Representing and Reasoning with Modular Ontologies (2007)

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223 Atanasoff Hall. July 10, 2007, Ames, IA, USA. 1/54 Iowa State University Department of Computer Science Artificial Intelligence Research Laboratory Representing and Reasoning with Modular Ontologies Ph.D. Dissertation Defense Major advisor: Vasant Honavar Jie Bao Artificial Intelligence Research Laboratory Computer Science Department Iowa State University Ames, IA USA 50011 Email: [email protected] July 10, 2007

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Transcript of Representing and Reasoning with Modular Ontologies (2007)

Page 1: Representing and Reasoning with Modular Ontologies (2007)

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Representing and Reasoning with Modular Ontologies

Ph.D. Dissertation Defense

Major advisor: Vasant Honavar

Jie Bao

Artificial Intelligence Research LaboratoryComputer Science Department

Iowa State University Ames, IA USA 50011

Email: [email protected]

July 10, 2007

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Outline

• Introduction– Motivation, desiderata and state-of-the-art of

modular ontologies• Representing Modular Ontology

– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology

– Distributed reasoning in P-DL using tableau algorithm

• Privacy-Preserving Reasoning with Hidden Knowledge

• Collaborative Building of Modular Ontologies

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From Web to Semantic Web

Ontology: a “PhD Candidate” is a “Student”

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Semantic Web

Figure courtesy of Tim Berners-Lee, AAAI 2006

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A Very Very Short DL Primer

• Description Logics (DL): – a knowledge representation

formalism to describe ontologies

– the foundation for web ontology languages, e.g., OWL

• Ontology example– A Dog is an Animal– A Dog eats some DogFood– goofy is a Dog

concept

role

individual

axioms

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DL Families• ALC

– ⊔ (disjunction): Child = Boy ⊔ Girl– ⊓ (conjunction): Mother = Female ⊓ Parent (existential restriction): Parent = hasChild.Human (value restriction): Human ⊑ hasBrother.Man (negation): Boy ⊑ Girl

• SHOIQ– S=ALC+transitive role : Trans(hasSibling)– H (role hierarchy): hasBrother ⊑ hasSibling– O (nominal, i.e., concept that has single instance): Sun, France– I (inverse role): hasChild = hasParent-

– Q (qualified number restriction): Human ⊑ (=2 hasParent.Human)

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From Web Pages to Ontologies

• Web: Network effect

[Diagram: Joanne Luciano, Predictive Medicine; Drug discovery demo using RDF, Sideran Seamark and Oracle 10g]

• Web pages: web Ontologies : semantic web

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Distributed, Modular Ontologies

Distributed ontology modules• Are produced by autonomous participants

– Are limited in their scope – Represent different points of view– Have (potentially) partially overlapping domains

• Lack global semantics– Need contextualized semantics

• Need selective or partial knowledge reuse • Need distributed inference algorithms without forcing

ontology integration• Should facilitate network effect

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Analogy: Paper Writing

Recent development in modular ontologies…

In this paper, we present two algorithms A and B to …

(Alice, 2001)

(Bob, 2007)

Combining Ontologies

Ontology Modularization

Recent development in modular ontologies…

In this paper, we extend the algorithm A proposed by (Alice,2001) …

Same global domain: modular ontologies Multiple independent participants

Possible (partial) reuseContextualized Semantics

Citation is not copy+paste, hence does not result in a single, combined document

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Modular Ontology Languages: State-of-the-art overview

CЄ (SHOIN(D))

OWL

1998 2002 2003 2004 2005 2006 2007

C-OWLC-OWLCTXML

E-Connections

P-DL

DDLDFOL

DDL with Role Concept

Mapping

CЄ(SHIF(D))IHN+s

DL ALCPC SHOIQP

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Ontology Reuse in OWL: Syntactic Importing

• The OWL primitive intended to support ontology reuse is owl:import

• One can use owl:import to copy-and-paste an ontology into another

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Analogy: Paper Writing in OWL fashion

Recent development in modular ontologies…

In this paper, we present two algorithms A and B to …

(Alice, 2001)

