Functional Dependencies

Notation

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

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> http://diagrams.bitplan.com/render/png/0x9019d413.png

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

Synthesis

• https://www.comp.nus.edu.sg/~lingtw/papers/bernstein.pdf

Links

• https://en.wikipedia.org/wiki/Category:Database_theory
• https://en.wikipedia.org/wiki/Functional_dependency
• https://en.wikipedia.org/wiki/Database_normalization
• https://en.wikipedia.org/wiki/First_normal_form
• https://en.wikipedia.org/wiki/Second_normal_form
• https://en.wikipedia.org/wiki/Third_normal_form
• https://en.wikipedia.org/wiki/Boyce%E2%80%93Codd_normal_form
• https://en.wikipedia.org/wiki/Lossless_join_decomposition
• https://en.wikipedia.org/wiki/Candidate_key
• https://en.wikipedia.org/wiki/Surrogate_key
• https://stackoverflow.com/questions/tagged/functional-dependencies