Managing Completeness of Web Data

Managing Completeness of Web Data
Fariz Darari
PhD Supervisor: Werner Nutt
Supported by the project MAGIC, funded by the province of Bolzano
Fariz Darari (unibz) Managing Completeness of Web Data Oct 20, 2015 1 / 38

About Us

Research Group
Sorted by distance to Werner’s ofﬁce :)

Bozen-Bolzano

Motivation

Completeness statements are already there

However . . .
Completeness statements are available
but only in natural language
Unclear what data completeness & query completeness mean
No techniques to check whether data completeness entails
query completeness

Solution Ideas
Solution: RDF-ize completeness statements

Solution Ideas
Solution: Formalize data completeness & query completeness

Solution Ideas
Solution: Formalize data completeness & query completeness
No techniques to check whether data completeness entails
query completeness
Solution: Develop techniques to check whether data completeness
entails query completeness

Solutions

Background: RDF
Grd = { (resDogs, dir, tarantino),
(resDogs, act, tarantino) }

Background: SPARQL
SELECT
Qsdir = ({ ?m }, { (?m, dir, tarantino) })
ASK
Qadir = ({ }, { (?m, dir, tarantino) })
CONSTRUCT
Qcdir = ({ (?m, dir, tarantino) }, { (?m, dir, tarantino) })

Story: Incomplete Data Source
An incomplete data source of Reservoir Dogs,
Gdbp = (Ga
dbp, Gi
dbp):
Ga
dbp = {(resDogs, dir, tarantino)}

Story: Incomplete Data Source
An incomplete data source of Reservoir Dogs,
Gdbp = (Ga
dbp, Gi
dbp):
Gi
dbp = {(resDogs, dir, tarantino), (resDogs, act, tarantino)}

Story: Completeness Statement
Ga
Gi
From (Ga
dbp, Gi
dbp), we can say that DBpedia is complete
for movies directed by Tarantino:
Cdir = Compl((?m, dir, tarantino) | ∅)

Story: Completeness Statement
Ga
Gi
From (Ga
dbp, Gi
dbp), we can say that DBpedia is complete
for movies directed by Tarantino:
Cdir = Compl((?m, dir, tarantino) | ∅)
However, it is not complete for actors in movies directed by Tarantino:
Cact = Compl((?m, act, ?a) | (?m, dir, tarantino))

Story: Query Completeness
Ga
Gi
Consequently, when we ask for all movies directed by Tarantino
over DBpedia:
Qdir = ({?m}, {(?m, dir, tarantino)})
the query completeness Compl(Qdir ) is obtained.

Story: Query Completeness
Ga
Gi
However, if we ask for all movies directed by and starring Tarantino:
Qdir+act = ({?m}, {(?m, dir, tarantino), (?m, act, tarantino)})
the query completeness Compl(Qdir+act ) is not obtained.

Incomplete Data Source
Deﬁnition (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.

Completeness Statement
Deﬁnition (Completeness Statement)
Let P1 be a non-empty BGP 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.

Satisfaction of Completeness Statements
To a statement
C = Compl(P1 | P2),
we associate the CONSTRUCT query
QC = (P1, P1 ∪ P2).
Then, we say:
C is satisﬁed by an incomplete data source G = (Ga, Gi),
written G |= C, if
QC Gi ⊆ Ga
.

Completeness Statements in RDF
Cact = Compl((?m, act, ?a) | (?m, dir, tarantino))
lv:dataset a void:Dataset;
c:hasComplStmt lv:csAct.
lv:csAct c:hasPattern [c:subject [c:varName "m"];
c:predicate s:actor;
c:object [c:varName "a"]];
c:hasCondition [c:subject [c:varName "m"];
c:predicate s:director;
c:object lmdb:Quentin_Tarantino].

Query Completeness
Deﬁnition (Query Completeness)
Let Q be a 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
Q Gi = Q Ga .

Completeness Entailment
Problem Deﬁnition (Completeness Entailment)
Let C be a set of completeness statements and Q a 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).

