disjoint relation (disjointRelation)

This predicate relates any number of Relations. (disjointRelation @ROW) means that any two relations in @ROW have no tuples in common. As a consequence, the intersection of all of the relations in @ROW is the null set.

Ontology

SUMO / STRUCTURAL-ONTOLOGY

Class(es)

class

inheritable relation

predicate

variable arity relation
is instance of

disjoint relation

Coordinate term(s)

assignment fn greatest common divisor fn least common multiple fn list fn contrary attribute disjoint decomposition exhaustive attribute exhaustive decomposition holds partition

Axioms (15)

disjoint relation is internally related to disjoint.

(relatedInternalConcept disjointRelation disjoint)

If and ? are disjoint and rel is a member of "()", then rel is an instance of relation.

(=>
      (and
            (disjointRelation @ROW)
            (inList
                  ?REL
                  (ListFn @ROW)))
      (instance ?REL Relation))

If and ? are disjoint and rel1 is a member of "()" and rel2 is a member of "()" and rel1 %&has number argument(s), then rel2 %&has number argument(s).

(=>
      (and
            (disjointRelation @ROW)
            (inList
                  ?REL1
                  (ListFn @ROW))
            (inList
                  ?REL2
                  (ListFn @ROW))
            (valence ?REL1 ?NUMBER))
      (valence ?REL2 ?NUMBER))

If the number number argument of rel1 is an instance of class1 and the number number argument of rel2 is an instance of class2 and class1 is disjoint from class2, then rel1 and rel2 are disjoint.

(=>
      (and
            (domain ?REL1 ?NUMBER ?CLASS1)
            (domain ?REL2 ?NUMBER ?CLASS2)
            (disjoint ?CLASS1 ?CLASS2))
      (disjointRelation ?REL1 ?REL2))

If the number number argument of rel1 is a subclass of class1 and the number number argument of rel2 is a subclass of class2 and class1 is disjoint from class2, then rel1 and rel2 are disjoint.

(=>
      (and
            (domainSubclass ?REL1 ?NUMBER ?CLASS1)
            (domainSubclass ?REL2 ?NUMBER ?CLASS2)
            (disjoint ?CLASS1 ?CLASS2))
      (disjointRelation ?REL1 ?REL2))

If range of rel1 is an instance of class1 and range of rel2 is an instance of class2 and class1 is disjoint from class2, then rel1 and rel2 are disjoint.

(=>
      (and
            (range ?REL1 ?CLASS1)
            (range ?REL2 ?CLASS2)
            (disjoint ?CLASS1 ?CLASS2))
      (disjointRelation ?REL1 ?REL2))

If the values returned by rel1 are subclasses of class1 and the values returned by rel2 are subclasses of class2 and class1 is disjoint from class2, then rel1 and rel2 are disjoint.

(=>
      (and
            (rangeSubclass ?REL1 ?CLASS1)
            (rangeSubclass ?REL2 ?CLASS2)
            (disjoint ?CLASS1 ?CLASS2))
      (disjointRelation ?REL1 ?REL2))

If and ? are disjoint and rel1 is a member of "()" and rel2 is a member of "()" and rel1 is not equal to rel2 and rel1() holds, then rel2() doesn't hold.

(=>
      (and
            (disjointRelation @ROW1)
            (inList
                  ?REL1
                  (ListFn @ROW1))
            (inList
                  ?REL2
                  (ListFn @ROW1))
            (not
                  (equal ?REL1 ?REL2))
            (holds ?REL1 @ROW2))
      (not
            (holds ?REL2 @ROW2)))

synonymous external concept and subsumed external concept are disjoint.

(disjointRelation synonymousExternalConcept subsumedExternalConcept subsumingExternalConcept)

sub attribute and successor attribute are disjoint.

(disjointRelation subAttribute successorAttribute)

manner and attribute are disjoint.

(disjointRelation manner attribute)

resource and result are disjoint.

(disjointRelation resource result instrument)

increases likelihood and decreases likelihood are disjoint.

(disjointRelation increasesLikelihood decreasesLikelihood independentProbability)

crosses and connected are disjoint.

(disjointRelation crosses connected)

meets spatially and overlaps spatially are disjoint.

(disjointRelation meetsSpatially overlapsSpatially)