modular ontologies - a formal investigation of semantics and expressivity

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ASWC, Sept 7, 2006, Beijing, China 1

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Modular Ontologies - A Formal Investigation of Semantics and

ExpressivityJie Bao, Doina Caragea and Vasant G Honavar

Artificial Intelligence Research Laboratory, Department of Computer Science,

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

{baojie,dcaragea, honavar}@cs.iastate.edu

ASWC, Sept 7, 2006, Beijing, China 2

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Outline

• Desiderata of Modular Ontologies

• Abstract Modular Ontology (AMO)

• Semantics & Expressivity Comparison

• Summary & Conclusion

ASWC, Sept 7, 2006, Beijing, China 3

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Modularity

ASWC, Sept 7, 2006, Beijing, China 4

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

A Modular Semantic Web

Visualising the Semantic Web by Juan C. Dürsteler

ASWC, Sept 7, 2006, Beijing, China 5

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Modular Ontologies

• What is modular ontology?– An ontology that is composed by a set of smaller

(semantically) connected component ontologies

• Why modular ontology ?– Collaborative Ontology Building– Selective Ontology Reuse– Selective Knowledge Hiding– Distributed Data Management– Large Ontology Storage and Reasoning

ASWC, Sept 7, 2006, Beijing, China 6

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

OWL Limitations• owl:imports: syntactic

modularization• No localized semantics

– Reasoning is possible only with the integrated ontology

• No partial reuse– Reuse all or nothing– E.g. OpenCyc OWL file

needs 9 hours to load into Protege

owl:imports

Syntactic import:“copy and paste”

ASWC, Sept 7, 2006, Beijing, China 7

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Modular Ontology Approaches

CЄ (SHOIN(D))

OWL

1998 2002 2003 2004 2005 2006

C-OWLC-OWLCTXML

E-Connections

P-OWL

(Planning)

P-DL

DDLDFOLRole<->Concept

Mapping

CЄ(SHIF(D)) IHN+s

ASWC, Sept 7, 2006, Beijing, China 8

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Requirements

• Semantic soundness– Reasoning correctness

– Module autonomy

• Needed language features– Concept relations

– Role relations

– …

ASWC, Sept 7, 2006, Beijing, China 9

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Localized Semantics

Integrated ontology

Materialized Global Model

Modular ontology

Local Models

ASWC, Sept 7, 2006, Beijing, China 10

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Exact Reasoning

vv

Integrated ontology Modular ontology

C D vvC D

ASWC, Sept 7, 2006, Beijing, China 11

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Directional Semantic Relations

vvD E

vvD E

ASWC, Sept 7, 2006, Beijing, China 12

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Transitive Reusability

vvC D vvD E vvE F

vvC F

ASWC, Sept 7, 2006, Beijing, China 13

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Decidability

is answerable in finite steps

vvC D

ASWC, Sept 7, 2006, Beijing, China 14

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Language Features• Concept Subsumption• Concept Construction with

Foreign Concepts• Concept Construction with Role

Restrictions.• Role Inclusion• Role Inversion• Role Construction• Transitive Role• Nominal Correspondence

1:C v 2: D1:C v 2: D1:C u2: D1:C u2: D

9(1: R):(2 : D)9(1 : R):(2 : D)

1:P v 2: R1:P v 2: R1:P = 2:R¡1:P = 2:R¡

1:P u2: R1:P u2: R

1:x=2:y1:x=2:yTrans(1:P), 1:P used in 2

ASWC, Sept 7, 2006, Beijing, China 15

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Outline

• Desiderata of Modular Ontologies

• Abstract Modular Ontology (AMO)

• Semantics & Expressivity Comparison

• Conclusion

ASWC, Sept 7, 2006, Beijing, China 16

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Local Points of View

The domain

agents agents

Multiple observers of a domain

ASWC, Sept 7, 2006, Beijing, China 17

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Abstract Modular Ontology (AMO)

DL2DL1

DL3

r13

r231

r132

1

Semantics

Δ1 Δ2

Δ3

ASWC, Sept 7, 2006, Beijing, China 18

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

(General) Domain Relations

r13neighbourOf

r13friendOf

Δ1 Δ3

ASWC, Sept 7, 2006, Beijing, China 19

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Image Domain Relation

r13

Δ1

Δ3

ASWC, Sept 7, 2006, Beijing, China 20

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Concept Image

r13

Agent3: "these objects in my mind state correspond to the conceptLeg from agent 1’s mind state"

Legm1Legm1

Leg1! 3 : r!13(Legm1 )Leg1! 3 : r!13(Legm1 )

ASWC, Sept 7, 2006, Beijing, China 21

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Role Image

P1! 3P1! 3

r13

P

Δ1 Δ3

Agent3: "these object pairs in my mind state correspond to object pairs

P from agent 1’s mind state"

ASWC, Sept 7, 2006, Beijing, China 22

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Possible AMO Expressivity Features

ASWC, Sept 7, 2006, Beijing, China 23

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Semantic Soundness Definitions

• Localized Semantics: local domains {Δi} are not necessarily identical

• Decidability (of concept C w.r.t AMO O): there is an algorithm to decide in finite steps whether there is a common model <{mi}, {rij}> of C and O.

