Class TRANSITIVE-RELATION

• Defined in theory: Frame-ontology
• Source code: frame-ontology.lisp

Slots on this class:

Documentation:

Relation R is transitive if R(x,y) and R(y,z) implies R(x,z).

Instance-Of: Class

Subclass-Of: Binary-relation

Superclass-Of: Equivalence-relation, Partial-order-relation

Implication Axioms:

(=> (And (Holds ?R ?X ?Y) (Holds ?R ?Y ?Z)) (Holds ?R ?X ?Z))

Equivalence Axioms:

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

Axioms:

(Binary-Relation ?R)

Other Related Axioms:

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

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

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