Alumni Fasilkom UI Raih Best EMCL Master Thesis Award 2013 – Fakultas Ilmu Komputer Universitas Indonesia

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Completeness Statements about RDF Data Sources and Their Use for Query Answering

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Research Story

Fariz Darari

Werner Nutt Giuseppe Pirrò Simon Razniewski

EMCL Workshop 2014, Vienna

Fariz Darari (EMCL Workshop 2014) Completeness Reasoning @ Linked Data 1 / 38

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Slides about Research

In this color!

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Slides about Research Story (Meta-Research)

In this color!

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Story: Motivation

I want to do a project and a thesis.

I like Semantic Web.

What can be a good research topic? Finding a good research topic (and good supervisor) is also part of research!

Werner: “Hi, we are doing research about completeness reasoning on databases”

Me: “Why not also on the Semantic Web?”

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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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Motivation

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Story: Literature Study

Hmm..for realizing my goal, what should I learn?

Aha, I need to learn Semantic Web, I think the Semantic Web Technologies course offered by FUB would be useful for me

Aha, I also need to learn existing work on completeness reasoning for databases, I guess this paper¹is worth to read!

1Completeness of Queries over Incomplete Databases by Simon and Werner

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Story: Google (and your supervisors) are

your Googles, ask them!

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Story: Start Doing Real Research – Problem Understanding

Completeness reasoning on databases has been investigated

Hmm..butdatabasesare different thanLinked Data, what should be adjusted?

Well, in Linked Data, instead ofdatabases, we haveRDF data sources

Well, in Linked Data, instead ofSQL, we haveSPARQLas a query language

Well, Linked Data also ismore open, more heterogeneous and federated

Well, Linked Data also hasontologies

Then, I have to discuss these issues with my supervisors!

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Incomplete Data Source

Quentin Tarantino is missing..

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Incomplete Data Source

An incomplete data source of Tarantino movies, G_dbp = (G^a_dbp,G_dbpⁱ ):

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Incomplete Data Source

An incomplete data source of Tarantino movies, G_dbp = (G^a_dbp,Gⁱ_dbp):

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Incomplete Data Source

An incomplete data source of Tarantino movies, Gdbp = (G^a_dbp,G_dbpⁱ ):

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Incomplete Data Source

Anincomplete data sourceis a pair of two graphs, G = (G^a,Gⁱ), whereG^a ⊆Gⁱ.

We callG^a theavailablegraph and Gⁱ theidealgraph.

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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)| ∅),

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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Completeness Statements: Examples

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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Completeness Statement: Definition

LetP1 be a non-empty BGP (Basic Graph Pattern) and P2a BGP.

Acompleteness statementis defined as Compl(P1|P2)

where we callP1thepatternandP2thecondition of the statement.

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Satisfaction of Completeness Statements

To the statement

C =Compl(P1 |P2),

we associate theCONSTRUCTquery QC = (P1,P1∪P2).

Then, we say:

C issatisfiedby an IDS G= (G^a,Gⁱ), writtenG |=C, if JQCKGⁱ ⊆G^a.

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Completeness Statements

Cdir =Compl((?m,type,Movie),(?m,director,tarantino)| ∅)

Question:G_dbp |=Cdir?

Yes, becauseJQC_dirKGⁱ_dbp ⊆G^a_dbp.

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Completeness Statements

Cdir =Compl((?m,type,Movie),(?m,director,tarantino)| ∅)

Question:G_dbp |=Cdir?

Yes, becauseJQCdirKG_dbpⁱ ⊆G^a_dbp.

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Completeness Statements

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

Question:Gdbp |=Cact?

No, because among the results ofJQCactKG_dbpⁱ ,

there is(reservoirDogs,actor,tarantino)not inG^a_dbp.

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Completeness Statements

Question:Gdbp |=Cact?

No, because among the results of JQCactKG_dbpⁱ ,

there is(reservoirDogs,actor,tarantino)not inG^a_dbp.

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Completeness Statements in RDF

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Query Completeness: Example

Qdir = ({?m},{(?m,type,Movie),(?m,director,tarantino)})

Then,JQdirKGⁱ_dbp =JQdirK^G^adbp, and thereforeGdbp |=Compl(Qdir).

