Class TOTAL-ORDER-RELATION

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

Slots on this class:

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

Subclass-Of: Partial-order-relation

Implication Axioms:

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

Equivalence Axioms:

(<=> (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)))))

Axioms:

(Partial-Order-Relation ?R)

Other Related Axioms:

(<=> (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)))))