TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2242-2242	Transitive relation is disjoint from intransitive relation
(documentation TransitiveRelation ChineseLanguage "一个 BinaryRelation ?REL 是传递关系如果所有的 ?INST1， ?INST2和 ?INST3 是(?REL ?INST1 ?INST2) 和 (?REL ?INST2 ?INST3) 意味着 (?REL ?INST1 ?INST3)。")	chinese_format.kif 1848-1850
(documentation TransitiveRelation EnglishLanguage "A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3.")	Merge.kif 2244-2246
(subclass TransitiveRelation BinaryRelation)	Merge.kif 2241-2241	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 15570-15570	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 22899-22899	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 7811-7811	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 15725-15725	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 6114-6114	conjugate is an instance of transitive relation
(instance connectedBodyPart TransitiveRelation)	Mid-level-ontology.kif 10910-10910	a %1 is connected to a &%TransitiveRelation$transitive relation"" is an instance of transitive relation
(instance covers TransitiveRelation)	Mid-level-ontology.kif 28451-28451	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4062-4062	crosses is an instance of transitive relation
(instance dependentGeopoliticalArea TransitiveRelation)	Government.kif 446-446	dependent geopolitical area is an instance of transitive relation
(instance developmentalForm TransitiveRelation)	Merge.kif 13635-13635	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 7937-7937	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 7985-7985	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 7789-7789	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5209-5209	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 13372-13372	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 13417-13417	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1758-1758	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9265-9265	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7494-7494	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1746-1746	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 3934-3934	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 4710-4710	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4141-4141	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 885-885	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 15734-15734	sister is an instance of transitive relation

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antecedent

(=>
    (instance ?REL TransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
        (=>
            (and
                (?REL ?INST1 ?INST2)
                (?REL ?INST2 ?INST3))
            (?REL ?INST1 ?INST3))))

Merge.kif 2248-2255

If an entity is an instance of transitive relation,
then for all another entity, a third entity and a fourth entity
- if the entity the other entity and the third entity and the entity the third entity and the fourth entity,
- then the entity the other entity and the fourth entity

consequent

(=> (equivalenceRelationOn ?RELATION ?CLASS) (and (instance ?RELATION TransitiveRelation) (instance ?RELATION SymmetricRelation) (reflexiveOn ?RELATION ?CLASS)))	Merge.kif 3594-3599	If a binary relation is an equivalence relation on a class, then the binary relation is an instance of transitive relation and the binary relation is an instance of symmetric relation and the binary relation is reflexive on the class
(=> (partialOrderingOn ?RELATION ?CLASS) (and (reflexiveOn ?RELATION ?CLASS) (instance ?RELATION TransitiveRelation) (instance ?RELATION AntisymmetricRelation)))	Merge.kif 3537-3542	If a binary relation is partial ordering on a class, then the binary relation is reflexive on the class and the binary relation is an instance of transitive relation and the binary relation is an instance of antisymmetric relation

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