disjoint (disjoint)

Classes are disjoint only if they share no instances, i.e. just in case the result of applying IntersectionFn to them is empty.

Ontology

SUMO / STRUCTURAL-ONTOLOGY

Class(es)

class

inheritable relation

binary predicate
is instance of

symmetric relation
is instance of

irreflexive relation
is instance of

disjoint

Coordinate term(s)

back fn front fn arc weight attribute authors before before or equal causes causes subclass citizen closed on connected connected engineering components contains information cooccur copy date decreases likelihood developmental form distributes documentation duration during earlier editor element employs equal equivalence relation on exploits expressed in language faces family relation finishes frequency graph part greater than greater than or equal to has purpose has skill holds during holds obligation holds right hole identity element in list in scope of interest increases likelihood independent probability inhabits inhibits initial list instance interior part inverse irreflexive on larger less than less than or equal to manner material measure meets spatially meets temporally modal attribute overlaps partially overlaps spatially overlaps temporally parent partial ordering on partly located path length possesses precondition prevents property publishes range range subclass refers reflexive on related internal concept sibling smaller starts sub attribute sub collection sub graph sub list sub organizations sub plan sub process sub proposition subclass subrelation subsumes content class subsumes content instance successor attribute successor attribute closure superficial part temporal part time total ordering on trichotomizing on uses valence version

Type restrictions

disjoint(set or class, set or class)

Related WordNet synsets

antitype: an opposite or contrasting type
dichotomy: classification into two opposed parts: "the dichotomy between eastern and western culture"
disjoint: (mathematics) having no elements in common

Axioms (42)

class1 is disjoint from class2 if and only if

class1 is an instance of set or class
class2 is an instance of set or class
for all inst holds: inst is not an instance of class1 or inst is not an instance of class2

(<=>
      (disjoint ?CLASS1 ?CLASS2)
      (and
            (instance ?CLASS1 SetOrClass)
            (instance ?CLASS2 SetOrClass)
            (forall
                  (?INST)
                  (not
                        (and
                              (instance ?INST ?CLASS1)
                              (instance ?INST ?CLASS2))))))

disjoint relation is internally related to disjoint.

(relatedInternalConcept disjointRelation disjoint)

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))

disjoint decomposition is internally related to disjoint.

(relatedInternalConcept disjointDecomposition disjoint)

corpuscular object is disjoint from substance.

(disjoint CorpuscularObject Substance)

collection is disjoint from self connected object.

(disjoint Collection SelfConnectedObject)

linguistic expression is disjoint from icon.

(disjoint LinguisticExpression Icon)

natural language is disjoint from constructed language.

(disjoint NaturalLanguage ConstructedLanguage)

attribute is disjoint from quantity.

(disjoint Attribute Quantity)

complex number is disjoint from real number.

(disjoint ComplexNumber RealNumber)

rel is an instance of binary relation
the number argument of rel is an instance of class1 or the number argument of rel is a subclass of class1
the number argument of rel is an instance of class2 or the number argument of rel is a subclass of class2 or range of rel is an instance of class2 or the values returned by rel are subclasses of class2
class1 is disjoint from class2

, then rel is an instance of asymmetric relation.

(=>
      (and
            (instance ?REL BinaryRelation)
            (or
                  (domain ?REL 1 ?CLASS1)
                  (domainSubclass ?REL 1 ?CLASS1))
            (or
                  (domain ?REL 2 ?CLASS2)
                  (domainSubclass ?REL 2 ?CLASS2)
                  (range ?REL ?CLASS2)
                  (rangeSubclass ?REL ?CLASS2))
            (disjoint ?CLASS1 ?CLASS2))
      (instance ?REL AsymmetricRelation))

object attitude is disjoint from propositional attitude.

(disjoint ObjectAttitude PropositionalAttitude)

if class is disjointly decomposed into ,
then for all item1,item2 holds: if item1 is a member of "()" and item2 is a member of "()" and item1 is not equal to item2, then item1 is disjoint from item2

(=>
      (disjointDecomposition ?CLASS @ROW)
      (forall
            (?ITEM1 ?ITEM2)
            (=>
                  (and
                        (inList
                              ?ITEM1
                              (ListFn @ROW))
                        (inList
                              ?ITEM2
                              (ListFn @ROW))
                        (not
                              (equal ?ITEM1 ?ITEM2)))
                  (disjoint ?ITEM1 ?ITEM2))))

if superclass is an instance of pairwise disjoint class,
then for all class1,class2 holds: if class1 is an instance of superclass and class2 is an instance of superclass, then class1 is equal to class2 or class1 is disjoint from class2

(=>
      (instance ?SUPERCLASS PairwiseDisjointClass)
      (forall
            (?CLASS1 ?CLASS2)
            (=>
                  (and
                        (instance ?CLASS1 ?SUPERCLASS)
                        (instance ?CLASS2 ?SUPERCLASS))
                  (or
                        (equal ?CLASS1 ?CLASS2)
                        (disjoint ?CLASS1 ?CLASS2)))))

graph element is disjoint from graph.

(disjoint GraphElement Graph)

solid angle measure is disjoint from plane angle measure.

(disjoint SolidAngleMeasure PlaneAngleMeasure)

sexual reproduction is disjoint from asexual reproduction.

(disjoint SexualReproduction AsexualReproduction)

organ or tissueprocess is disjoint from organism process.

(disjoint OrganOrTissueProcess OrganismProcess)

pathologic process is disjoint from physiologic process.

(disjoint PathologicProcess PhysiologicProcess)

leaving an organization is disjoint from joining an organization.

(disjoint LeavingAnOrganization JoiningAnOrganization)

heating is disjoint from cooling.

(disjoint Heating Cooling)

uncovering is disjoint from covering.

(disjoint Uncovering Covering)

damaging is disjoint from repairing.

(disjoint Damaging Repairing)

attaching is disjoint from detaching.

(disjoint Attaching Detaching)

separating is disjoint from combining.

(disjoint Separating Combining)

decoding is disjoint from encoding.

(disjoint Decoding Encoding)

astronomical body is disjoint from geographic area.

(disjoint AstronomicalBody GeographicArea)

salt water area is disjoint from fresh water area.

(disjoint SaltWaterArea FreshWaterArea)

stream water area is disjoint from static water area.

(disjoint StreamWaterArea StaticWaterArea)

non flowering plant is disjoint from flowering plant.

(disjoint NonFloweringPlant FloweringPlant)

invertebrate is disjoint from vertebrate.

(disjoint Invertebrate Vertebrate)

warm blooded vertebrate is disjoint from cold blooded vertebrate.

(disjoint WarmBloodedVertebrate ColdBloodedVertebrate)

bird is disjoint from mammal.

(disjoint Bird Mammal)

canine is disjoint from feline.

(disjoint Canine Feline)

noun phrase is disjoint from verb phrase.

(disjoint NounPhrase VerbPhrase)

room is disjoint from building.

(disjoint Room Building)

fabric is disjoint from stationary artifact.

(disjoint Fabric StationaryArtifact)

clothing is disjoint from stationary artifact.

(disjoint Clothing StationaryArtifact)

subjective assessment attribute is disjoint from objective norm.

(disjoint SubjectiveAssessmentAttribute ObjectiveNorm)