efficient query answering against dynamic rdf databases

Efficient Query Answering againstDynamic RDF Databases

François Goasdoué, Ioana Manolescu,Alexandra Roatis

Université Paris-Sud & Inria Saclay (OAK project)

20 March 2013

Overview

EDBT 2013 Efficient Query Answering against Dynamic RDF Databases 2 / 35

The Resource Description Framework

Basic Graph Pattern Queries

Contributions

Experiments

Related Work

Conclusion

The Resource Description Framework

The Resource Description Framework (RDF)


⊲ graph-based data model⊲ W3C standard




RDF Graph:

⊲ set oftriples: s p o s ∈ U ∪B, p ∈ U, o ∈ U ∪B ∪ L

U – URIs,L – literals (constants),B – blank nodes

thesubjectshas thepropertypwith the value: theobjecto




RDF Graph:




⊲ built-in property: rdf:type

specify to whichclassesa resource belongs




RDF Graph:




⊲ built-in property: rdf:type

specify to whichclassesa resource belongs

Constructor Triple Relational notation

Class assertion s rdf:type o o(s)Property assertion s p o p(s, o)

Blank nodes


⊲ feature of RDF⊲ supportunknown URI/literal tokens

Blank nodes



Example:

the country of_:b1 is Italy

Blank nodes



Example:

the country of_:b1 is Italythe city of the same_:b1 is Genoa

Blank nodes



Example:

the country of_:b1 is Italythe city of the same_:b1 is Genoa

the population ofGenoais an unspecified value_:b2

Running example


book1

“Good Omens”

“Neil Gaiman”

“Terry Pratchett”

Book

English

_:b0

_:b1

Language

writtenIn

hasLanguage

Publication

rdfs:subClassOf

rdfs:subClassOf

rdfs:domain

rdfs:range rdfs:subPropertyOf

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type

RDF Schema (RDFS)


⊲ feature of RDF⊲ enhance the descriptions in graphs⊲ declaresemantic constraintsbetween classes and properties

RDF Schema (RDFS)


⊲ feature of RDF⊲ enhance the descriptions in graphs⊲ declaresemantic constraintsbetween classes and properties

Built-in properties:

⊲ subclass relationships:rdfs:subClassOf⊲ subproperty relationships:rdfs:subPropertyOf⊲ typing the first attribute (domain) of a property:rdfs:domain⊲ typing the second attribute (range) of a property:rdfs:range

Constructor Triple Relational notation

Subclass constraint s rdfs:subClassOf o s ⊆ o

Subproperty constraint s rdfs:subPropertyOf o s ⊆ o

Domain typing constraint s rdfs:domain o Πdomain(s) ⊆ o

Range typing constraint s rdfs:range o Πrange(s) ⊆ o

Running example


book1

“Good Omens”

“Neil Gaiman”


Book

English

_:b0

_:b1

Language

writtenIn

hasLanguage

Publication

rdfs:subClassOf

rdfs:subClassOf

rdfs:domain

rdfs:range rdfs:subPropertyOf

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type

Open-world assumption and RDF entailment


TheRDF data model is based on theopen-world assumption.→ deductive constraints – implicitlypropagate tuples

Implicit triples→ considered part of the graph – not explicitly present





Entailment – reasoning mechanismset ofexplicit triples& someentailment rules

deriveimplicit information







Exhaustive application of entailment rules→ saturation(a.k.a.closure)

The saturation of a graph isunique (up to blank node renaming).







Exhaustive application of entailment rules→ saturation(a.k.a.closure)

The saturation of a graph isunique (up to blank node renaming).

Entailment is part of the RDF specification itself.

The semantics of an RDF graph is its saturation.

Entailment rules by example




1)

book1Book

Publication

rdfs:subClassOf

rdf:type

rdf:type



1)

book1Book

Publication

rdfs:subClassOf

rdf:type

rdf:type

2)

book1writtenIn

hasLanguage English

rdfs:subPropertyOf writtenIn hasLanguage



1)

book1Book

Publication

rdfs:subClassOf

rdf:type

rdf:type

2)

book1writtenIn

hasLanguage English


3)

book1writtenIn

Book English

rdfs:domain writtenInrdf:type



1)

book1Book

Publication

rdfs:subClassOf

rdf:type

rdf:type

2)

book1writtenIn

hasLanguage English


3)

book1writtenIn

Book English

rdfs:domain writtenInrdf:type

4)

book1writtenIn

Language English

rdfs:range writtenInrdf:type

Basic Graph Pattern Queries

Basic Graph Pattern (BGP) Queries


⊲ subset of SPARQL

⊲ BGP –conjunction of triple patterns(or triples)

