TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2445-2445	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)。")	Merge.kif 2449-2451
(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 2446-2448
(subclass TransitiveRelation BinaryRelation)	Merge.kif 2444-2444	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 16439-16439	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 21536-21536	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 8241-8241	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 16598-16598	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 6177-6177	conjugate is an instance of transitive relation
(instance covers TransitiveRelation)	Mid-level-ontology.kif 27478-27478	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4304-4304	crosses is an instance of transitive relation
(instance dependentGeopoliticalArea TransitiveRelation)	Government.kif 446-446	dependent geopolitical area is an instance of transitive relation
(instance developmentalForm TransitiveRelation)	Merge.kif 14215-14215	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 8372-8372	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 8419-8419	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 8217-8217	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5090-5090	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 13906-13906	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 13956-13956	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1886-1886	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9569-9569	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7904-7904	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1873-1873	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 4168-4168	located is an instance of transitive relation
(instance meronym TransitiveRelation)	engineering.kif 74-74	meronym is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 5015-5015	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4378-4378	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 964-964	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 16609-16609	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 2453-2460

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 3809-3814	If a binary relation is an equivalence relation on a set or 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 set or class
(=> (partialOrderingOn ?RELATION ?CLASS) (and (reflexiveOn ?RELATION ?CLASS) (instance ?RELATION TransitiveRelation) (instance ?RELATION AntisymmetricRelation)))	Merge.kif 3745-3750	If a binary relation is partial ordering on a set or class, then the binary relation is reflexive on the set or 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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