TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2345-2345	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 2347-2349	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 2344-2344	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 16521-16521	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 25811-25811	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 8211-8211	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 16676-16676	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 7430-7430	conjugate is an instance of transitive relation
(instance connectedBodyPart TransitiveRelation)	Mid-level-ontology.kif 13287-13287	connected is an instance of transitive relation
(instance covers TransitiveRelation)	Merge.kif 16051-16051	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4224-4224	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 14473-14473	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 8418-8418	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 8481-8481	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 8151-8151	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5695-5695	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 14196-14196	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 14241-14241	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1854-1854	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9832-9832	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7834-7834	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1842-1842	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 4090-4090	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 4923-4923	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4320-4320	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 16685-16685	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 2351-2358

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 3728-3733	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 3665-3670	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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