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

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

informationFuzzy 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)

ContributionIt 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

OutlineQueries in crisp DLRDF StoresThe fuzzy DL f-SHINFuzzy Extensions to QueriesFuzzy OWL Syntax in TriplesSesame integration with FiREEvaluation

Queries in DLsConjunctive 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

( ) . ( , )q X Y conj X Y

RDF StoresData storage systems for storing and querying

ontologiesSesame, Jena, Kowari

Ontologies are stored in various triples formatRDF/XMLN TriplesTurtle

Support of Query languages SPARQLSeRQL (Sesame)

Plugins for incoplete OWL DL querying and reasoning (Sesame-OWLim)

Fuzzy SHIN - SyntaxA fuzzy extension of DL SHINf-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 ServicesEntailment

“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 QueriesConjunctive 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

1

( ) . ( ( , ) )n

i ii

q X Y atom X Y k

1

( ) . ( ( , ) : )n

i ii

q X Y atom X Y k

Fuzzy OWL Syntax in TriplesRefication

Weak and ill defined modelLimited support by RDF tools

DatatypesConcrete feature like datatypes are not

appropriate for the representation of abstract information like fuzzy assertions

The proposed syntaxIs simple and clearIs based on the use of blank nodes and

properties

Fuzzy OWL Syntax in TriplesFuzzy concept assertion paul frdf:membership _:paulmembTall .

_:paulmembTall rdf:type Tall.

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

_:paulmembTall frdf:ineqType “>=” .

Fuzzy role assertionpaul frdf:paulFriendOffrank frank.

frdf:paulFriendOffrank rdf:type FriendOf.

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

frdf:paulFriendOffrank frdf:ineqType “>=”.

Fuzzy Reasoning Engine FiREIt 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 APICurrently supports F-SHINThe 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 FiRERDF-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-IConjunctive threshold Queries (CTQs)

FiRE Syntaxx,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 SesameThe results are visualized by FiRE

Querying-IIGeneral Fuzzy Conjunctive Queries (GFCQs)

FiRE Syntaxx,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 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

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> : 0.721 1 2 2 4 4

1 2 4

( ) ( ) ... ( )

...

k d k d k d

k k k

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

concepts Very_Short, Short, Normal_Height, Tall, Very_Tall

The set of Roles consisted of some special characteristicsi.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 intereste.g. Scientist≡Male⊓Serious ⊓ (40s ⊔ 50s) ⊓ ∃has-eyeCondition.Glasses

ResultsExplicit knowledge

2140 individuals82 Concepts 20 Roles29469 assertions (Fuzzy KRSS)

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

Lukasiewicz Fuzzy negation c(a) = 1-aLukasiewicz 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 QuerySELECT ?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")

...

}