TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2330-2330	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	Transitive relation is disjoint from intransitive relation
(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 2332-2334	Transitive relation is disjoint from intransitive relation
(documentation TransitiveRelation JapaneseLanguage "BinaryRelation ?REL は、すべての ?INST1, ?INST2, および ?INST3 に対して (?REL ?INST1 ?INST2) および (?REL ?INST2 ?INST3) が (?REL ?INST1 ?INST3) を意味する場合、推移的である。")	japanese_format.kif 469-471	Transitive relation is disjoint from intransitive relation
(subclass TransitiveRelation BinaryRelation)	Merge.kif 2329-2329	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 16506-16506	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 25830-25830	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 8196-8196	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 16661-16661	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 7449-7449	conjugate is an instance of transitive relation
(instance connectedBodyPart TransitiveRelation)	Mid-level-ontology.kif 13305-13305	connected is an instance of transitive relation
(instance covers TransitiveRelation)	Merge.kif 16036-16036	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4209-4209	crosses is an instance of transitive relation
(instance dependentGeopoliticalArea TransitiveRelation)	Government.kif 421-421	dependent geopolitical area is an instance of transitive relation
(instance developmentalForm TransitiveRelation)	Merge.kif 14458-14458	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 8403-8403	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 8466-8466	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 8136-8136	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5495-5495	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 14181-14181	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 14226-14226	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1839-1839	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9817-9817	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7819-7819	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1827-1827	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 4075-4075	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 4908-4908	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4305-4305	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 920-920	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 16670-16670	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 2336-2343

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 3713-3718	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 3650-3655	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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