q(x):- t1, . . . , tα

ti = si pi oi, si, pi ∈ U ∪B ∪ V, oi ∈ U ∪B ∪ V ∪ L

x ∈ V (distinguished variables)





q(x):- t1, . . . , tα



query evaluationtreats blank nodesin a query asnon-distinguished variables





q(x):- t1, . . . , tα



query evaluationtreats blank nodesin a query asnon-distinguished variables

Example:

q(x, y):- x hasAuthor z, x rdf:type y≡

q(x, y):- x hasAuthor _:b0, x rdf:type y

Query answering


Problem:

queryevaluation6= queryanswering

Query answering


Problem:


the evaluation of a query only uses the graph’sexplicit triplesmay lead to anincomplete answer set

the(complete) answer setis obtained by evaluating the queryagainst the graph’ssaturation

Query answering


Problem:




Solution:

decoupleRDF entailment from query evaluation

Query answering


Problem:




Solution:

decoupleRDF entailment from query evaluation

Perform apre-processingstep to deal with entailed triples:

⊲ on the database –data saturation⊲ on the queries –query reformulation

Data saturation vs. Query reformulation


Data saturation

Advantages:

⊲ straightforward⊲ easy to implement

Drawbacks:

⊲ computation time⊲ additional storage space⊲ must be recomputed upon

database updates

Example:

the YAGO2 dataset doubles insize when computing theRDFS-closure→ 33M to 64M triples

Query reformulation

Advantages:

⊲ database saturation does not needto be (re)computed

Drawbacks:

⊲ every incoming query must bereformulated

⊲ reformulations can beprohibitively large

⊲ difficult to optimize

Example:

a single atom query over YAGO2,can yield of union of > 300 000queries

Contributions

Contributions


1. The database (DB) fragment of RDFextending previously studied fragments by the support ofblank nodes

2. Novel BGP query answering techniques for this DB fragmentdesigned to work on top of on anystandard conjunctive query processor

(i) an efficientincremental RDF saturation maintenance algorithm

(ii) a novelreformulation-based query answering algorithm

3. Thorough performance comparison and analysis

The database (DB) fragment of RDF


⊲ restricts entailment toRDFS entailment⊲ doesnot restrict graphs in any way




An RDF database: db = 〈D, S〉

D & S – disjoint sets of triplesD (RDF) – instance level→ assertionsS (RDFS)– schema level→ semantics




An RDF database: db = 〈D, S〉

D & S – disjoint sets of triplesD (RDF) – instance level→ assertionsS (RDFS)– schema level→ semantics

db =

⟨

book1

“Good Omens”

“Neil Gaiman”


Book

English

_:b0 Language

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type ,

Book

_:b1

Language

writtenIn

hasLanguage

Publication

rdfs:subClassOf

rdfs:subClassOf

rdfs:domain

rdfs:range rdfs:subPropertyOf⟩

Query reformulation algorithm


Reformulate(q, db)

⊲ fixpoint algorithm(13 reformulation rules)



Reformulate(q, db)

⊲ fixpoint algorithm(13 reformulation rules)⊲ reformulatesq into aset of queriess.t.theunionof theevaluationsof these queriesondb produces the correct answer



Reformulate(q, db)


Book

_:b1

Language writtenIn

hasLanguage

Publicationrdfs:subClassOf

rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

Reformulate(q, db) =

q(x, y):- x rdf:type y



Reformulate(q, db)


Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf


q(x, y):- x rdf:type y∪

q(x,Publication):- x rdf:type Publication



Reformulate(q, db)


Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf



q(x,Publication):- x rdf:type Publication∪

q(x,Publication):- x rdf:type Book



Reformulate(q, db)


Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf




q(x,Publication):- x rdf:type Book∪

q(x,Publication):- x writtenIn z



Reformulate(q, db)


Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf




q(x,Publication):- x rdf:type Book∪

q(x,Publication):- x writtenIn z

∪ . . .∪q(x, _:b1):- x rdf:type _:b1

∪ . . .



Reformulate(q, db)


Book

_:b1

Language writtenIn

hasLanguage

Publication

LanguageEnglish

book1 _:b1

rdfs:subClassOf

rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

rdf:type

rdf:type

q(x, _:b1):- x rdf:type _:b1



Reformulate(q, db)


Book

_:b1

Language writtenIn

hasLanguage

Publication

LanguageEnglish

book1 _:b1

rdfs:subClassOf

rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

rdf:type

rdf:type


≡q(x, _:b1):- x rdf:type z



Reformulate(q, db)


Book

_:b1

Language writtenIn

hasLanguage

Publication

LanguageEnglish

book1 _:b1

rdfs:subClassOf

rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

rdf:type

rdf:type


≡q(x, _:b1):- x rdf:type z

Answer set:{〈book1, _:b1〉, 〈English, _:b1〉}wrong answer



Reformulate(q, db)

