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Storing and Querying Fuzzy Knowledge in the Semantic Web

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### 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

N. Simou, G. Stoilos, V. Tzouvaras,

G. Stamou, S. Kollias

nsimou@image.ece.ntua.gr

4th International Workshop on Uncertainty Reasoning for the Semantic Web

Sunday 26th October, 2008 Karlsruhe, Germany

Motivation

- Ontologies and OWL Language play a significant role in the Semantic Web
- Optimized Reasoners (Fact, Pellet)
- Various tools for storing and querying OWL ontologies
- Crisp DLs lack the ability to represent uncertain information
- Fuzzy DLs
- Fuzzy Reasoners (FiRE, fuzzyDL)
- No work on persistent storage and querying for expressive fuzzy DLs ([Straccia2007] and [Pan 2007] are based on fuzzy DL-Lite)

Contribution

- It presents a novel framework for persistent storage and querying of expressive fuzzy knowledge bases
- It integrates Fuzzy Reasoner FiRE with the RDF Triple Store Sesame
- It provides experimental evaluation of the proposed architecture using a real-world industrial use case scenario

Outline

- Queries in crisp DL
- RDF Stores
- The fuzzy DL f-SHIN
- Fuzzy Extensions to Queries
- Fuzzy OWL Syntax in Triples
- Sesame integration with FiRE
- Evaluation

Queries in DLs

- Conjunctive Queries
- e.g. x <- Man(x) ^ hasChild(x,y) ^ Man(y)
- Query answering algorithms for crisp DLs
- Are highly complex
- A practically scalable system is not available
- Various tools support queries for crisp DLs

RDF Stores

- Data storage systems for storing and querying ontologies
- Sesame, Jena, Kowari
- Ontologies are stored in various triples format
- RDF/XML
- N Triples
- Turtle
- Support of Query languages
- SPARQL
- SeRQL (Sesame)
- Plugins for incoplete OWL DL querying and reasoning (Sesame-OWLim)

Fuzzy SHIN - Syntax

- A fuzzy extension of DL SHIN
- f-SHIN concepts are formed in the same way as in SHIN

C,D ::=⊤ | ⊥ | ¬C | C⊓ D | C⊔ D |∃R.C | ∀R.C| ≥nR | ≤nR

R,P::= R- | Trans(R) | P⊑R

- Assertions are extended to fit uncertainty

〈 nick : Tall≥ 0.7 〉

〈 (nick, theo) : isFriend≥0.6 〉

Fuzzy SHIN - Inference Services

- Entailment
- “Does axiom Ψ logically follow from the ontology T?”
- Satisfiability
- “Can the concept C have any instances with degree of participation ⋈ n in models of ontology T?”
- Subsumption
- “Is the concept D more general than the concept C in models of the ontology T?”
- Greatest Lower Bound (GLB)
- “What is the greatest degree n that our ontology entails an individual a to participate in a concept C?”

Fuzzy Extensions to Queries

- Conjunctive threshold Queries (CTQs) [Pan2007 et al]
- E.g. x <- Tall(x)>0.6 ^ hasFriend(x,y)>0.7 ^ Short(y) > 0.8
- General Fuzzy Conjunctive Queries (GFCQs) [Pan2007 et al]
- E.g. x <- Tall(x):0.6 ^ hasFriend(x,y):0.7 ^ Short(y):0.8
- Supported only in Fuzzy DL-Lite

Fuzzy OWL Syntax in Triples

- Refication
- Weak and ill defined model
- Limited support by RDF tools
- Datatypes
- Concrete feature like datatypes are not appropriate for the representation of abstract information like fuzzy assertions
- The proposed syntax
- Is simple and clear
- Is based on the use of blank nodes and properties

Fuzzy OWL Syntax in Triples

- Fuzzy concept assertion

paul frdf:membership _:paulmembTall .

_:paulmembTall rdf:type Tall.

_:paulmembTall frdf:degree “n^^xsd:float”.

_:paulmembTall frdf:ineqType “>=” .

- Fuzzy role assertion

paul frdf:paulFriendOffrank frank.

frdf:paulFriendOffrank rdf:type FriendOf.

frdf:paulFriendOffrank frdf:degree “n^^xsd:float”.

frdf:paulFriendOffrank frdf:ineqType “>=”.

Fuzzy Reasoning Engine FiRE

- It is a JAVA based implementation available at

www.image.ece.ntua.gr/~nsimou/FiRE/

- Can be used through a user friendly interface or as an API
- Currently supports F-SHIN
- The reasoning algorithm uses the fuzzy tableau [Stoilos 2007]
- Its syntax is based on Knowledge Representation System Specification appropriately extended to fit uncertainty

E.g. (instance eve Model >= 0.7)

(related peter eve has-friend >= 0.8)

Sesame integration with FiRE

- RDF-Store Sesame is used as a back end for storing and querying.
- FiRE is used as a front end permitting a user to
- Write or edit a fuzzy knowledge base (Fuzzy KRSS Format)
- Ask the GLB of all the individuals of the KB in all the concepts (primitive and defined) of the KB
- Export the explicit and implicit knowledge to a Sesame repository using the proposed Fuzzy OWL syntax
- Import a fuzzy knowledge base from a Sesame repository
- Perform CTQs and GFCQs

