Presentation of "Querying Linked Data and Büchi automata" in SMAP 2014

1. Querying Linked Data and Büchi automata
Konstantinos Giannakis and Theodore Andronikos
Department of Informatics
Ionian University
tkgiann; andronikosu@ionio.gr
9th Int. Workshop on Semantic and Social Media
Adaptation and Personalization
Corfu, Greece,
November 6, 2014
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 1 / 22

2. 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

3. Initial thoughts (1/2)
• Booming develpment of semantic technologies and
applications.
• 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

4. 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

5. 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

6. 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

7. 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/
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8. LOD evolution
(a) LOD cloud 2007 (b) LOD cloud 2009
(c) LOD cloud 2011
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 8 / 22

9. 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-lexical
knowledge, Vrandecíc et al.)
• !-automata
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 9 / 22

10. Web(s) of LD and LD machines
Web of Linked Data
Let T = (U Y B) U (U Y B Y L) denotes the infinite set of all RDF
triples. W = (D, data, adoc) defines the Web of LD where D is the set
of 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 a
finite set of states; two read-only input tapes: i) an input tape and ii) a
right-infinite Web tape; two work tapes: iii) a two-way infinite work
tape 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 computability
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11. 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 steps
producing 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 output
tape at each step of the computation is a prefix of a
possible encoding of q(W) and in finite horizon it returns
some output.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 11 / 22

12. 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

13. !-Computability
• !-automata.
Infinite input.
Acceptance conditions
Example for the !-regular expression ppfuqfdq!
.
nat1
nat2
mis
f
f
u; d
d
• Büchi automata.
Büchi acceptance condition.
It accepts the runs for which In() X F H (F „ Q).
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 13 / 22

14. 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

15. Schema
query1
query2
sg1
sg2
sg3
sg4
sg5
sg6
sg7
graph1
graph2
graph3
sg8
server1
server2
.............
.............
Figure: Query mechanism on an infinite Web of LD.
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16. Successfull eventual computation
• Infinite query - result in finite horizon, inifinite link traversal
result
sea..
rch search search search
result
.....
Figure: Eventual computability of SPARQL queries on an infinite
Web of LD.
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17. Our automaton
.
s0
s1
s2
s3
s4
o
w
o
u
o
u
o
Figure: It accepts the !-regular language upppwoq oquq pouq!. The
properties of eventual computability are satisfied.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 17 / 22

18. Adding complexity
.
s0
s1
s2
s3
s4
o
w
o
u
o
u;w
o
Figure: It accepts the !-regular language upppwoq oquq
popu wqq!. The properties of eventual computability are satisfied.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 18 / 22

19. Discussion
• Verification of eventually computable SPARQL queries on
webs of LD.
• Schema of a Büchi automaton accepting infinite
sequences of read URIs
• Novel approach, combining such queries with automata
with infinite input.
Need for deeper coverage of the mechanism of querying
infinite interlinked data.
• LOD project and similar efforts - perfect examples of
systems with infinite behaviour.
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 19 / 22

20. 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

21. 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 and
Semantics. Elsevier Science, 1990, pp. 133–192.
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22. Any Questions?
Thank you for your attention!
K. Giannakis and T. Andronikos Querying Linked Data and Büchi automata 22 / 22