TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2334-2334	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 2336-2338
(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
(subclass TransitiveRelation BinaryRelation)	Merge.kif 2333-2333	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 16417-16417	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 24222-24222	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 8134-8134	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 16572-16572	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 6487-6487	conjugate is an instance of transitive relation
(instance connectedBodyPart TransitiveRelation)	Mid-level-ontology.kif 11983-11983	connected is an instance of transitive relation
(instance covers TransitiveRelation)	Merge.kif 15947-15947	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4200-4200	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 14366-14366	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 8341-8341	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 8404-8404	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 8102-8102	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5425-5425	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 14089-14089	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 14134-14134	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1844-1844	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9730-9730	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7785-7785	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1832-1832	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 4072-4072	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 4896-4896	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4293-4293	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 927-927	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 16581-16581	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 2340-2347

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 3714-3719	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 3651-3656	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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