Querying-I

- Conjunctive threshold Queries (CTQs)
- FiRE Syntax

x,y <- Man(x) ^ Tall(x)> 0.6 ^ hasfriend(x,y) > 0.7 ^ Woman(y) ^ GoodLooking(y) >= 0.8

- The query is converted to a SPARQL query based on the Fuzzy OWL syntax in triples
- The query is evaluated by Sesame
- The results are visualized by FiRE

Querying-II

- General Fuzzy Conjunctive Queries (GFCQs)
- FiRE Syntax

x,y <- Man(x)^ Tall(x) : 0.6 ^ has-friend(x,y) : 0.7 ^ Woman(y) ^ GoodLooking(y) : 0.8

- A SPARQL query is constructed in a way that
- The 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 implication
- Fuzzy aggregation queries using fuzzy aggregation functions
- Fuzzy weighted queries using weighted t-norms
- The results are visualized by FiRE

Fuzzy Query Examples

(instance peter Man)

(instance peter Thin >= 0.6 )

(instance peter Clever >= 0.8 )

(instance peter Tall >= 0.7 )

(instance eve Model >= 0.7)

(related peter eve has-friend >= 0.7)

- x,y <- Tall(x) > 0.2 ^ Clever(x) > 0.3 ^ has-friend(x,y) > 0.4 ^ Model(y) > 0.6
- x :peter y:eve
- x,y <- Tall(x) : 0.2 ^ Clever(x) : 0.3 ^ has-friend(x,y) : 0.4 ^ Model(y) : 0.6
- Using fuzzy aggregation queries
- i.e.
- <x,y> <peter eve> : 0.72

Use case

- A production company had a database of 2140 models used for casting purposes
- Rich information was stored for each model...
- i.e. age, height, body type, fitness type, tooth condition…
- Inaccessible to the producers because
- The information was fuzzy
- The information was not semantically organized
- Retrieval of models based on threshold criteria was inaccurate
- The combination of information about models that would form profession-like characteristics (like Teacher, Mafia, Scientist ) was extremely difficult

The Fuzzy Knowledge base

- The set of Concepts consisted of the features described in the database
- Age was fuzzified giving concepts Baby, Kid, Teen, 20s,30s,40s, 60s and Old
- Height was fuzzified depending on the model’s gender giving concepts Very_Short, Short, Normal_Height, Tall, Very_Tall
- The set of Roles consisted of some special characteristics
- i.e. has-hairLength, has-hairColor…
- The set of individuals consisted of the models
- An expressive terminology was defined with 33 concepts that refered to the professions of interest
- e.g. Scientist≡Male⊓Serious ⊓ (40s ⊔ 50s) ⊓ ∃has-eyeCondition.Glasses

Results

- Explicit knowledge
- 2140 individuals
- 82 Concepts 20 Roles
- 29469 assertions (Fuzzy KRSS)
- Using GLB for all individuals in all the concepts of the KB
- 2430 implicit assertions were extracted (Fuzzy KRSS)
- Average time was 1112 milliseconds per individual
- Upload 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)

Conclusions

- Limitations
- Not complete query answering system
- Queries are issued against stored assertions to an RDF repository
- Queries on Sesame Repositories are not scalable
- Dependence on size of the repository
- Dependence on the number of query atoms
- …However
- Incompleteness is minimized by GLB
- Query 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 base

- A fuzzy knowledge base is a triple

Σ= (T ,R, A)where:

- T is a finite set of fuzzy inclusion axioms: A ⊑ C or fuzzyequivalence axioms : A≡C, called a fuzzy TBox
- R is a finite set of fuzzy transitive role axioms: Trans(R) orfuzzy 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 - Semantics

- A fuzzy interpretation is a pair I= (ΔI× .I) where ΔIis the domain of interpretation and .I is the interpretation function which maps
- An individual name α∈ Ito 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
- Lukasiewicz Fuzzy negation c(a) = 1-a
- Lukasiewicz Fuzzy intersection t(a,b) = min(a,b)
- Lukasiewicz Fuzzy union u(a,b) = max (a,b)
- Kleenes-Dienes Fuzzy implication ℑ(a,b) = max(1-a, b)

A SPARQL Query

SELECT ?x WHERE {

?x ns5:membership ?Node1 .

?Node1 rdf:type ?Concept1 .

?Node1 ns5:ineqType ?IneqType1 .

?Node1 ns5:degree ?Degree1 .

FILTER regex (?Concept1 , "CONCEPTS#Tall")

FILTER regex (?IneqType1 ,">")

FILTER (?Degree1 >= "0.8^^xsd:float")

?BlankRole2 ns5:ineqType ?IneqType2 .

?BlankRole2 ns5:degree ?Degree2 .

?BlankRole2 rdf:type ?Role2 .

?x BlankRole2 ?y .

FILTER regex (?Role2 , "ROLES#has-friend")

FILTER regex (?IneqType1 ,">")

FILTER (?Degree2 >= "1.0^^xsd:float")

...

}

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