Querying Linked Data and Büchi automata

Querying Linked Data and Büchi automata

Konstantinos Giannakis and Theodore Andronikos

Department of InformaticsIonian University

tkgiann, [email protected]

9th Int. Workshop on Semantic and Social MediaAdaptation and Personalization

Corfu, Greece,November 6, 2014

K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 1 / 22

Outline of our work

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Linked Data• SPARQL queries on them

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Infinite nature• Social Networking Applications• Linked Open Numbers

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Büchi automata• Their use in verification of webs of Linked Data.


Initial thoughts (1/2)

• Booming develpment of semantic technologies andapplications.

• Social media and multimedia.

• Smart devices.

• Applications need to be efficient, trustworthy and verified.• Achieve what they promise (or what they are designed for).


Initial thoughts (2/2)

• Social data -> living organism

• Linked Data project -> “Living" Data project

• Concurrent and ongoing process.

• Computation on these data sources.


LOD and Social Data

Figure: Datasets1.

1“Linking Open Data cloud diagram 2014, by M. Schmachtenberg, C. Bizer, A. Jentzsch and R. Cyganiak.

http://lod-cloud.net/"


Some background

• SPARQL• RDF query language• Basic graph pattern matching

• Linked Open Data• “900,129 documents describing 8,038,396 resources2"


http://lod-cloud.net/"


Linked Open Data

Figure: LOD Cloud3


http://lod-cloud.net/"K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 7 / 22

LOD evolution

(a) LOD cloud 2007 (b) LOD cloud 2009

(c) LOD cloud 2011K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 8 / 22

Related Works

• Ontology evaluation and verification methodologies

• Graph pattern queries (“Querying regular graph patterns",Barceló et al.)

• Web of Linked Data

• Linked Open Numbers (“Leveraging non-lexicalknowledge", Vrandecíc et al.)

• ω-automata


Web(s) of LD and LD machines

Web of Linked DataLet T = (U Y B) ˆ U ˆ (U Y B Y L) denotes the infinite set of all RDFtriples. W = (D, data, adoc) defines the Web of LD where D is the setof symbols representing LD documents, data is a total mapping data:D Ñ 2T and adoc is a partial, surjective mapping adoc = U Ñ D.

LD machine 4

An LD machine is a multi-tape Turing machine with five tapes and afinite set of states; two read-only input tapes: i) an input tape and ii) aright-infinite Web tape; two work tapes: iii) a two-way infinite worktape and iv) a right-infinite link traversal tape; and v) a right-infinite,append-only output tape [...].

4SPARQL for a Web of Linked Data: Semantics and computabilityK. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 10 / 22

Query computability

˝ Finitely computable queries.• An LD query q is finitely computable if there exists an LD

machine which terminates after a finite number of stepsproducing a possible encoding of q(W ) on its output tape.

˝ Eventually computable queries.• An LD query q is eventually computable if there exists an

LD machine at whose computation the word on the outputtape at each step of the computation is a prefix of apossible encoding of q(W ) and in finite horizon it returnssome output.


Infinite horizon

• Two SPARQL query semantics• Full-web semantics.

• the scope of each query is the full set of LD on the Web.

• Reachability-based semantics.• restricted scope of SPARQL queries to data reachable

through specific links, using a given initial set of URIs.


ω-Computability

• ω-automata.• Infinite input.• Acceptance conditions• Example for the ω-regular expression ppfuq˚fdqω

..

nat1

..

mis

.

nat2

.

f

.

f

.

u, d

.

d

• Büchi automata.• Büchi acceptance condition.• It accepts the runs ρ for which In(ρ) X F ‰ H (F Ď Q).


Queries on infinite graphs of graphs

• We assume infinite web of LD• Reachability is guaranteed (remember, we refer to Linked

Data)• Acceptance is defined by a set of final states.• We intentionally ignore the existance of different query

plans• food for (future) thought.

• Infinite data/queries -> infinite computation


Schema

..

graph1

.

graph2

.

graph3

.

sg1

.

sg2

.

sg3

.

sg4

.

sg5

.

sg6

.

sg7

.

sg8

.

server1

.

server2

.

query1

.

query2

.....

.............

.

.............

Figure: Query mechanism on an infinite Web of LD.


Successfull eventual computation

• Infinite query -> result in finite horizon, inifinite link traversal

..search. search. search. search.

result

.

result

. .....

Figure: Eventual computability of SPARQL queries on an infiniteWeb of LD.


Our automaton

..

s0

.

s1

..

s2

.

s3

.

s4

.

o

.

w

.

o

.

u

.

o

.

u

.

o

Figure: It accepts the ω-regular language upppwoq ` oquq˚ pouqω. Theproperties of eventual computability are satisfied.


Adding complexity

..

s0

.

s1

..

s2

.

s3

.

s4

.

o

.

w

.

o

.

u

.

o

.

u,w

.

o

Figure: It accepts the ω-regular language upppwoq ` oquq˚

popu ` wqqω. The properties of eventual computability are satisfied.


Discussion

• Verification of eventually computable SPARQL queries onwebs of LD.

• Schema of a Büchi automaton accepting infinitesequences of read URIs

• Novel approach, combining such queries with automatawith infinite input.

• Need for deeper coverage of the mechanism of queryinginfinite interlinked data.

• LOD project and similar efforts -> perfect examples ofsystems with infinite behaviour.


Future work

♢ Büchi automata with LTL combined with the “eventual"character of such queries.

♢ Introduction of probabilities and probabilistic semantics.

♢ Issues of decidability, complexity and query performance.

♢ Introduction of temporal concepts.


Key References

BIZER, C., AND SCHULTZ, A.Benchmarking the performance of storage systems that expose sparql endpoints.World Wide Web Internet And Web Information Systems (2008).

HARTIG, O.Sparql for a web of linked data: Semantics and computability.In The Semantic Web: Research and Applications. Springer, 2012, pp. 8–23.

HARTIG, O., BIZER, C., AND FREYTAG, J.-C.Executing SPARQL queries over the web of linked data.Springer, 2009.

LOVRENCIC, S., AND CUBRILO, M.Ontology evaluation-comprising verification and validation.In CECIIS-2008 (2008).

THOMAS, W.Automata on infinite objects.In Handbook of Theoretical Computer Science, vol. B: Formal Models andSemantics. Elsevier Science, 1990, pp. 133–192.


Any Questions?

Thank you for your attention!


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Querying Linked Data and Büchi automata

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