(Bob, 2007)

Combining Ontologies

Ontology Modularization

Recent development in modular ontologies…

In this paper, we extend the algorithm A proposed by (Alice,2001) …

copy+paste

• no partial reuse• loss of context

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DDL

• Distributed Description Logics (DDL) [Borgida & Serafini, 2002]

– Allows “bridge rules” between concepts across ontology modules

– Bridge rules between roles are similar

• Semantics given by “domain relations”

PetAnimal

Dog

(onto)

(into)

I1Dog

Pet I2Animal I1

r12

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DDL Semantics: Problem with Bridge Rules

DDL bridge rules are not compositional: • r13 cannot be inferred from r12 and r23

• Knowledge is not transitively reusable!

1:Chicken 2:Birdvv

3:Animal

vvChicken Animal ?vv

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DDL Semantics: Problem with Bridge Rules

1: Fly

1: Bird

2:Penguin

Bird Penguin

~Fly Penguin

DDL bridge rules do not preserve concept unsatisfiability across modules

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E-Connections

• E-connections allow multiple links between two local domains [Grau, 2005]

• Links can be used to construct local concepts

PetOwner

Pet

PetOwner

Petowns

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E-Connections [Grau, 2005]

• A concept cannot be declared in an ontology as a subclass of a foreign concept;

• A property cannot be declared as sub-relation of a foreign property;

• An individual cannot be declared as an instance of a foreign concept;

• A pair of individuals cannot instantiate a foreign property;

• The use of E-Connections semantics with owl:imports syntax leads to several difficulties

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Section summary

• OWL – No localized or contextualized semantics, – No partial reuse.

• DDL – Allows inter-module concept inclusions (but not inter-module roles)– In general, does not support transitive knowledge reuse or

preservation of unsatisfiability

• E-Connections– Allows inter-module roles (but not concept inclusions)– Presents strong expressivity limitation

• P-DL aims to overcome these limitations

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Outline

• Introduction– Motivation, desiderata and state-of-the-art of

modular ontologies• Representing Modular Ontology

– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology

– Distributed reasoning in P-DL using tableau algorithm

• Privacy-Preserving Reasoning with Hidden Knowledge

• Collaborative Building of Modular Ontologies

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Package-Based Description Logics (P-DL)

• P-DL support semantic importing

O1 (Animal) O2 (Pet)

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Syntax of P-DL

• Package and Importing

Pii

Male, Female

Pj

• Contextualized negation– There is no global negation, but only contextualized negation for

each package– Example:

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Semantics of P-DL

• Localized Semantics

PeopleAnimals

O1 O2

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Semantics of P-DL

• Semantic importing akin to “citation”

• Package 2 cites package 1 for the definition of ‘1:Dog’– Interpretation of ‘1:Dog’ is the same on the shared

portions of the local domains of packages 1 and 2– The two packages need not agree on the interpretation of

other unrelated concepts (e.g., Cats)

• P-DL supports selective knowledge reuse

P1 P2

1:Dog 2:PetDog 1:Dogvv

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Semantics of P-DL

• Domain relations are composi-tionally consistent

r13=r23 O

r12

• More requirements are needed when importing of roles and nominals are allowed.

x x’

ΔI1 ΔI2

1:DogI11:DogI2

r12

ΔI3

r13 r23

x’’1:DogI3

• Importing establishes one-to-one domain relations

• (1:Dog)I2 =r12(1:DogI1)

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Semantics of P-DL

²

²importee

importer consequences

• Each package witnesses consequences from its own point of view (using its local and imported knowledge)

importer consequences

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Properties of P-DL

• Exact Reasoning: – extending an ontology in the classic way and in the

modular way will ensure same inferential results.

vv

Integrated ontology Modular ontology

Dog Animal vvDog Animal

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Properties of P-DL

• Directional Relation

vvD EvvA B

vvA B

vvD EX

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Properties of P-DL

• The preservation of unsatisfiability

• Transitive Reusability

Dogvv

vvDog Animal

Pet Animalvv

P1 P2 P3

(Pj imports Pi)

