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Completeness Statements about RDF Data Sources and
Their Use for Query Answering
Fariz Darari
Werner Nutt
Giuseppe Pirrò
S...
Motivation

Fariz Darari (ISWC 2013)

Completeness Reasoning @ Linked Data

Oct 23rd, 2013

2 / 30
Motivation
http://www.imdb.com/title/tt0105236/fullcredits?ref_=tt_ov_st_sm#cast

Completeness
statement about the
IMDB da...
Motivation

Fariz Darari (ISWC 2013)

Completeness Reasoning @ Linked Data

Oct 23rd, 2013

4 / 30
Motivation

Fariz Darari (ISWC 2013)

Completeness Reasoning @ Linked Data

Oct 23rd, 2013

5 / 30
Motivation

Fariz Darari (ISWC 2013)

Completeness Reasoning @ Linked Data

Oct 23rd, 2013

6 / 30
Incomplete Data Source

Quentin Tarantino is missing..

Fariz Darari (ISWC 2013)

Completeness Reasoning @ Linked Data

Oc...
Incomplete Data Source
An incomplete data source of Tarantino movies,
a
i
Gdbp = (Gdbp , Gdbp ):

Fariz Darari (ISWC 2013)...
Incomplete Data Source
An incomplete data source of Tarantino movies,
a
i
Gdbp = (Gdbp ,Gdbp ):

Fariz Darari (ISWC 2013)
...
Incomplete Data Source
An incomplete data source of Tarantino movies,
a
i
Gdbp = (Gdbp , Gdbp ):

Fariz Darari (ISWC 2013)...
Incomplete Data Source

Incomplete Data Source
An incomplete data source is a pair of two graphs,
G = (Ga , Gi ), where Ga...
Completeness Statements: Examples
To express that a source is complete
for all the triples about movies directed by Tarant...
Completeness Statements: Examples
To express that a source is complete
for all the triples about movies directed by Tarant...
Completeness Statement: Definition

Let P1 be a non-empty BGP (Basic Graph Pattern) and
P2 a BGP.
A completeness statement ...
Satisfaction of Completeness Statements
To the statement
C = Compl(P1 | P2 ),
we associate the CONSTRUCT query
QC = (P1 , ...
Completeness Statements
Cdir = Compl((?m, type, Movie), (?m, director , tarantino) | ∅)

Question: Gdbp |= Cdir ?
Fariz Da...
Completeness Statements
Cdir = Compl((?m, type, Movie), (?m, director , tarantino) | ∅)

Question: Gdbp |= Cdir ?
a
Yes, b...
Completeness Statements

Cact = Compl((?m, actor , ?a) | (?m, type, Movie), (?m, director , tara)

Question: Gdbp |= Cact ...
Completeness Statements

Cact = Compl((?m, actor , ?a) | (?m, type, Movie), (?m, director , tara)

Question: Gdbp |= Cact ...
Completeness Statements in RDF

Cact = Compl((?m, actor , ?a) | (?m, type, Movie), (?m, director , tara)

Fariz Darari (IS...
Query Completeness: Example
Qdir = ({?m}, {(?m, type, Movie), (?m, director , tarantino)})

Fariz Darari (ISWC 2013)

Comp...
Query Completeness: Example
Qdir = ({?m}, {(?m, type, Movie), (?m, director , tarantino)})

Then, Qdir

i
Gdbp

Fariz Dara...
Query Completeness: Definition

Definition
Let Q be a SELECT query. We write
Compl(Q)
to say that Q is complete.
An incomple...
Completeness Entailment

Let C be a set of completeness statements and
Q a SELECT query.
We say that C entails the complet...
Completeness Reasoning
Transfer Operator
For any set C of completeness statements and a graph G,
we define the transfer ope...
Completeness Reasoning
Transfer Operator
For any set C of completeness statements and a graph G,
we define the transfer ope...
Completeness of Basic Queries

Theorem
Let C be a set of completeness statements and
Q = (W , P) a basic query. Then,
C |=...
Completeness Reasoning: Example
Consider the set of completeness statements
Cdir ,act = { Cdir , Cact }
and the query
Qdir...
Completeness Reasoning: Example
Consider the set of completeness statements
Cdir ,act = { Cdir , Cact }
and the query
Qdir...
Completeness Reasoning: Example
Cdir ,act = { Cdir , Cact }
Qdir +act = ({ ?m }, Pdir +act )
Therefore,
˜
TCdir ,act (Pdir...
Completeness Reasoning: Example
Cdir ,act = { Cdir , Cact }
Qdir +act = ({ ?m }, Pdir +act )
Therefore,
˜
TCdir ,act (Pdir...
Completeness Reasoning: Example
Cdir ,act = { Cdir , Cact }
Qdir +act = ({ ?m }, Pdir +act )
Therefore,
˜
TCdir ,act (Pdir...
Completeness Reasoning: Example
Cdir ,act = { Cdir , Cact }
Qdir +act = ({ ?m }, Pdir +act )
Therefore,
˜
TCdir ,act (Pdir...
Completeness Reasoning: Example
Cdir ,act = { Cdir , Cact }
Qdir +act = ({ ?m }, Pdir +act )
Therefore,
˜
TCdir ,act (Pdir...
The framework can also be applied to:

DISTINCT Queries
OPT Queries
Queries with RDFS Data Sources

Fariz Darari (ISWC 201...
Federated Framework

Fariz Darari (ISWC 2013)

Completeness Reasoning @ Linked Data

Oct 23rd, 2013

27 / 30
CoRner: Completeness Reasoner

Can check the completeness of a subset of SPARQL
queries depending on the completeness stat...
Conclusions and Future Work

We developed a theoretical framework for the expression of
completeness statements about data...
Terima kasih, grazie, danke!!

