Functional Dependencies

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Notation

In Database theory: [math]\{A,B\}\to \{C,D\}[/math] is abbreviated to: [math]AB\to CD[/math]

Simple hierarchical Example

9 single entries for 2022 sorted by social media followers

query

# WF 2022-06-08
# Singles published in 2022
SELECT
?single ?language ?collectionId ?collection ?collectionType ?performerId ?performer ?followerCount ?youtubeVideoId  (year(?publicationDate) as ?publicationYear)
WHERE
{
  # instanceof
  ?singleId wdt:P31 wd:Q134556. # Must be of a single
  ?singleId rdfs:label ?single.
  FILTER(LANG(?single)='en')

  #https://www.wikidata.org/wiki/Property:P361 - part of / ist Teil von
  ?singleId wdt:P361 ?collectionId.
  ?collectionId rdfs:label ?collection.
  FILTER(LANG(?collection)='en')

  # https://www.wikidata.org/wiki/Property:P407 language/ Sprache des Werkes
  ?singleId wdt:P407 ?languageId.
  ?languageId rdfs:label ?language.
  FILTER(LANG(?language)='en')

  # https://www.wikidata.org/wiki/Property:P1651 YouTube-Video-Kennung
  ?singleId wdt:P1651 ?youtubeVideoId.

  ?collectionId wdt:P31 ?collectionTypeId.
  ?collectionTypeId rdfs:label ?collectionType.
  FILTER(LANG(?collectionType)='en').

  # https://www.wikidata.org/wiki/Property:P175 Performer /Interpret
  ?singleId wdt:P175 ?performerId.
  ?performerId rdfs:label ?performer
  FILTER(LANG(?performer)='en')

  # https://www.wikidata.org/wiki/Property:P8687 followers / Follower
  #{
     #SELECT (max(?followerCount) as ?follower)
     #WHERE {
     ?performerId wdt:P8687 ?followerCount.
     #}
     #GROUP BY ?performerId
  #}
  #https://www.wikidata.org/wiki/Property:P577 Publication date / Veröffentlichungsdatum
  ?singleId wdt:P577 ?publicationDate.
  FILTER(year(?publicationDate) = 2022).
} ORDER BY  DESC(?followerCount)
LIMIT 9

try it!

result

A B C D E F G H I J
single language collectionId collection collectionType performerId performer followerCount youtubeVideoId publicationYear
Let Somebody Go English http://www.wikidata.org/entity/Q107597380 Music of the Spheres album http://www.wikidata.org/entity/Q83287 Selena Gomez 65629044 EptPhiK_q0E 2022
As It Was English http://www.wikidata.org/entity/Q111343757 Harry's House album http://www.wikidata.org/entity/Q3626966 Harry Styles 36156370 H5v3kku4y6Q 2022
Let Somebody Go English http://www.wikidata.org/entity/Q107597380 Music of the Spheres album http://www.wikidata.org/entity/Q45188 Coldplay 23541189 EptPhiK_q0E 2022
Bam Bam English http://www.wikidata.org/entity/Q56071495 Camila Cabello singles discography singles discography http://www.wikidata.org/entity/Q47447 Ed Sheeran 17661915 -8VfKZCOo_I 2022
Bam Bam English http://www.wikidata.org/entity/Q111083420 Familia album http://www.wikidata.org/entity/Q47447 Ed Sheeran 17661915 -8VfKZCOo_I 2022
Sacrifice English http://www.wikidata.org/entity/Q110400486 Dawn FM album http://www.wikidata.org/entity/Q2121062 The Weeknd 15549868 VafTMsrnSTU 2022
Out of Time English http://www.wikidata.org/entity/Q110400486 Dawn FM album http://www.wikidata.org/entity/Q2121062 The Weeknd 15549868 2fDzCWNS3ig 2022
Bam Bam English http://www.wikidata.org/entity/Q56071495 Camila Cabello singles discography singles discography http://www.wikidata.org/entity/Q18810940 Camila Cabello 12717885 -8VfKZCOo_I 2022
Bam Bam English http://www.wikidata.org/entity/Q111083420 Familia album http://www.wikidata.org/entity/Q18810940 Camila Cabello 12717885 -8VfKZCOo_I 2022

Functional Dependencies

The functional dependencies in this example are derived from the structure of the SPARQL query

  • A≡single
  • B≡language
  • C≡collectionId
  • D≡collection
  • E≡collectionType
  • F≡performerId
  • G≡performer
  • H≡followerCount
  • I≡youtubeVideoId
  • J≡publicationYear
  • [math]A\to BCFIJ[/math]
  • [math]C\to DE[/math]
  • [math]F\to GH[/math]

[math]R={{\{A,B,C,D,E,F,G,H,I,J\}},{A\to BCFIJ,C\to DE,F\to GH}}[/math]

functional dependencies diagram

The following diagram shows the functional dependencies of this example. The nodes represent the attributes and the edges the dependencies.

Attribute Closures

The attribute closure is the set of all attributes that are "reachable/determinable" from a given attribute node. In this example the results are quite obvious since the functional dependencies form a tree and the reachable nodes are all nodes of the subtree of a given attribute.

attribute closure
A ABCDEFGHIJ
B B
C CDE
D D
E E
F FGH
G G
H H
I I
J J

Candidate Keys

There is only a single candidate key: A≡single

It is the only attribute that has the full set of attributes as it's closure. A≡single is also a super key and primary key

Synthesis

Links

Wikipedia

The following graph shows some relevant wikipedia articles. If the nodes are not clickable in your browser you might want to open the svg image in a separate tab to get a clickable version of this graph.

Other

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