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P-DL Families

• P – package extension with importing of any type of names (concept, role and nominal)– P- - acyclic importing: if P (directly or indirectly) imports

Q, then Q cannot (directly or indirectly) import P– PC – importing of concept names only

• Examples: – ALCPC

[Bao et al,CRR 2006] – ALCPC

-[Bao et al,WI 2006] – SHIQP[Bao et al,ISWC 2007]

– SHOIQP[Bao et al,AAAI 2007]

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DDL and E-connections vs P-DL• P-DL can simulate

– DDL with bridge rules using subsumption between • imported concepts and local concepts • imported roles and local roles

– (one-way binary) E-Connections using roles that relate a local concept with an imported concept

• DDL, E-Connection or their combination cannot simulate P-DL– One-to-one domain relations cannot be simulated by

DDL or E-Connections– P-DL, unlike DDL and E-connections, supports transitive

reuse of knowledge

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Section Summary

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Section Summary

(Details in dissertation Table 4.4)

1,4 Limited Support 2,3 May be simulated using syntactical encoding

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Outline

• Introduction– Motivation, desiderata and state-of-the-art of

modular ontologies• Representing Modular Ontology

– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology

– Distributed reasoning in P-DL using tableau algorithm

• Privacy-Preserving Reasoning with Hidden Knowledge

• Collaborative Building of Modular Ontologies

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Tableau Algorithm

• Description Logics usually uses the Tableau Algorithm [Baader & Sattler 2001] for reasoning tasks.

• A tableau is a representation of a model– A model for an ontology represents a world which satisfies

assertions in the ontology.

– Decidable DLs typically have tree models [Vardi,1996]

• Tableau algorithms try to check concept satisfiability w.r.t. a KB by constructing a tree that is the model of the concept and the KB

Ontology: Man ⊑ Human Model:Man

Human

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Tableau Algorithm: Example

goofyL(goofy)={Dog, Animal, eats.DogFood }

foo L(foo)={DogFood }

{eats}

Completion Tree (Tableau)

Note: the tableau is simplified for demonstration purpose

Dog Animal⊑Dog ⊑ eats.DogFood

DogFood ⊑ hasTM.Brand

DogFood ⊑ soldBy.Supermarket

If “Dog” is satisfiable? pedigreeL(pedigree)={Brand }

{hasTM}

walmartL(walmart)={Supermarket}

{soldBy}

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Reasoning for Modular Ontology

• Major Considerations: – Avoid integrating ontology modules– Minimize local memory cost– Respect module autonomy, e.g., privacy

• Question: can we reason with P-DL without – (syntactic level) an integrated ontology ?– (semantic level) a (materialized) global tableau ?

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Federated Reasoning

• There are multiple local reasoners, one for each package– Each local reasoner only knows and uses local knowledge – A reasoner may ask another reasoner (by messages) about the

meaning of imported names .

What is a “Dog”?

“Dog” is a type of “Animal”

Dog

Dog ⊑ AnimalP2 P1

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Distributed Tableau

(Virtual) combined tableau for the (conceptual) integrated ontology from all packages

Distributed tableau • each local tableau is a fragment of the virtual global tree• thus, each local tableau is a forest• a node may be “shared” among local tableaux (indicated by domain relations)

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Construction of Distributed Tableau

• Developed algorithms ALCPC, ALCPC-, SHIQP

• Basics of the algorithm: – Intra-tableau expansion rules: e.g., if C⊓D L(x), then

{C,D} <= L(x)– Inter-tableau expansion rules: e.g., if C L(x), C

is defined in another package P, then send a reporting message r(x,C) to the reasoner of P.

– Termination: is guaranteed using suitable blocking rules.

– The algorithm is proven to be sound and complete.

