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
Ä
Linked Data• SPARQL queries on them
Ä
Infinite nature• Social Networking Applications• Linked Open Numbers
Ä
Büchi automata• Their use in verification of webs of Linked Data.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 2 / 22
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).
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 3 / 22
Initial thoughts (2/2)
• Social data -> living organism
• Linked Data project -> “Living" Data project
• Concurrent and ongoing process.
• Computation on these data sources.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 4 / 22
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/"
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 5 / 22
Some background
• SPARQL• RDF query language• Basic graph pattern matching
• Linked Open Data• “900,129 documents describing 8,038,396 resources2"
2“Linking Open Data cloud diagram 2014, by M. Schmachtenberg, C. Bizer, A. Jentzsch and R. Cyganiak.
http://lod-cloud.net/"
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 6 / 22
Linked Open Data
Figure: LOD Cloud3
3“Linking Open Data cloud diagram 2014, by M. Schmachtenberg, C. Bizer, A. Jentzsch and R. Cyganiak.
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
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 9 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 11 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 12 / 22
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).
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 13 / 22
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
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 14 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 15 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 16 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 17 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 18 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 19 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 20 / 22
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.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 21 / 22
Any Questions?
Thank you for your attention!
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 22 / 22
Top Related