Class Partial-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 is an partial-order if it is reflexive, asymmetric, and transitive.

Instance-Of: Class, Relation, Set

Subclass-Of:

Antisymmetric-Relation, Antisymmetric-Relation, Reflexive-Relation, Reflexive-Relation, Transitive-Relation ...

Superclass-Of: Total-Order-Relation

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Slots:

Arity: 2

Equivalence Axioms for Partial-Order-Relation:

(<=> (Partial-Order-Relation ?R)
     (And (Reflexive-Relation ?R)
          (Antisymmetric-Relation ?R)
          (Transitive-Relation ?R)))

Implication Axioms mentioning Partial-Order-Relation:

(=> (Total-Order-Relation ?R) (Partial-Order-Relation ?R))

Equivalence Axioms mentioning Partial-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)))))