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Example

• Check if PetDog is satisfiable as witnessed by O2

O1 (Animal) O2 (Pet)

{ other axioms … }

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Example• Each local reasoner maintains a local tableau. • Connections between local tableaux is created by a set of messages.

x1

{PetDog}

Local Reasoner 2(for package Pet)

R12(x1,Dog)

R12(x1,Animal)

{Animal}{DogFood}

x2

{eats}

R12(x2,Animal)

{eats}x2’

x1

{Dog,Carnirvore,Animal}’

Local Reasoner 1(for package Animal)

R12(<x1,x2>,eats)Expansion for other axioms in PAnimal

Note: the tableau is simplified for demonstration purpose

PetDog Dog⊑PetDog ⊑ eats.DogFood

Dog Carnivore⊑Carnivore Animal⊑

Carnivore ⊑ eats.Animal

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Section Summary• Distributed reasoning algorithms have been

designed for P-DL:– Federated: no integration of all ontology modules is

required;– Peer-to-peer: each local reasoner only requires local

knowledge;– Parallel: subtasks in reasoning can be explored

concurrently by multiple reasoners;– Message-based: the overall reasoning process is

enabled by messages exchanged between local reasoners.

• Algorithms available for ALCPC-, ALCPC, SHIQP

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Outline

• Introduction– Motivation, desiderata and state-of-the-art of

modular ontologies• Representing Modular Ontology

– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology

– Distributed reasoning in P-DL using tableau algorithm

• Privacy-Preserving Reasoning with Hidden Knowledge

• Collaborative Building of Modular Ontologies

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Partially Hidden Knowledge

Locally visible:Has date

Globally visible:Has activity

Bob’ schedule ontology

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Privacy-Preserving Reasoning

• A reasoner should not expose hidden knowledge

• However, such hidden knowledge may still be (indirectly) used in safe queries.

QueriesYes

Unknown

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Privacy-Preserving Reasoning

• Practical algorithms designed for– Hierarchical ontologies. (e.g. biological ontologies)– Description Logics (e.g. SHIQ)– Open for P-DL

• Applications– Privacy protection in medical information system– Secure web service – Query answering in p2p applications– …

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Outline

• Introduction– Motivation, desiderata and state-of-the-art of

modular ontologies• Representing Modular Ontology

– Using Package-based Description Logics (P-DL)• Reasoning with Modular Ontology

– Distributed reasoning in P-DL using tableau algorithm

• Privacy-Preserving Reasoning with Hidden Knowledge

• Collaborative Building of Modular Ontologies

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Collaborative Ontology Building

Ontology modularity facilitates collaborative building• Each package can be independently developed• Different curators can concurrently edit the ontology on

different packages• Ontology can be only partially loaded• Unwanted interactions are minimized by limiting term and

axiom visibility

Prototypes• COB-Editor [Bao et al, BIDM 2006]

• WikiOnt [Bao & Honavar, EON 2004]

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Iowa State University Department of Computer ScienceArtificial Intelligence Research LaboratoryThe COB Editor

Pig Package

Cattle Package

Chicken Package

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WikiOnt 2 (Ongoing)

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Contributions

Figure courtesy of Tim Berners-Lee, AAAI 2006

• Formal investigation on requirements of modular ontologies • The specification of Package-based Description Logics (P-DL) which overcomes many semantic problems and expressivity limitations of existing approaches

Chapter 3,4

Distributed reasoning algorithms for modular ontologies• federated, no integration required• peer-to-peer• parallel reasoning, scalable for large ontologies• message-based

Chapter 5Privacy-preserving inference with hidden knowledge• general framework• practical algorithms for hierarchies and DL

Chapter 6

Collaborative Building of Modular Ontologies• Software prototypes: WikiOnt and COB-Editor

Chapter 7

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Results

• Presentations– Academic Conferences: AAAI-07, RR-07 (Web Reasoning and Rule System), WI-

06 (Web Intelligence), ISWC-06(International Semantic Web Conference), ASWC-06 (Asian Semantic Web Conference, Best Paper)

– Industrial Conferences: SemGrail (Microsoft) 2007, Semantic Technology Conference 2007

• Funding– Results of this study formed the basis of proposals on modular

ontologies that were funded by NSF (IIS-0639230) and ISU CIAG (Center for Integrated Animal Genomics)