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Query Completeness: Example

Qdir = ({?m},{(?m,type,Movie),(?m,director,tarantino)})

Then,JQdirKG_dbpⁱ =JQdirK^G^adbp, and thereforeG_dbp |=Compl(Qdir).

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Query Completeness: Definition

Definition

LetQ be aSELECTquery. We write Compl(Q) to say thatQ is complete.

An incomplete data sourceG = (G^a,Gⁱ)satisfiesCompl(Q), written

G |=Compl(Q) if and only if JQK^Gⁱ =JQK^G^a.

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Story: Defining Theorems to Prove

Theorems are formal representations of goals you want to achieve (remember the first slides about motivation) In fact..all the definitions and framework introduced before are actually to well-define these theorems

Hmm..I am sure these theorems should hold!

Then, I have to discuss these issues with my supervisors!

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Completeness Entailment

LetC be a set of completeness statements and QaSELECTquery.

We say thatC entails the completeness ofQ, written C |=Compl(Q),

if any incomplete data source satisfyingC also satisfiesCompl(Q).

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Completeness Reasoning

Transfer Operator

For any setC of completeness statements and a graphG, we define thetransfer operatorTC:

TC(G) = [

C∈ C

JQCK^G

Prototypical Graph

LetQ= (W,P)be aSELECTquery.

Theprototypical graph P˜ is the graph resulting

from the mapping of variables inP to fresh, unique IRIs.

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Completeness Reasoning

Transfer Operator

For any setC of completeness statements and a graphG, we define thetransfer operatorTC:

TC(G) = [

C∈ C

JQCK^G

Prototypical Graph

LetQ = (W,P)be aSELECTquery.

Theprototypical graphP˜ is the graph resulting

from the mapping of variables inP to fresh, unique IRIs.

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Completeness of Basic Queries

Theorem

LetC 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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Story: Start Doing The Hardcore Part - Proving Theorems

Argh, I got stuck

This proving theorems stuff always haunts me!

But:

Because you are Excellent Marvelous Champion Legendary (aka EMCL)

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Story: Start Doing The Hardcore Part - Proving Theorems (2)

Get the proof idea first

Generate some concrete examples of the problems with their solutions from the theorem you want to prove Discuss with your supervisors

Now, start to prove in detail

There is a problem on this, and that, then refine your proof idea, go back to the first point

Start doing the above points until (hopefully :) you are able to prove it

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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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Completeness Reasoning: Example

Consider the set of completeness statements Cdir,act ={Cdir,Cact}

and the query

Qdir+act = ({?m},Pdir+act) Then,

P˜dir+act =

{(c?m,type,Movie),(c?m,director,tarantino),(c?m,actor,tarantino)}.

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Completeness Reasoning: Example

C_dir_,act ={Cdir,Cact} Qdir+act = ({?m},Pdir+act)

Therefore,

TC_dir,act( ˜Pdir+act)

=JQC_dirKP^˜dir+act ∪JQCactKP^˜dir+act

={(c?m,type,Movie),(c?m,director,tara),(c?m,actor,tara)}

= ˜Pdir+act. Thus,C_dir,act |=Compl(Qdir+act)

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Completeness Reasoning: Example

Therefore,

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Completeness Reasoning: Example

Therefore,

={(c?m,type,Movie),(c?m,director,tara),

(c?m,actor,tara)}

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Completeness Reasoning: Example

Therefore,

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Completeness Reasoning: Example

Therefore,

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The framework can also be applied to:

DISTINCTQueries: with set semantics

OPTQueries: eg. get all people and in case they are not single, get also their spouse

Queries with RDFS Data Sources: incorporating ontologies

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Federated Framework

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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 athttp://rdfcorner.wordpress.com/.

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Story: Cooling Down, or is it?

I have got all the results

But, I haven’t started writing the thesis yet Nooo, I will miss the deadline :(

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Story: Cooling Down - Alternative

I have got all the results

And, I have started writing the thesis since the very beginning (right after I have studied the literature) I think I can manage to meet the deadline :)

Aha, I think our research results can be also useful if shown to the Semantic Web community, why not to try submit it at ISWC 2013? – Another research story :)

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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 inVoIDdescriptions, and implemented the framework inCoRner.

We are interested in studying completeness reasoning with more expressive queries and OWL 2.

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Terima kasih, grazie, danke!!

Link to References