Class Transitive-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: Relation R is transitive if R(x,y) and R(y,z) implies R(x,z).

Has-Instance: Subclass-Of

Instance-Of: Class, Relation, Set

Subclass-Of: Binary-Relation, Relation, Set

Superclass-Of: Equivalence-Relation, Partial-Order-Relation, Total-Order-Relation

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Slots:

Arity: 2

Implication Axioms for Transitive-Relation:

(=> (Transitive-Relation ?R)
    (=> (And (Holds ?R ?X ?Y) (Holds ?R ?Y ?Z)) (Holds ?R ?X ?Z)))

Equivalence Axioms for Transitive-Relation:

(<=> (Transitive-Relation ?R)
     (And (Binary-Relation ?R)
          (=> (And (Holds ?R ?X ?Y) (Holds ?R ?Y ?Z))
              (Holds ?R ?X ?Z))))

Implication Axioms mentioning Transitive-Relation:

(=> (Equivalence-Relation ?R) (Transitive-Relation ?R))

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

Equivalence Axioms mentioning Transitive-Relation:

(<=> (Equivalence-Relation ?R)
     (And (Reflexive-Relation ?R)
          (Symmetric-Relation ?R)
          (Transitive-Relation ?R)))

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