• Community Involvement– 4 workshop organization efforts on related topics (SWeCka

2006,2007, Modular Ontologies (WoMo) 2006,2007)

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Future Work

• Modular Ontology Framework– Understanding modular ontology using DL + rules; RDF

modularity

• Extending P-DL– ABox, Query, Syntax, Interfaces and Views

• Distributed Reasoning– Implementation, SHOIQ reasoning, optimization

• Privacy-Preserving Reasoning – P-DL, RDF, medical ontologies

• Applications– WikiOnt2, Semantic Data Integration (INDUS project)

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Acknowledgement• Major advisor: Vasant Honavar• Modular Ontology Group: Giora Slutzki, Doina Caragea, George

Voutsadakis• COB-Editor Group: LaRon Hughes, Zhiliang Hu, Peter Wong, James

Reecy, • Medical Ontology Building: Yu Cao, Wallapak Tavanapong, • INDUS Group: Doina Caragea, Jyotishman Pathak, Neeraj Koul, Jaime

Reinoso-Castillo• Discussion: Gary Leavens, Dae-ki Kang, Rafael-Armando Jordan,

Adrian Silvescu, Kewei Tu, Jun Zhang, Feihong Wu, Changhui Yan, Hua Pei, Hua Ming, and other members of the AI Lab.

• Non-ISU collaboration: Jeff Pan, Yimin Wang, Luciano Serafini, Andrei Tamilin, Zhengxiang Pan and Jing Mei.

• Research supported by funding from National Science Foundation (IIS 0219699,0639230),National Institutes of Health (GM 066387), and Center for Integrated Animal Genomics, Iowa State University, and grants from USDA NAGRP Bioinformatics Coordination Project.

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Backup

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Why not owl:imports?

• owl:imports does not preserve semantics of imported concepts or roles as defined in the source ontology (loss of

context) • owl:imports does not support partial reuse

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Hidden Knowledge vs. Incomplete Knowledge

• Open World Assumption (OWA)

• An ontology may have only incomplete knowledge about a domain– KB: Dog is Animal– Query: if Cat is Animal ? Unknown

if Cat is not Animal ? Also unknown

• Hidden knowledge can be protected as if it is incomplete knowledge

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Privacy-Preserving Reasoner• A privacy-preserving reasoner should be

– History independent: it answers in the same way regardless the history of past queries

– Honest: it never “lies”

– History safe: answers and visible knowledge combined cannot be used to infer hidden knowledge

q R A {Y,N,U}

KB

q R

KBfalse

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Example: Hierarchies

unknownYES

a

b

c

d

OWA: there may be another path that connects a and d but is not included in the visible graph (thus a→d does not imply b→c )

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Example: Hierarchies

a

b

c

d

e

Y

Y

a

b

c

d

e

“unsafe” graph “safe” graph

Reasoning Strategy:

Safety Scope:

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Privacy-preserving reasoning with DL

• Critical visible knowledge (Kvc) contains existing knowledge about Sig(Kh)• If we can ensure Kv + QY will not give extra information about Sig(Kh), other than

that Kvc, then the reasoner is safe• Conservative Extension[Grau etal, 2006]: α of Sig(Kvc), Kvc|= α iff Kv+QY |= α• Practical algorithm exists for SHIQ (using “local ontologies”[Grau et al, IJCAI 2007])

Hidden knowledge (Kh)

Visible knowledge (Kv)

Critical visible knowledge (Kvc)

C ⊑ D

C ⊑ R.D

G ⊑ H

axioms that contain names in Sig(Kh)

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Privacy-preserving reasoning with P-DL

• Still an open problem

• Key issue: message safety

r(x,Dog), r(x,Animal)

Dog ⊑ Animal P1

Dog ⊑ Animal inferred!

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Section Summary

• Selective knowledge reuse using partially hidden knowledge

• Privacy-preserving reasoning based on the open world assumption

• Practical algorithms available for hierarchies and DL SHIQ.

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

WikiOnt

• A web browser based ontology editor

• Using Wiki script to store ontologies

• With features to support team work, version control, page locking, and navigation.