Completeness Statements at ISWC 2013
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Transcript of Completeness Statements at ISWC 2013
Completeness Statements about RDF Data Sources andTheir Use for Query Answering
Fariz Darari
Werner NuttGiuseppe Pirrò
Simon Razniewski
Presented at ISWC 2013Supported by SWSA with the Travel Grant
Oct 23rd, 2013
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 1 / 30
Motivation
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 2 / 30
Motivation
Completeness statement about the IMDB data source
Quentin Tarantinowas the character
Mr. Brown
…………………………
……………
http://www.imdb.com/title/tt0105236/fullcredits?ref_=tt_ov_st_sm#cast
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 3 / 30
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 Oct 23rd, 2013 7 / 30
Incomplete Data Source
An incomplete data source of Tarantino movies,Gdbp = (Ga
dbp,Gidbp):
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 8 / 30
Incomplete Data Source
An incomplete data source of Tarantino movies,Gdbp = (Ga
dbp,Gidbp):
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 9 / 30
Incomplete Data SourceAn incomplete data source of Tarantino movies,Gdbp = (Ga
dbp,Gidbp):
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 10 / 30
Incomplete Data Source
Incomplete Data SourceAn 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
Completeness Statements: Examples
To express that a source is completefor 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 completefor 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
Completeness Statements: Examples
To express that a source is completefor 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 completefor 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
Completeness Statement: Definition
Let P1 be a non-empty BGP (Basic Graph Pattern) andP2 a BGP.A completeness statement is defined as
Compl(P1 | P2)
where we call P1 the pattern and P2 the conditionof the statement.
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 13 / 30
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
JQCKGi ⊆ Ga.
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 14 / 30
Completeness Statements
Cdir = Compl((?m, type,Movie), (?m,director , tarantino) | ∅)
Question: Gdbp |= Cdir ?
Yes, because JQCdir KGidbp⊆ Ga
dbp.
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 15 / 30
Completeness Statements
Cdir = Compl((?m, type,Movie), (?m,director , tarantino) | ∅)
Question: Gdbp |= Cdir ?Yes, because JQCdir KGi
dbp⊆ Ga
dbp.Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 15 / 30
Completeness Statements
Cact = Compl((?m,actor , ?a) | (?m, type,Movie), (?m,director , tara))
Question: Gdbp |= Cact?
No, because among the results of JQCact KGidbp
,there is (reservoirDogs,actor , tarantino) not in Ga
dbp.
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 16 / 30
Completeness Statements
Cact = Compl((?m,actor , ?a) | (?m, type,Movie), (?m,director , tara))
Question: Gdbp |= Cact?No, because among the results of JQCact KGi
dbp,
there is (reservoirDogs,actor , tarantino) not in Gadbp.
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 16 / 30
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
Query Completeness: Example
Qdir = ({?m}, {(?m, type,Movie), (?m,director , tarantino)})
Then, JQdirKGidbp
= JQdirKGadbp
, and therefore Gdbp |= Compl(Qdir ).
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 18 / 30
Query Completeness: Example
Qdir = ({?m}, {(?m, type,Movie), (?m,director , tarantino)})
Then, JQdirKGidbp
= JQdirKGadbp
, and therefore Gdbp |= Compl(Qdir ).Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 18 / 30
Query Completeness: Definition
DefinitionLet 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 JQKGi = JQKGa .
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 19 / 30
Completeness Entailment
Let C be a set of completeness statements andQ a SELECT query.We say that C entails the completeness of Q, written
C |= Compl(Q),
if any incomplete data source satisfying Calso satisfies Compl(Q).
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 20 / 30
Completeness Reasoning
Transfer OperatorFor any set C of completeness statements and a graph G,we define the transfer operator TC:
TC(G) =⋃
C∈C
JQCKG
Prototypical Graph
Let Q = (W ,P) be a SELECT query.The prototypical graph P̃ is the graph resultingfrom the mapping of variables in P to fresh, unique IRIs.
