Relation PROPER-SUBSET

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

Slots on this relation:

Documentation:

The sentence {tt (proper-subset $tau_1$ $tau_2$)} is true if the set denoted by $tau_1$ is a subset of the set denoted by $tau_2$ but not vice-versa.

Instance-Of: Relation

Arity: 2

Subrelation-Of: Subset

Equivalence Axioms:

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

Other Related Axioms:

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

(Exists (?U)
        (And (Bounded ?U)
             (Not (Empty ?U))
             (Forall (?X)
                     (=> (Member ?X ?U)
                         (Exists (?Y)
                                 (And (Member ?Y ?U)
                                      (Proper-Subset ?X ?Y)))))))

Notes:

• Source: KIF Version 3.0 Specification