Link to References

Fariz Darari (ISWC 2013)

Completeness Reasoning @ Linked Data

Oct 23r...
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Completeness Statements at ISWC 2013

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Completeness statements make explicit which information is complete for data sources. They can be used to ensure the completeness of query answers.

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Transcript of "Completeness Statements at ISWC 2013"

  1. 1. Completeness Statements about RDF Data Sources and Their Use for Query Answering Fariz Darari Werner Nutt Giuseppe Pirrò Simon Razniewski Presented at ISWC 2013 Supported by SWSA with the Travel Grant Oct 23rd, 2013 Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 1 / 30
  2. 2. Motivation Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 2 / 30
  3. 3. Motivation http://www.imdb.com/title/tt0105236/fullcredits?ref_=tt_ov_st_sm#cast Completeness statement about the IMDB data source …………… Quentin Tarantino was the character Mr. Brown …………… …………… Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 3 / 30
  4. 4. Motivation Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 4 / 30
  5. 5. Motivation Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 5 / 30
  6. 6. Motivation Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 6 / 30
  7. 7. Incomplete Data Source Quentin Tarantino is missing.. Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 7 / 30
  8. 8. Incomplete Data Source An incomplete data source of Tarantino movies, a i Gdbp = (Gdbp , Gdbp ): Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 8 / 30
  9. 9. Incomplete Data Source An incomplete data source of Tarantino movies, a i Gdbp = (Gdbp ,Gdbp ): Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 9 / 30
  10. 10. Incomplete Data Source An incomplete data source of Tarantino movies, a i Gdbp = (Gdbp , Gdbp ): Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 10 / 30
  11. 11. Incomplete Data Source Incomplete Data Source An incomplete data source is a pair of two graphs, G = (Ga , Gi ), where Ga ⊆ Gi . We call Ga the available graph and Gi the ideal graph. Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 11 / 30
  12. 12. Completeness Statements: Examples To express that a source is complete for all the triples about movies directed by Tarantino, we use the statement Cdir = Compl((?m, type, Movie), (?m, director , tarantino) | ∅), Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 12 / 30
  13. 13. Completeness Statements: Examples To express that a source is complete for all the triples about movies directed by Tarantino, we use the statement Cdir = Compl((?m, type, Movie), (?m, director , tarantino) | ∅), To express that a source is complete for all triples about actors in movies directed by Tarantino, we use Cact = Compl((?m, actor , ?a) | (?m, type, Movie), (?m, director , tara)) Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 12 / 30
  14. 14. Completeness Statement: Definition Let P1 be a non-empty BGP (Basic Graph Pattern) and P2 a BGP. A completeness statement is defined as Compl(P1 | P2 ) where we call P1 the pattern and P2 the condition of the statement. Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 13 / 30
  15. 15. Satisfaction of Completeness Statements To the statement C = Compl(P1 | P2 ), we associate the CONSTRUCT query QC = (P1 , P1 ∪ P2 ). Then, we say: C is satisfied by an IDS G = (Ga , Gi ), written G |= C, if QC Fariz Darari (ISWC 2013) Gi ⊆ Ga . Completeness Reasoning @ Linked Data Oct 23rd, 2013 14 / 30
  16. 16. Completeness Statements Cdir = Compl((?m, type, Movie), (?m, director , tarantino) | ∅) Question: Gdbp |= Cdir ? Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 15 / 30
  17. 17. Completeness Statements Cdir = Compl((?m, type, Movie), (?m, director , tarantino) | ∅) Question: Gdbp |= Cdir ? a Yes, because QCdir Gdbp ⊆ Gdbp . i Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 15 / 30
  18. 18. Completeness Statements Cact = Compl((?m, actor , ?a) | (?m, type, Movie), (?m, director , tara) Question: Gdbp |= Cact ? Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 16 / 30
  19. 19. Completeness Statements Cact = Compl((?m, actor , ?a) | (?m, type, Movie), (?m, director , tara) Question: Gdbp |= Cact ? No, because among the results of QCact Gdbp , i a there is (reservoirDogs, actor , tarantino) not in Gdbp . Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 16 / 30
  20. 20. Completeness Statements in RDF Cact = Compl((?m, actor , ?a) | (?m, type, Movie), (?m, director , tara) Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 17 / 30
  21. 21. Query Completeness: Example Qdir = ({?m}, {(?m, type, Movie), (?m, director , tarantino)}) Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 18 / 30
  22. 22. Query Completeness: Example Qdir = ({?m}, {(?m, type, Movie), (?m, director , tarantino)}) Then, Qdir i Gdbp Fariz Darari (ISWC 2013) = Qdir a Gdbp , and therefore Gdbp |= Compl(Qdir ). Completeness Reasoning @ Linked Data Oct 23rd, 2013 18 / 30
