ontolingua/frame-ontology.lisp

Arity: 1

Documentation:

A relation R is an total-order if it is partial-order for which either R(x,y) or R(y,x) for every x or y in its exact-domain.

Instance-Of: Class, Relation, Set

Subclass-Of:

Partial-Order-Relation, Antisymmetric-Relation, Binary-Relation, Reflexive-Relation, Transitive-Relation ...

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Slots:

Arity: 2

Implication Axioms for Total-Order-Relation:

(=> (Total-Order-Relation ?R)
    (=> (And (Instance-Of ?X (Exact-Domain ?R))
             (Instance-Of ?Y (Exact-Domain ?R)))
        (Or (Holds ?R ?X ?Y) (Holds ?R ?Y ?X))))

Equivalence Axioms for Total-Order-Relation:

(<=> (Total-Order-Relation ?R)
     (And (Partial-Order-Relation ?R)
          (=> (And (Instance-Of ?X (Exact-Domain ?R))
                   (Instance-Of ?Y (Exact-Domain ?R)))
              (Or (Holds ?R ?X ?Y) (Holds ?R ?Y ?X)))))