N. Simou, G. Stoilos, V. Tzouvaras, G. Stamou, S. Kollias [email protected]4th International Workshop on Uncertainty Reasoning for the Semantic Web Sunday 26 th October, 2008 Karlsruhe, Germany Storing and Querying Fuzzy Knowledge in the Semantic Web National Technical University of Athens, Greece School of Electrical and Computer Engineering Department of Computer Science Image, Video and Multimedia Laboratory
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N. Simou, G. Stoilos, V. Tzouvaras, G. Stamou, S. Kollias [email protected] 4th International Workshop on Uncertainty Reasoning for the Semantic.
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N. Simou, G. Stoilos, V. Tzouvaras, G. Stamou, S. Kollias
4th International Workshop on Uncertainty Reasoning for the Semantic Web
Sunday 26th October, 2008 Karlsruhe, Germany
Storing and Querying Fuzzy Knowledge in the Semantic
Web
National Technical University of Athens, GreeceSchool of Electrical and Computer EngineeringDepartment of Computer ScienceImage, Video and Multimedia Laboratory
MotivationOntologies and OWL Language play a
significant role in the Semantic WebOptimized Reasoners (Fact, Pellet)Various tools for storing and querying OWL
ontologiesCrisp DLs lack the ability to represent uncertain
A SPARQL query is constructed in a way thatThe membership degrees of every Role or Concept used in
atoms criteria are retrieved for the individuals that satisfy all the atoms
The results are processed according to the query weights by FiRE permitting Fuzzy threshold queries using fuzzy implicationFuzzy aggregation queries using fuzzy aggregation
functionsFuzzy weighted queries using weighted t-norms
Use caseA production company had a database of 2140
models used for casting purposesRich information was stored for each model...
i.e. age, height, body type, fitness type, tooth condition…
Inaccessible to the producers becauseThe information was fuzzy The information was not semantically organizedRetrieval of models based on threshold criteria was
inaccurateThe combination of information about models that
would form profession-like characteristics (like Teacher, Mafia, Scientist ) was extremely difficult
The Fuzzy Knowledge baseThe set of Concepts consisted of the features
described in the databaseAge was fuzzified giving concepts Baby, Kid, Teen, 20s,30s,40s,
60s and OldHeight was fuzzified depending on the model’s gender giving
Using GLB for all individuals in all the concepts of the KB2430 implicit assertions were extracted (Fuzzy KRSS)Average time was 1112 milliseconds per individualUpload time to Sesame repository varied
from 200 millisecs in an empty repository (0-10.000 triples) to 700 millisecs in repository (over 500.000 triples)
Total 529.926 triples (Fuzzy OWL Triples)
ResultsQuery Native
100.000 250.000 500.000
Memory100.000 250.000 500.000
x <- Scientist(x) >= 0.6 1042 2461 3335 894 2368
3332
x <- Father(x)^ Teacher(x)>= 0.8 ^ NormalHeight(x)>= 0.5
1068 2694 3932 994 2524
3732
x <- Legs(x)^Eyes(x)>= 0.8 ^ 20s(x)>=0.5^hashairLength(x,y)^ Long(y)>= 0.7
1352 2876 4021 1002 2650
3809
x <- Scientist(x):0.6 2562 4173 3935 3042 4543
6027
x <- Father(x)^ Teacher(x) :0.8 ^NormalHeight(x):0.5
4318 6694 8935 4341 7896
9306
x <- Legs(x)^Eyes(x):0.8 ^ 20s(x):0.5^hashairLength(x,y)^Long(y):0.7
5423 6998 9230 5420 6879
9974
ConclusionsLimitations
Not complete query answering systemQueries are issued against stored assertions to an RDF
repositoryQueries on Sesame Repositories are not scalable
Dependence on size of the repositoryDependence on the number of query atoms
…HoweverIncompleteness is minimized by GLBQuery answering for crisp DLs is still an open
problem Query algorithms are highly complex No practically scalable system is known
References[Pan2007] J.Z. Pan, G. Stamou, G. Stoilos, and E.
Thomas. Expressive querying over fuzzy DL-Lite ontologies. In Proceedings of the International Workshop on Description Logics (DL 2007), 2007.
[Stoilos2007] G.Stoilos, G.Stamou, V.Tzouvaras, J.Z.Pan, and I.Horrocks. Reasoning with very expressive fuzzy description logics. Journal of Artificial Intelligence Research, 30(5):273-320, 2007.
[Straccia2007] U.Straccia and G.Visco. DLMedia: an ontology mediated multimedia information retrieval system. In Proceeedings of the International Workshop on Description Logics (DL 2007), 2007.
Questions - Acknowledgements
Thank you!
This work is supported by the FP6 Network of Excellence EU project X-Media (FP6-026978) and K-space (IST-2005-027026).
Fuzzy SHIN - Knowledge baseA fuzzy knowledge base is a triple
Σ= (T ,R, A) where:T is a finite set of fuzzy inclusion axioms: A ⊑
C or fuzzy equivalence axioms : A ≡ C, called a fuzzy TBox
R is a finite set of fuzzy transitive role axioms: Trans(R) or fuzzy role inclusion axioms P ⊑ R, called a fuzzy RBox
A is a finite set of fuzzy assertions: a : C⟨ ⋈ n ⟩ or ⟨ (a, b) : R ⋈ n ⟩, where ⋈ ∈ {≥,>,<, ≤}, called a fuzzy ABox.
Fuzzy SHIN - SemanticsA fuzzy interpretation is a pair I= (ΔI× .I) where ΔI is the
domain of interpretation and .I is the interpretation function which maps
An individual name α ∈ I to an element α I ∈ ΔI
A concept name A to a membership function AI : ΔI →[0,1]A role name R to a membership function RI : ΔI× ΔI
→[0,1]
Fuzzy set theoretic operations are used to give semantics to complex concepts