Class SIMPLE-SET

• Defined in theory: Kif-sets
• Source code: kif-sets.lisp

Slots on this class:

Documentation:

A simple set is a set that can be a member of another set.

Instance-Of: Class

Subclass-Of: Bounded, Set, Thing

Range-Of: Setof

Equivalence Axioms:

(<=> (Simple-Set ?X) (And (Set ?X) (Bounded ?X)))

Axioms:

(Bounded ?X)

(Set ?X)

Other Related Axioms:

(<=> (Simple-Set ?X) (And (Set ?X) (Bounded ?X)))

(=> (Setof $X $Y) (Simple-Set $Y))

(=> (= (Generalized-Union ?Set-Of-Sets) ?Set)
    (Forall (?S) (=> (Member ?S ?Set-Of-Sets) (Simple-Set ?S))))

(=> (= (Generalized-Intersection ?Set-Of-Sets) ?Set)
    (Forall (?S) (=> (Member ?S ?Set-Of-Sets) (Simple-Set ?S))))

Notes:

• The constraint that simple-set is a subclass-of thing is specified as part of the definition of THING, but it needs to be here, too, for bootstrapping reasons.
• Source: KIF Version 3.0 Specification