TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2311-2311	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 2313-2315
(subclass TransitiveRelation BinaryRelation)	Merge.kif 2310-2310	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 16196-16196	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 24110-24110	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 8065-8065	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 16351-16351	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 6453-6453	conjugate is an instance of transitive relation
(instance connectedBodyPart TransitiveRelation)	Mid-level-ontology.kif 11803-11803	connected is an instance of transitive relation
(instance covers TransitiveRelation)	Mid-level-ontology.kif 29658-29658	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4176-4176	crosses is an instance of transitive relation
(instance dependentGeopoliticalArea TransitiveRelation)	Government.kif 457-457	dependent geopolitical area is an instance of transitive relation
(instance developmentalForm TransitiveRelation)	Merge.kif 14179-14179	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 8270-8270	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 8333-8333	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 8033-8033	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5334-5334	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 13902-13902	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 13947-13947	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1821-1821	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9663-9663	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7716-7716	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1809-1809	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 4048-4048	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 4866-4866	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4269-4269	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 916-916	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 16360-16360	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 2317-2324

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 3690-3695	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 3627-3632	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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