⊲ fixpoint algorithm(13 reformulation rules)⊲ reformulatesq into aset of queriess.t.theunionof thenon-standard evaluationsof these queries ondb produces the correctanswer

Book

_:b1

Language writtenIn

hasLanguage

Publication

LanguageEnglish

book1 _:b1

rdfs:subClassOf

rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

rdf:type

rdf:type


6≡q(x, _:b1):- x rdf:type z

Answer set:{〈book1, _:b1〉}correct answer



Reformulate(q, db)

⊲ fixpoint algorithm(13 reformulation rules)⊲ reformulatesq into aset of queriess.t.theunionof thenon-standard evaluationsof these queries ondb produces the correctanswer⊲ size of the output:O((6 ∗#db2)#q)

Database saturation algorithm


Saturate(db)

⊲ fixpoint algorithm (4 saturation rules)



Saturate(db)

⊲ fixpoint algorithm (4 saturation rules)⊲ explicitlyadds todb all its implicit triples



Saturate(db)

⊲ fixpoint algorithm (4 saturation rules)⊲ explicitlyadds todb all its implicit triples

Saturate(db) = db ∪

book1

Language

Publication

_:b1

English

rdf:type

rdf:type

hasLanguage

rdf:type



Saturate(db)

⊲ fixpoint algorithm (4 saturation rules)⊲ explicitlyadds todb all its implicit triples⊲ size of the output:O(#db2)



Saturate(db)

⊲ fixpoint algorithm (4 saturation rules)⊲ explicitlyadds todb all its implicit triples⊲ size of the output:O(#db2)⊲ computation time:O(#db3)



Saturate(db)

⊲ fixpoint algorithm (4 saturation rules)⊲ explicitlyadds todb all its implicit triples⊲ size of the output:O(#db2)⊲ computation time:O(#db3)

What about updates?

Saturation maintenance algorithm


Saturate+(db)

⊲ multisetvariant ofSaturate(db)⊲ allowssaturation maintenance upon updates

Saturation maintenance algorithm


Saturate+(db)

⊲ multisetvariant ofSaturate(db)⊲ allowssaturation maintenance upon updates

Saturate+(db) = db ∪

Book

book1

Language

Publication

_:b1

English

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type

Example of instance insertion


Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

book1

_:b1 Book

“Good Omens”

“Neil Gaiman”


English

_:b0 Language

Publication

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type

To insert the triple:

book1 FrenchwrittenIn



Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

book1

_:b1 Book

“Good Omens”

“Neil Gaiman”


English

_:b0 Language

Publication

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type



First saturate the triple usingdb:

book1

Language

Book

Publication

_:b1

French

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type



Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

book1

_:b1 Book

“Good Omens”

“Neil Gaiman”


English

French

_:b0 Language

Publication

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type

hasLanguage

rdf:type

writtenIn



First saturate the triple usingdb:

book1

Language

Book

Publication

_:b1

French

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type

Theninsert the explicit triple

andthe inferred ones indb.

Example of schema deletion


Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

book1

_:b1 Book

“Good Omens”

“Neil Gaiman”


English

_:b0 Language

Publication

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type

To delete the triple:

BookwrittenInrdfs:domain



Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:domain

rdfs:range

rdfs:subPropertyOf

book1

_:b1 Book

“Good Omens”

“Neil Gaiman”


English

_:b0 Language

Publication

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type



First infer affected data triplesusingdb:

book1

Book

Publication

_:b1

rdf:type

rdf:type

rdf:type



Book

_:b1

Language writtenIn

hasLanguage


rdfs:subClassOf

rdfs:range

rdfs:subPropertyOf

book1

_:b1 Book

“Good Omens”

“Neil Gaiman”


English

_:b0 Language

Publication

hasTitle

hasAuthor

hasAuthor

rdf:type

translatedTo

writtenIn

rdf:type

rdf:type

rdf:type

hasLanguage

rdf:type



First infer affected data triplesusingdb:

book1

Book

Publication

_:b1

rdf:type

rdf:type

rdf:type

Thendelete the explicit triple

andthe inferred ones fromdb.

