This was presented at ISWC 2013 in Sydney, Australia. Abstract: With thousands of RDF data sources available on the Web covering disparate and possibly overlapping knowledge domains, the problem of providing high-level descriptions (in the form of metadata) of their content becomes crucial. In this paper we introduce a theoretical framework for describing data sources in terms of their completeness. We show how existing data sources can be described with completeness statements expressed in RDF. We then focus on the problem of the completeness of query answering over plain and RDFS data sources augmented with completeness statements. Finally, we present an extension of the completeness framework for federated data sources.

1. Completeness Statements about RDF Data Sources and
Their Use for Query Answering
Fariz Darari
Werner Nutt
Giuseppe Pirrò
Simon Razniewski
Oct 23rd, 2013
Supported by the project MAGIC: Managing Completeness of Data,
funded by the province of Bozen- Bolzano
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2. Motivation
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3. Motivation
Completeness
statement about the
IMDB data source
Quentin Tarantino
was the character
Mr. Brown
……………
……………
……………
http://www.imdb.com/title/tt0105236/fullcredits?ref_=tt_ov_st_sm#cast
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4. Motivation
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5. Motivation
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6. Motivation
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7. Incomplete Data Source
Quentin Tarantino is missing..
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8. Incomplete Data Source
An incomplete data source of Tarantino movies,
Gdbp = (Ga
dbp, Gi
dbp):
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9. Incomplete Data Source
An incomplete data source of Tarantino movies,
Gdbp = (Ga
dbp,Gi
dbp):
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10. Incomplete Data Source
An incomplete data source of Tarantino movies,
Gdbp = (Ga
dbp, Gi
dbp):
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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.
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12. Incomplete Data Source
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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) | ∅),
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data 13 / 31

14. 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))
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15. 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.
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16. 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 Gi ⊆ Ga
.
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17. Completeness Statements
Cdir = Compl((?m, type, Movie), (?m, director, tarantino) | ∅)
Question: Gdbp |= Cdir ?
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18. Completeness Statements
Cdir = Compl((?m, type, Movie), (?m, director, tarantino) | ∅)
Question: Gdbp |= Cdir ?
Yes, because QCdir Gi
dbp
⊆ Ga
dbp.
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19. Completeness Statements
Cact = Compl((?m, actor, ?a) | (?m, type, Movie), (?m, director, tara)
Question: Gdbp |= Cact ?
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20. Completeness Statements
Cact = Compl((?m, actor, ?a) | (?m, type, Movie), (?m, director, tara)
Question: Gdbp |= Cact ?
No, because among the results of QCact Gi
dbp
,
there is (reservoirDogs, actor, tarantino) not in Ga
dbp.
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21. Completeness Statements in RDF
Cact = Compl((?m, actor, ?a) | (?m, type, Movie), (?m, director, tara)
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22. Query Completeness: Example
Qdir = ({?m}, {(?m, type, Movie), (?m, director, tarantino)})
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23. Query Completeness: Example
Qdir = ({?m}, {(?m, type, Movie), (?m, director, tarantino)})
Then, Qdir Gi
dbp
= Qdir Ga
dbp
, and therefore Gdbp |= Compl(Qdir ).
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24. 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) if and only if Q Gi = Q Ga .
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25. 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).
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26. Completeness Reasoning
Transfer Operator
For any set C of completeness statements and a graph G,
we define the transfer operator TC:
TC(G) =
C∈ C
QC G
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27. Completeness Reasoning
Transfer Operator
For any set C of completeness statements and a graph G,
we define the transfer operator TC:
TC(G) =
C∈ C
QC G
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.
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28. Completeness of Basic Queries
Theorem
Let C be a set of completeness statements and
Q = (W, P) a basic query. Then,
C |= Compl(Q) if and only if ˜P = TC(˜P).
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29. 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) }.
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30. 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) }
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31. Completeness Reasoning: Example
Cdir,act = { Cdir , Cact }
Qdir+act = ({ ?m }, Pdir+act )
Therefore,
TCdir,act
(˜Pdir+act )
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32. Completeness Reasoning: Example
Cdir,act = { Cdir , Cact }
Qdir+act = ({ ?m }, Pdir+act )
Therefore,
TCdir,act
(˜Pdir+act )
= QCdir ˜Pdir+act
∪ QCact ˜Pdir+act
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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),
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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) }
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35. 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 )
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36. The framework can also be applied to:
DISTINCT Queries
OPT Queries
Queries with RDFS Data Sources
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37. Federated Framework
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38. 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/.
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39. 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.
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40. Terima kasih, grazie, danke!!
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