Representing and Reasoning with Modular Ontologies

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Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Representing and Reasoning with Modular Ontologies

Jie Bao and Vasant G Honavar

1Artificial Intelligence Research Laboratory, Department of Computer Science,

Iowa State University, Ames, IA 50011-1040, USA.

{baojie, honavar}@cs.iastate.edu

AAAI 2006 Fall Symposium on Semantic Web for Collaborative Knowledge Acquisition (SweCka 2006), October 13-15 2006, Hyatt Crystal City, Arlington, VA, USA

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Outline

• The need for modular ontologies

• Representing and reasoning with modularity

• Representing and reasoning with hidden knowledge

• Related work and Conclusions

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Modularity

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The Need for Modular Ontologies(MO)• Modularity

– A large ontology usually contains components covering sub-domains of the domain in question.

– Ontologies need fine-grained organizational structure to enable partial reuse.

– Ontologies on the semantic web are distributed and connected to each other.

• Selective Knowledge Hiding– Ontology modules are usually autonomous– Security, Privacy, Copyright concerns.

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Modular Ontology Example

Computer Science Dept Ontology Registrar’s Office Ontology

GraduateOK v : 9f ails:CoreCourseGraduateOK v PrelimOKPrelimOK(J ie)

CsCoreCourse(cs511)fails(3304,cs511)SSN(3304,123456789)

Semantic Relations

CsCoreCourse v CoreCourseJ ie= 3304

Hidden Knowledge

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Outline





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Package-based Description Logics• A package is an ontology

module that captures a sub-domain;

• Each term has a home package• A package can import terms

from other packages• Package extension is denoted as

P– PC :Package extension with only

concept name importing

– E.g., ALCPC = ALC + PC

General Pet

Wild Livestock

Animal ontology

PetDogPet

DogGeneral

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Package: Example

O1 (General Animal) O2 (Pet)

It uses ALCP, but not ALCPC

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P-DL Semantics

• Clear and unambiguous semantics is a prerequisite for reasoning

• Semantics: meaning of language forms. • Description Logics (DL) usually has model-theoretical semantics

Syntax Semantics

Man Human

In every world (interpretation), anybody who is a Man is also a Human

{x|Man(x)} {x|Human(x)}

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Interpretations

Interpretation: In every world that conforms to the ontology

Ontology:

Dog I

AnimalI

• For any instance x of Dog, x is also an instance of Animal.

goofyI

• The individual goofy in the world is a Dog.

eatsI

• There is a y in the world, that a Dog x eats y and y is a DogFood

DogFoodI

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Tableau

Dog(goofy)

Animal(goofy)( eats.DogFood)(goofy)

eats(goofy,foo)DogFood(foo)

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

fooL(foo)={DogFood }

eats

ABox Representation Completion Tree Representation

Note: both representations are simplified for demostration purpose

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Local Interpretations

AnimalI

CarnivoreI

DogI

goofy

fooI

DogI

PetIPetDogI

pluto

eatsI

1

1

1

2

2

2

22

DogFoodI 2

AnimalI2

O1 O2

A modular ontology may have multiple (local) interpretations for its modules

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Semantics of Importing

O1 O2importing

AnimalI

CarnivoreI

DogI

fooI

DogI

PetIPetDogI

pluto

eatsI

1

1

1

2

2

2

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DogFoodI 2

AnimalI2

goofy pluto, DogI1 DogI2=

goofy

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Model Projection

x

CI

x

CI1

x’

CI2

x’’CI3

Global model

local models

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Tableau Projection

x1

{A1,B1}

{A2}

{A3,B3}

{B2}x2 x3

x4

x1

{A1}

{A2}

{A3}

x2

x4

x1

{B1}

{B3}

{B2}x3

x4

The (conceptual) global tableau Local Reasoner

for package ALocal Reasonerfor package B

Shared individuals mean partially overlapped local models

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Build Tableau for ALCPC

Tableau Expansion for ALCPC with acyclic importing

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Messages

y y{C?}T1 T2

y y{C}

C(y)T1 T2

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Advantages• Reasoning without the integration of ontology

modules:– (syntactic level) no integrated terminology– (semantic level) no (materialized) global tableau

• Result is always the same as that obtained from an reasoner over the integrated ontology.– Can avoid many reasoning difficulties in other

approaches.

• Supports stronger expressivity: both inter-module subsumption and inter-module role relations

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Outline





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Selective Knowledge Hiding

Locally visible:Has date

Globally visible:Has activity

Bob’ schedule ontology

Alice’ schedule ontology

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Scope Limitation Modifier • Defines the visible scope of a term or axiom• SLM of an ontology term or axiom t

– is a boolean function V(t,r), where r is a package – r could access t iff V(t,r) = True.

• Example SLMs– Public (t,r): t is accessible from anywhere

– Private (t,r): t is only available in the home package

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SLM: exampleA schedule ontology

Hidden: details of the activity

Visible: there is an activity

Kv

Kh

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Concealable 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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Why It Is Possible

• 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 concealed as if it is incomplete knowledge

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Example: Graph Reachability

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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A Concealable Reasoner

Unknown(Hidden knowledge)

Y N

Y N

Unknown(Incomplete knowledge)

Yes

Subsumption query

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Safe Scope Policy

• Hidden knowledge should not be inferred from the visible part of the ontology.– –

• Is it safe enough?– What if an attacker memorizes previous query results?

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History-safe Scope Policy

a

b

c

d

e

YES

YES

Open problem: history-safe scope policy for expressive P-DL

a

b

c

d

e

• History-safe scope policy for taxonomy ontologies – can be reduced to graph

reachability– hidden knowledge should be

closed: if the hidden part infers x→y, then there is no path in the whole graph from x to y that contains a visible edge (visible knowledge).

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Outline





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Related Work

• Modular ontologies– Distributed Description Logics (DDL) (Borgida &

Serafini 2002) – E-Connections (Grau, Parsia, & Sirin 2004)– Semantic Importing (Pan, Serafini & Zhao 2006)

• Knowledge Hiding– Encryption of ontology (Giereth 2005)– Access control (Godik & Moses 2002)

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More DetailsP-DL Syntax and Semantics• Bao, J.; Caragea, D.; and Honavar, V. (2006) Towards collaborative

environments for ontology construction and sharing. In International Symposium on Collaborative Technologies and Systems (CTS 2006). IEEE Press. 99–108.

• Bao, J.; Caragea, D.; and Honavar, V.(2006) Modular ontologies - a formal investigation of semantics and expressivity. In R. Mizoguchi, Z. Shi, and F. Giunchiglia (Eds.): Asian Semantic Web Conference 2006, LNCS 4185, 616–631.

• Bao, J.; Caragea, D.; and Honavar, V. (2006) On the semantics of linking and importing in modular ontologies. In I. Cruz et al. (Eds.): ISWC 2006, LNCS 4273. 72–86.

P-DL Reasoning• Bao, J.; Caragea, D.; and Honavar, V. (2006) A tableau-based

federated reasoning algorithm for modular ontologies. Accepted by 2006 IEEE/WIC/ACM International Conference on Web Intelligence (In Press).

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Thanks !

Representing and Reasoning with Modular Ontologies

Education

dog i animal

ontology ontology

model projection x c

c o r e c o u r s e

package r

example o

v p r e

general animal o