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Fuzzy Description Logics for Uncertainty Management and Applications

Jidi (Judy) Zhao

2010-6-22

TALK OUTLINE

•Motivation•Problems and Solutions•Applications

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User Interface & Applications

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SEMANTIC WEB APPLICATION ARCHITECTURE

6/22/2010

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UNCERTAINTY RELATED ISSUES

User Interface & Applications

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LIMITATIONS OF PRECISE REASONING

Concepts without well-defined boundaries often have to be defined with ‘artificial’boundariesOriginally uncertain relationships have to be forced into precise relationships for knowledge representationDistorting reality and expert thinkingGiving up important uncertain propertiesLoss of authentic representation

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MOTIVATION:FROM PRECISE TO UNCERTAIN

Uncertainty is an intrinsic feature of real-world knowledgeBased on uncertain facts (evidence)Applying uncertain axioms and rulesAdopting uncertainty ontology-based reasoningResulting in conclusions that are uncertain to some degreeBetter resembling human reasoning in its use of approximate information and uncertainty to generate decisions

OUR APPROACH (I)

Objective: Structure specialist knowledge (both precise and vague) in a way that an automated system can reason with the evidence in a manner similar to specialistsWhat approach can we take to formalize uncertainty-related semantic knowledge?

Description LogicFuzzy sets and fuzzy Logic

Develop a scheme for defining fuzzy concepts and relations

Membership functionInterval-based with lower and upper bounds: [l, u]

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OUR APPROACH (II)Norm—Parameterized Fuzzy Description Logic

F-OWL (Fuzzy OWL)Fuzzy extension to OWL 1 Abstract syntax / functional-style syntaxCore semantics based on the Norm—Parameterized Fuzzy Description Logic 8

FUZZY CONCEPTS: MEMBERSHIP FUNCTIONS

Right-shoulder function:rightShoulder(r1,r2,a,b)

Left-shoulder function:leftShoulder(r1,r2,a,b)

Triangular function:triangular(r1,r2,a,b,c)

Crisp function:crisp(r1,r2,a,b)

Trapezoidal function:trapezoidal(r1,r2,a,b,c,d)

Bell-shaped functionf(x)=1/(1+(x-b)2)

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INTERVAL-BASED FUZZY CONCEPTS

Fuzzy Concept 1 (left)Syntax: FuzzyClass(ClassName

lowerMembershipFunction(triangular(r1 r2 a1 b c1)) upperMembershipFunction(triangular(r1 r2 a b c)))

Fuzzy Concept 2 (right)Syntax: FuzzyClass(ClassName

lowerMembershipFunction(triangular(r1 r2 a1 b1 c1)) upperMembershipFunction(trapezoidal(r1 r2 a b c d)))

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F-OWLFuzzy Axioms

Class(ClassName complete ClassDescription)Class(ClassName partial ClassDescription)Class(ClassName implies ClassDescription degrees(l u))

Fuzzy AssertionsIndividual(IndividualName type(ClassNamedegrees(l u)))Individual(IndividualName value(PropertyNameIndividualName2 degrees(l u)))

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Fuzzy Operationsfuzzy intersection (t-norm)fuzzy union (s-norm)fuzzy set complement (negation)

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Core Reasoning AlgorithmBased on tableau algorithm with fuzzy extension

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HEALTH CARE EXAMPLEDomain: women’s breast cancer diagnosisKnown:

breast cancer classificationrisk factors such as age, inheritance, and symptomshow risk factors are related to breast cancerpatient records

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HEALTH CARE EXAMPLE

The cancer ontology consists of two parts:(1) background knowledge captured in a crisp ontology(2) fuzzy statements augmenting the classical ontology

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HEALTH CARE EXAMPLE:A PRECISE TBOX ON WOMEN’S BREAST CANCER

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HEALTH CARE EXAMPLE:

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HEALTH CARE EXAMPLE:

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HEALTH CARE EXAMPLE:

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HEALTH CARE EXAMPLE:

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A tumour mass is lobular if it has a contour with some deep undulations. The margins of a mass are microlobulated if they have concavities which produce several shallow undulations.

HEALTH CARE EXAMPLE: FUZZY TBOX//Define some fuzzy concepts

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HEALTH CARE EXAMPLE: FUZZY TBOX//Define fuzzy axiomsClass(Lobularity complete intersectionOf(

restriction(hasUndulationsNumbersomeValuesFrom(Some))

restriction(hasUndulationDepth allValuesFrom(Deep))))Class(LobulatedTumour complete intersectionOf(

Tumour restriction(hasShapesomeValuesFrom(Lobularity)))Class(WomanWithLobulatedTumour complete intersectionOf(

Woman restriction(hasTumoursomeValuesFrom(LobulatedTumour)))

Class(Woman implies LifetimeBRCRisk degrees(0 0.13))Class(BRCA1mutation implies

IncreasedBRCRiskfromGeneMutation degrees(0.6 0.8))22

HEALTH CARE EXAMPLE: FUZZY TBOXClass(OldWoman implies IncreasedBRCRiskfromAge degrees(0.027 0.041))Class(YoungWoman implies IncreasedBRCRiskfromAge degrees(0 0.027))Class(WomanMotherWithBRC implies IncreasedBRCRiskfromHeredity

degrees(0.05 0.05))Class(WomanAddictToAlcohol implies IncreasedBRCRiskfromAlcohol

degrees(0.08 0.08))Class(WomanOverweightAfMnopause implies

IncreasedBRCRiskfromObesity degrees(0.18 0.18))Class(WomanWithBRCInShortTerm

complete intersectionOf(Woman unionOf(IncreasedBRCRiskfromGeneMutation IncreasedBRCRiskfromAgeIncreasedBRCRiskfromHeredity IncreasedBRCRiskfromAlcoholIncreasedBRCRiskfromObesity IncreasedBRCRiskfromPersHistIncreasedBRCRiskfromRace IncreasedBRCRiskfromHormonesIncreasedBRCRiskfromDiet)))

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HEALTH CARE EXAMPLE: FUZZY ABOX//Abox, IndividualsIndividual(Helen type(Woman)

value (hasTumour TumourMass1) value(hasMother Mary degrees(1 1)))

Individual(Mary type(WomanWithBRCA1Mutation degrees(1, 1)))Individual(Ann type(WomanWithMotherBRCAffected degrees(1, 1)))Individual(Helen type(WomanAged5060 degrees(1, 1)))Individual(Helen type(WomanWithMotherBRCAffected degrees(1, 1)))Individual(TumourMass1 type(Tumour)

value (hasUndulationsNumber 3) value (hasUndulationDepth 0.5) )

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HEALTH CARE EXAMPLEDecision-making problems:

diagnose the features of a breast cancer tumour (instance range entailment)diagnose a particular woman’s risk of developing breast cancer (instance range entailment)find all women with a high risk of developing breast cancer (f-retrieval)

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PROTOTYPE: FALCAS

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SUMMARY

Proposed managing uncertain knowledge by combining Semantic Web Technologies for Description Logic and Fuzzy LogicIntroduced uncertain knowledge representation formalisms Illustrated a use case in health care

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