Relation SUBRELATION-OF

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

Slots on this relation:

Documentation:

A relation R is a subrelation-of relation R' if, viewed as sets, R is a subset of R'. In other words, every tuple of R is also a tuple of R'. In some more words, if R holds for some arguments arg_1, arg_2, ... arg_n, then R' holds for the same arguments. Thus, a relation and its subrelation must have the same arity, which could be undefined.

In CycL, subrelation-of is called #%genlSlots.

Instance-Of: Relation

Arity: 2

Domain: Relation

Range: Relation

Equivalence Axioms:

(<=> (Subrelation-Of ?Child-Relation ?Parent-Relation)
     (And (Relation ?Child-Relation)
          (Relation ?Parent-Relation)
          (Forall (?Tuple)
                  (=> (Member ?Tuple ?Child-Relation)
                      (Member ?Tuple ?Parent-Relation)))))

Other Related Axioms:

(=> (Subrelation-Of $X $Y) (Relation $Y))

(=> (Subrelation-Of $X $Y) (Relation $X))

(=> (Subrelation-Of ?Child-Relation ?Parent-Relation)
    (=> (Defined (Arity ?Parent-Relation))
        (= (Arity ?Child-Relation) (Arity ?Parent-Relation))))

(<=> (Subrelation-Of ?Child-Relation ?Parent-Relation)
     (=> (Holds ?Child-Relation @Arguments)
         (Holds ?Parent-Relation @Arguments)))

(<=> (Subrelation-Of ?Child-Relation ?Parent-Relation)
     (And (Relation ?Child-Relation)
          (Relation ?Parent-Relation)
          (Forall (?Tuple)
                  (=> (Member ?Tuple ?Child-Relation)
                      (Member ?Tuple ?Parent-Relation)))))

(Subrelation-Of Direct-Instance-Of Instance-Of)

(Subrelation-Of Direct-Subclass-Of Subclass-Of)

(<=> (Total-On ?Relation ?Domain-Relation)
     (Subrelation-Of (Exact-Domain ?Relation) ?Domain-Relation))

(Subrelation-Of Alias =)

(Subrelation-Of Exhaustive-Subclass-Partition Subclass-Partition)

Notes:

• Do the arities of the relations have to match?

  No. Used to be defined this way, but it was an unnecessary restriction. If the parent relation has a (fixed) arity, then the child's arity must be equal to it. However, the child could be of fixed arity and the parent undefined (variable) arity.