Relation SUBSET

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

Slots on this relation:

Documentation:

The sentence {tt (subset $tau_1$ $tau_2$)} is true if and only if $tau_1$ and $tau_2$ are sets and the objects in the set denoted by $tau_1$ are contained in the set denoted by $tau_2$.

Instance-Of: Relation

Arity: 2

Domain: Set

Range: Set

Equivalence Axioms:

(<=> (Subset ?S1 ?S2)
     (And (Set ?S1)
          (Set ?S2)
          (Forall (?X) (=> (Member ?X ?S1) (Member ?X ?S2)))))

Other Related Axioms:

(=> (Subset $X $Y) (Set $Y))

(=> (Subset $X $Y) (Set $X))

(<=> (Subset ?S1 ?S2)
     (And (Set ?S1)
          (Set ?S2)
          (Forall (?X) (=> (Member ?X ?S1) (Member ?X ?S2)))))

(Subrelation-Of Proper-Subset Subset)

(<=> (Proper-Subset ?S1 ?S2)
     (And (Subset ?S1 ?S2) (Not (Subset ?S2 ?S1))))

(<=> (Set-Cover ?S @Sets) (Subset ?S (Union @Sets)))

(=> (Bounded ?V) (Bounded (Setofall ?U (Subset ?U ?V))))

Notes:

• Source: KIF Version 3.0 Specification