TransitiveRelation - Sigma Knowledge base Browser

appearance as argument number 1

(disjoint TransitiveRelation IntransitiveRelation)	Merge.kif 2468-2468	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 2472-2474
(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 2469-2471
(subclass TransitiveRelation BinaryRelation)	Merge.kif 2467-2467	Transitive relation is a subclass of binary relation

appearance as argument number 2

(instance ancestor TransitiveRelation)	Merge.kif 16569-16569	ancestor is an instance of transitive relation
(instance ancestorOrganization TransitiveRelation)	Mid-level-ontology.kif 21928-21928	ancestor organization is an instance of transitive relation
(instance before TransitiveRelation)	Merge.kif 8290-8290	before is an instance of transitive relation
(instance brother TransitiveRelation)	Merge.kif 16736-16736	brother is an instance of transitive relation
(instance conjugate TransitiveRelation)	Mid-level-ontology.kif 6181-6181	conjugate is an instance of transitive relation
(instance covers TransitiveRelation)	Mid-level-ontology.kif 27919-27919	covers is an instance of transitive relation
(instance crosses TransitiveRelation)	Merge.kif 4335-4335	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 14352-14352	developmental form is an instance of transitive relation
(instance during TransitiveRelation)	Merge.kif 8424-8424	during is an instance of transitive relation
(instance earlier TransitiveRelation)	Merge.kif 8471-8471	earlier is an instance of transitive relation
(instance finishes TransitiveRelation)	Merge.kif 8266-8266	finishes is an instance of transitive relation
(instance flows TransitiveRelation)	Geography.kif 5089-5089	flows is an instance of transitive relation
(instance geographicSubregion TransitiveRelation)	Merge.kif 14043-14043	geographic subregion is an instance of transitive relation
(instance geopoliticalSubdivision TransitiveRelation)	Merge.kif 14093-14093	geopolitical subdivision is an instance of transitive relation
(instance greaterThan TransitiveRelation)	Merge.kif 1909-1909	greater than is an instance of transitive relation
(instance interiorPart TransitiveRelation)	Merge.kif 9707-9707	interior part is an instance of transitive relation
(instance larger TransitiveRelation)	Merge.kif 7953-7953	larger is an instance of transitive relation
(instance lessThan TransitiveRelation)	Merge.kif 1896-1896	less than is an instance of transitive relation
(instance located TransitiveRelation)	Merge.kif 4195-4195	located is an instance of transitive relation
(instance multiplicativeFactor TransitiveRelation)	Merge.kif 5048-5048	multiplicative factor is an instance of transitive relation
(instance precondition TransitiveRelation)	Merge.kif 4409-4409	precondition is an instance of transitive relation
(instance properPart TransitiveRelation)	Merge.kif 978-978	proper part is an instance of transitive relation
(instance sister TransitiveRelation)	Merge.kif 16747-16747	sister is an instance of transitive relation
(instance smaller TransitiveRelation)	Merge.kif 7976-7976	smaller 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 2476-2483

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 3832-3837	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 3768-3773	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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