Experiments

Experimental setup


• implementation in Java 1.6• deployed on top of a PostgreSQL v8.5 server• 6 indexes – all permutations of the (s, p, o) columns• the spo index is clustering• dictionary encoding

Graph characteristics and saturation times:

Graph Storage Barton DBpedia DBLP

#Schema in memory 101 5, 666 41

#Instance Triple(s, p, o) 34× 106 27× 106 8.4× 106

#Saturation Sat(s, p, o) 39× 106 30× 106 12× 106

Saturation increase (%) 14.91 10.65 41.05

#Multiset SatM(s, p, o, isExp, count) 73.5× 106 66× 106 18.7× 106

Multiset increase (%) 116.89 227.37 121.97

tsat (s) 4, 294 2, 742 748

tsat+ (s) 4, 586 2, 977 799

Query answering


• 26 hand-picked queries (between 1 and 10 triple patterns – 6 on average)• similar query answering times onSat andSatM

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Graph updates


• no impact on reformulation• saturation needs to maintainSatM• insertions & deletions• updates of one triple on the data and the schema

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Saturation thresholds


Thesaturation thresholdof a queryq (st(q)):the smallest integern s.t.

n× tref (q) > n× t

sat(q) + tsat+

tref (q) – time to answerq throughreformulation(usingTriple)tsat(q) – time to answerq based onsaturation(usingSatM)tsat+ – time to saturatedb (createSatM)

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Related Work

Outline of the positioning of our work


Query languageexpressive power

SPARQL

BGP queriesrelational

conjunctivequeries RDF fragment

expressive powerDL DB

[1, 3, 5]

[4, 6, 7]

[2]

thiswork

[1] ADJIMAN, P., GOASDOUÉ, F., AND ROUSSET, M.-C. SomeRDFS in the semantic web.JODS 8(2007).

[2] ARENAS, M., GUTIERREZ, C., AND PÉREZ, J. Foundations of RDF databases. InReasoning Web(2009).

[3] CALVANESE, D., GIACOMO, G. D., LEMBO, D., LENZERINI, M., AND ROSATI, R. Tractable reasoning and efficient query answering indescription logics: The DL-Lite family.Journal of Automated Reasoning (JAR) 39, 3 (2007).

[4] GOASDOUÉ, F., KARANASOS, K., LEBLAY, J., AND MANOLESCU, I. View selection in semantic web databases.PVLDB(2011).

[5] GOTTLOB, G., ORSI, G., AND PIERIS, A. Ontological queries: Rewriting and optimization. InICDE (2011). Keynote.

[6] KAOUDI, Z., MILIARAKI, I., AND KOUBARAKIS, M. RDFS reasoning and query answering on DHTs. InISWC(2008).

[7] URBANI, J., VAN HARMELEN, F., SCHLOBACH, S., AND BAL, H. QueryPIE: Backward reasoning for OWL Horst over very largeknowledge bases. InISWC(2011).

Conclusion

Conclusion


Summary:

⊲ RDF fragment (extending those studied in the literature)⊲ novelsaturation-andreformulation-based query answering techniques

robust to instance and schema updates⊲ algorithms directly deployable on top of any RDBMS⊲ thorough performance comparison and analysis

Conclusion


Summary:

⊲ RDF fragment (extending those studied in the literature)⊲ novelsaturation-andreformulation-based query answering techniques

robust to instance and schema updates⊲ algorithms directly deployable on top of any RDBMS⊲ thorough performance comparison and analysis

Future work:

An automated strategy to choose between the two techniques:

Saturate+(db) / Reformulate(q, db)

Thank you!


I you attention

Question

_:b1

_:b2

_:b3

thankpay

ask

ask

ask

rdf:type

rdf:type

rdf:type

Open-world interpretation of RDFS constraints


Constraint interpretation:

⊲ closed-world assumption (CWA)any fact not present in the database is assumednot to holddatabase facts do not respect a constraint→ inconsistency

R1 ⊆ R2 – any tuple in the relationR1 must also be in the relationR2

⊲ open-world assumption (OWA)facts may hold even though they arenot in the database

R1 ⊆ R2 – any tuple in the relationR1 is also in the relationR2

TheRDF data model is based onOWA.

RDF meets Relational Database Management Systems (RDBMS)


RDF graphs:incomplete relational databases based onV-tables

V-tables:allow using variables in their tuples

using a variable multiple times allows expressing joins on unknown values

BGP query answeringboils down toconjunctive query evaluationon asaturated database.

Saturation (related work)


• J. Broekstra and A. Kampman“Inferencing and truth maintenance in RDF Schema: Exploring a naivepractical approach”in PSSS Workshop, 2003.

• B. Bishop, A. Kiryakov, D. Ognyanoff, I. Peikov, Z. Tashev, and R. Velkov“OWLIM: A family of scalable semantic repositories”Semantic Web, vol. 2, no. 1, 2011.

• C. Gutierrez, C. A. Hurtado, and A. A. Vaisman“RDFS update: From theory to practice”in ESWC, 2011.

efficient query answering against dynamic rdf databases

Data & Analytics

rdf entailment edbt

rdf schema rdfs edbt

rdf data model

efcient query

s p o s u b

subpropertyof o s o

subclassof rdfs

range rdfs