TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2370-2370	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 2372-2374	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 2369-2369	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 16543-16543	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 25802-25802	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 8233-8233	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 16698-16698	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 7426-7426	conjugate is an instance of transitive relation
(instance connectedBodyPart TransitiveRelation)	Mid-level-ontology.kif 13281-13281	connected is an instance of transitive relation
(instance covers TransitiveRelation)	Merge.kif 16073-16073	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4249-4249	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 14495-14495	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 8440-8440	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 8503-8503	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 8173-8173	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 6961-6961	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 14218-14218	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 14263-14263	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1879-1879	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9854-9854	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7859-7859	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1867-1867	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 4115-4115	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 4948-4948	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4345-4345	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 935-935	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 16707-16707	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 2376-2383

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 3753-3758	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 3690-3695	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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