Intuition: Completeness Entailment
Consider the set Cdir,act = { Cdir , Cact } of completeness statements
and the query Qdir+act = ({ ?m }, Pdir+act ) where
Pdir+act = { (?m, dir, tarantino), (?m, act, tarantino) }.

and the query Qdir+act = ({ ?m }, Pdir+act ).
˜Pdir+act = { ( ˜m, dir, tarantino), ( ˜m, act, tarantino) }

Therefore,
QCdir ˜Pdir+act
∪ QCact ˜Pdir+act
=

Therefore,
QCdir ˜Pdir+act
=
{ ( ˜m, dir, tarantino), ( ˜m, act, tarantino) } =

Therefore,
QCdir ˜Pdir+act
=
{ ( ˜m, dir, tarantino), ( ˜m, act, tarantino) } =
˜Pdir+act .
Thus,
Cdir,act |= Compl(Qdir+act ).

Prototypical Graph
Deﬁnition (Prototypical Graph)
Let Q = (W, P) be a query.
The freeze mapping ˜id is deﬁned as a mapping
from each variable ?v in P to a new IRI ˜v.
Instantiating the graph pattern P with ˜id yields the graph
˜P := ˜id P,
which we call the prototypical graph of Q.

Transfer Operator
QCdir ˜Pdir+act
Deﬁnition (Transfer Operator)
For any set C of completeness statements and a graph G,
we deﬁne the transfer operator TC that computes the union
of the evaluation over G of all CONSTRUCT queries
of the statements in C:
TC(G) =
C∈ C
QC G

Completeness Entailment Theorem
˜Pdir+act = TCdir,act
(˜Pdir+act )
Theorem (Completeness of Basic Queries)
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).

Query Class: DISTINCT Queries
Give us all Oscar-winning things:
Qawd = (Wawd , Pawd )d =
({?m}, { (?m, award, oscar), (?m, award, ?aw) })d
Complete for all Oscar-winning things:
Cos = Compl((?m, award, oscar) | ∅)
{ Cos } |= Compl(Qawd ) holds?

Query Class: OPT Queries
Give us all movies, and their awards, if any:
Qmaw = ({ ?m, ?aw }, ((?m, a, Movie) OPT (?m, award, ?aw)))
Complete for all movies and their awards:
Caw = Compl((?m, a, Movie), (?m, award, ?aw) | ∅)
{ Caw } |= Compl(Qmaw ) holds?

Query Class: Queries under RDFS Semantics
Give us all films:
Qfilm = ({ ?m }, { (?m, a, Film) })
Complete for all movies:
Cmovie = Compl((?m, a, Movie) | ∅)
Films are the same as movies:
Sfm = {(Film, subclass, Movie), (Movie, subclass, Film)}
{ Cmovie } |= Compl(Qfilm) wrt. Sfm holds?

Federated Completeness Statements

Timestamped Completeness Statements

Conclusions

Conclusions
Completeness statements can now be represented in RDF
We know how completeness statements can entail query
completeness in different query classes and
different settings of completeness statements

Future Work
Completeness statements for queries with negation
Completeness statements as session annotations
for RDF streams
Statistical completeness reasoning

Publications
Fariz Darari, Werner Nutt, Giuseppe Pirrò, Simon Razniewski: Completeness
Statements about RDF Data Sources and Their Use for Query Answering.
ISWC 2013.
Fariz Darari, Radityo Eko Prasojo, Werner Nutt: CORNER: A Completeness
Reasoner for SPARQL Queries Over RDF Data Sources. ESWC Posters and
Demos 2014.
Fariz Darari, Simon Razniewski, Werner Nutt: Bridging the Semantic Gap
between RDF and SPARQL using Completeness Statements. ISWC Posters
and Demos 2014.
Fariz Darari, Radityo Eko Prasojo, Werner Nutt: Expressing No-Value
Information in RDF. ISWC Posters & Demos 2015.
The latest results (timestamped statements and efﬁcient completeness
reasoning with 1 million statements) have been submitted to a journal.

Compl((myDaSePresentation, slide, ?s) | ∅)
Thank You!

Managing Completeness of Web Data

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