Class PARTIAL-ORDER-RELATION

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

Slots on this class:

Documentation:

A relation is an partial-order if it is reflexive, asymmetric, and transitive.

Instance-Of: Class

Subclass-Of: Asymmetric-relation, Reflexive-relation, Transitive-relation

Superclass-Of: Total-order-relation

Equivalence Axioms:

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

Axioms:

(Transitive-Relation ?R)

(Asymmetric-Relation ?R)

(Reflexive-Relation ?R)

Other Related Axioms:

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

(<=> (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)))))