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 21 / 30
Completeness Reasoning
Transfer OperatorFor any set C of completeness statements and a graph G,we define the transfer operator TC:
TC(G) =⋃
C∈C
JQCKG
Prototypical Graph
Let Q = (W ,P) be a SELECT query.The prototypical graph P̃ is the graph resultingfrom the mapping of variables in P to fresh, unique IRIs.
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 21 / 30
Completeness of Basic Queries
TheoremLet C be a set of completeness statements andQ = (W ,P) a basic query. Then,
C |= Compl(Q) if and only if P̃ = TC(P̃).
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 22 / 30
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
Completeness Reasoning: Example
Consider the set of completeness statements
Cdir ,act = {Cdir ,Cact }
and the query
Qdir+act = ({ ?m },Pdir+act)
Then,
P̃dir+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
Completeness Reasoning: Example
Cdir ,act = {Cdir ,Cact }
Qdir+act = ({ ?m },Pdir+act)
Therefore,
TCdir,act (P̃dir+act)
= JQCdir KP̃dir+act∪ JQCact KP̃dir+act
= { (c?m, type,Movie), (c?m,director , tara), (c?m,actor , tara) }= P̃dir+act .
Thus, Cdir ,act |= Compl(Qdir+act)
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
Completeness Reasoning: Example
Cdir ,act = {Cdir ,Cact }
Qdir+act = ({ ?m },Pdir+act)
Therefore,
TCdir,act (P̃dir+act)= JQCdir KP̃dir+act
∪ JQCact KP̃dir+act
= { (c?m, type,Movie), (c?m,director , tara), (c?m,actor , tara) }= P̃dir+act .
Thus, Cdir ,act |= Compl(Qdir+act)
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
Completeness Reasoning: Example
Cdir ,act = {Cdir ,Cact }
Qdir+act = ({ ?m },Pdir+act)
Therefore,
TCdir,act (P̃dir+act)= JQCdir KP̃dir+act
∪ JQCact KP̃dir+act
= { (c?m, type,Movie), (c?m,director , tara),
(c?m,actor , tara) }= P̃dir+act .
Thus, Cdir ,act |= Compl(Qdir+act)
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
Completeness Reasoning: Example
Cdir ,act = {Cdir ,Cact }
Qdir+act = ({ ?m },Pdir+act)
Therefore,
TCdir,act (P̃dir+act)= JQCdir KP̃dir+act
∪ JQCact KP̃dir+act
= { (c?m, type,Movie), (c?m,director , tara), (c?m,actor , tara) }
= P̃dir+act .
Thus, Cdir ,act |= Compl(Qdir+act)
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
Completeness Reasoning: Example
Cdir ,act = {Cdir ,Cact }
Qdir+act = ({ ?m },Pdir+act)
Therefore,
TCdir,act (P̃dir+act)= JQCdir KP̃dir+act
∪ JQCact KP̃dir+act
= { (c?m, type,Movie), (c?m,director , tara), (c?m,actor , tara) }= P̃dir+act .
Thus, Cdir ,act |= Compl(Qdir+act)
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 25 / 30
The framework can also be applied to:
DISTINCT QueriesOPT QueriesQueries with RDFS Data Sources
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 26 / 30
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 SPARQLqueries depending on the completeness statements ofa single data source.Developed in Java using the Apache Jena library.Takes three inputs:
Completeness statements in RDF formatA 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
Conclusions and Future Work
We developed a theoretical framework for the expression ofcompleteness statements about data sources, from whichwe can ensure query completeness.We provide a compact RDF representation of completenessstatements, which can be embedded in VoID descriptions,and implemented the framework in CoRner.We are interested in studying completeness reasoning withmore expressive queries and OWL 2.
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 29 / 30
Terima kasih, grazie, danke!!
Link to References
Fariz Darari (ISWC 2013) Completeness Reasoning @ Linked Data Oct 23rd, 2013 30 / 30