Relation Pairwise-Disjoint

• Defined in ontology: Kif-sets
• Source pathname: /tmp_mnt/vol/q/htw/cms/ontolingua/examples/kif/../../all-ontologies/kif/kif-sets.lisp

Instance-Of@Frame-Ontology: Relation@Ol-User%Kif-Relations, Set

Documentation@Ol%Frame-Ontology:

Sets are pairwise-disjoint if and only if every set is disjoint from every other set.

Notes:

• Source: KIF Version 3.0 Specification

Equivalence Axioms for Pairwise-Disjoint:

(<=> (Pairwise-Disjoint @Sets)
     (Forall (?S1 ?S2)
             (=> (Item@Ol-User%Kif-Lists ?S1 (Listof @Sets))
                 (Item@Ol-User%Kif-Lists ?S2 (Listof @Sets))
                 (Or (= ?S1 ?S2) (Disjoint ?S1 ?S2)))))

Axioms for Pairwise-Disjoint:

(Undefined@Ol-User%Kif-Extensions 
    (Arity@Frame-Ontology Pairwise-Disjoint))

Equivalence Axioms mentioning Pairwise-Disjoint:

(<=> (Set-Partition ?S @Sets)
     (And (= ?S (Union @Sets)) (Pairwise-Disjoint @Sets)))

Axioms mentioning Pairwise-Disjoint:

(Pairwise-Disjoint @Sets)