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	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 2336-2338	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 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 24453-24453	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 12174-12174	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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