  23. 23. Query Completeness: Definition Definition Let Q be a SELECT query. We write Compl(Q) to say that Q is complete. An incomplete data source G = (Ga , Gi ) satisfies Compl(Q), written G |= Compl(Q) Fariz Darari (ISWC 2013) if and only if Completeness Reasoning @ Linked Data Q Gi = Q Ga . Oct 23rd, 2013 19 / 30
  24. 24. Completeness Entailment Let C be a set of completeness statements and Q a SELECT query. We say that C entails the completeness of Q, written C |= Compl(Q), if any incomplete data source satisfying C also satisfies Compl(Q). Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 20 / 30
  25. 25. Completeness Reasoning Transfer Operator For any set C of completeness statements and a graph G, we define the transfer operator TC : TC (G) = QC G C∈ C Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 21 / 30
  26. 26. Completeness Reasoning Transfer Operator For any set C of completeness statements and a graph G, we define the transfer operator TC : TC (G) = QC G C∈ C Prototypical Graph Let Q = (W , P) be a SELECT query. ˜ The prototypical graph P is the graph resulting from the mapping of variables in P to fresh, unique IRIs. Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 21 / 30
  27. 27. Completeness of Basic Queries Theorem Let C be a set of completeness statements and Q = (W , P) a basic query. Then, C |= Compl(Q) Fariz Darari (ISWC 2013) if and only if Completeness Reasoning @ Linked Data ˜ ˜ P = TC (P). Oct 23rd, 2013 22 / 30
  28. 28. Completeness Reasoning: Example Consider the set of completeness statements Cdir ,act = { Cdir , Cact } and the query Qdir +act = ({ ?m }, Pdir +act ) where Pdir +act = { (?m, type, Movie), (?m, director , tarantino), (?m, actor , tarantino) }. Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 23 / 30
  29. 29. Completeness Reasoning: Example Consider the set of completeness statements Cdir ,act = { Cdir , Cact } and the query Qdir +act = ({ ?m }, Pdir +act ) Then, ˜ Pdir +act = { (c?m , type, Movie), (c?m , director , tarantino), (c?m , actor , tarantino) } Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 24 / 30
  30. 30. Completeness Reasoning: Example Cdir ,act = { Cdir , Cact } Qdir +act = ({ ?m }, Pdir +act ) Therefore, ˜ TCdir ,act (Pdir +act ) Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
  31. 31. Completeness Reasoning: Example Cdir ,act = { Cdir , Cact } Qdir +act = ({ ?m }, Pdir +act ) Therefore, ˜ TCdir ,act (Pdir +act ) = QCdir Pdir +act ∪ QCact ˜ Fariz Darari (ISWC 2013) ˜ Pdir +act Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
  32. 32. Completeness Reasoning: Example Cdir ,act = { Cdir , Cact } Qdir +act = ({ ?m }, Pdir +act ) Therefore, ˜ TCdir ,act (Pdir +act ) = QCdir Pdir +act ∪ QCact Pdir +act ˜ ˜ = { (c?m , type, Movie), (c?m , director , tara), Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
  33. 33. Completeness Reasoning: Example Cdir ,act = { Cdir , Cact } Qdir +act = ({ ?m }, Pdir +act ) Therefore, ˜ TCdir ,act (Pdir +act ) = QCdir Pdir +act ∪ QCact Pdir +act ˜ ˜ = { (c?m , type, Movie), (c?m , director , tara), (c?m , actor , tara) } Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
  34. 34. Completeness Reasoning: Example Cdir ,act = { Cdir , Cact } Qdir +act = ({ ?m }, Pdir +act ) Therefore, ˜ TCdir ,act (Pdir +act ) = QCdir Pdir +act ∪ QCact Pdir +act ˜ ˜ = { (c?m , type, Movie), (c?m , director , tara), (c?m , actor , tara) } ˜ = Pdir +act . Thus, Cdir ,act |= Compl(Qdir +act ) Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
  35. 35. The framework can also be applied to: DISTINCT Queries OPT Queries Queries with RDFS Data Sources Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 26 / 30
  36. 36. Federated Framework Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 27 / 30
  37. 37. CoRner: Completeness Reasoner Can check the completeness of a subset of SPARQL queries depending on the completeness statements of a single data source. Developed in Java using the Apache Jena library. Takes three inputs: Completeness statements in RDF format A SPARQL query (optional) an RDFS ontology Available at http://rdfcorner.wordpress.com/. Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 28 / 30
  38. 38. Conclusions and Future Work We developed a theoretical framework for the expression of completeness statements about data sources, from which we can ensure query completeness. We provide a compact RDF representation of completeness statements, which can be embedded in VoID descriptions, and implemented the framework in CoRner. We are interested in studying completeness reasoning with more expressive queries and OWL 2. Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 29 / 30
  39. 39. Terima kasih, grazie, danke!! Link to References Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 30 / 30
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