• Directional Semantic Relations: mj ² Cmj µ Dmjmj ² Cmj µ Dmj mi ² C ià j µ D ià jmi ² C ià j µ D ià j

ASWC, Sept 7, 2006, Beijing, China 24

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Semantic Soundness Definitions (2)

• Reusability

Ci ! j µ D i ! jCi ! j µ D i ! jCmi µ DmiCmi µ Dmi

C D

• Transitive ReusabilityΔ1 Δ2 Δ3

(an agent can infer local constraints based on observing constraints in other agents’ points of view)

ASWC, Sept 7, 2006, Beijing, China 25

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Semantic Soundness Definitions (3)

• Exact Reasoning– Compatible

beliefs of agents may be combined.

– Local models M can be merged into an integrated model M' s.t.

Physical World

LocalModels

Integrated Model(consensus)

ASWC, Sept 7, 2006, Beijing, China 26

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Outline

• Desiderata of Modular Ontologies

• Abstract Modular Ontology (AMO)

• Semantics & Expressivity Comparison

• Conclusion

ASWC, Sept 7, 2006, Beijing, China 27

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

DDL Semantics

DDL : C into D

DI

CI

(R.D)I

r(CI) DI

r(CI)= (R-.C)I

C onto D

DI

CI

r(CI) DI

r(CI)= (R-.C)I

1:Dog into 2:Animal

1:Dog onto 2:Hound

implicit domain disjointness

[Borgida and L. Serafini, 2002]

ASWC, Sept 7, 2006, Beijing, China 28

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Subsumption Propagation Problem

DDL domain relations are not transitively reusable

Cm1 C into D Dm2

Em3

D into EC into E ?

ASWC, Sept 7, 2006, Beijing, China 29

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Inter-module Unsatisfiability Problem

DDL allows arbitrary domain relations: loss of reasoning exactness

Flym1

~Fly onto Penguin

Penguinm2

Birdm1

Bird onto Penguin

ASWC, Sept 7, 2006, Beijing, China 30

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

DDL: Pros & Cons

• Pros– Localized Semantics– Directional Relation– Decidability transfer

• Cons– No support for role relations– No general module transitive reusability– No general reasoning exactness

ASWC, Sept 7, 2006, Beijing, China 31

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

E-Connections

• Local domains are disjoint

• It allows multiple “link” relations between two local domains

• Links can be used to construct local concepts

PetOwner

Petowns

PetOwner

Petowns

[Grau, 2005]

ASWC, Sept 7, 2006, Beijing, China 32

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

E-Connections Semantics

DI

(R.D)I = r-(DI)

R

DI(R.D)I=Δ 1\r-(Δ 2\DI)

R

ASWC, Sept 7, 2006, Beijing, China 33

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

E-Connections: Pros & Cons

• Pros– Localized Semantics– Decidability Transfer– Exact Reasoning (without generalized link)

• Cons– Very limited transitive reusability– No support for inter-module concept

subsumption

ASWC, Sept 7, 2006, Beijing, China 34

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

P-DL • Semantic Importing

O1 (General Animal) O2 (Pet)O1 (General Animal) O2 (Pet)

[Bao et al., 2006]

35

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

P-DL Semantics

• Domain relations are compositionally consistent: r13=r12

O

r23– Therefore domain relations are

transitively reusable.

x x’

ΔI1 ΔI2

CI1 CI2

r12

ΔI3

r13 r23

x’’CI3

• Domain relation: individual correspondence between local domains

• Importing establishes one-to-one domain relations – “Copied” individuals are

shared

36

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

P-DL Semantics (2)

x x’

ΔI1 ΔI2

CI1 CI2

r12

ΔI3

r13 r23

x’’CI3

x

CI

Global model obtained from localmodels by merging shared individuals

37

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Partially Overlapping Domains• Ensure unambiguous

communication between local models– satisfiability transfer– transitive reusability

• Overlapped domains represent the consensus of agents

• Non-sharing domains are still kept local.

x

CI

ASWC, Sept 7, 2006, Beijing, China 38

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

P-DL: Pros & Cons

• Pros– Localized Semantics– Exact Reasoning – Stronger Expressivity– Transitive Reusability

• Cons– Directional Semantic Relation does not always

hold– Decidable only if all modules use the same

decidable DL (e.g. OWL).

ASWC, Sept 7, 2006, Beijing, China 39

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Summary: Semantic Soundness

ASWC, Sept 7, 2006, Beijing, China 40

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Summary: Expressivity

ASWC, Sept 7, 2006, Beijing, China 41

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Outline

• Desiderata of Modular Ontologies

• Abstract Modular Ontology (AMO)

• Semantics & Expressvity Comparison

• Conclusion

ASWC, Sept 7, 2006, Beijing, China 42

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Summary

• We discussed– Semantic soundness and expressvity

requirements for modular ontologies– Comparsion of DDL, E-Connections and P-DL

under the AMO framework– Analysis of several semantic difficulties and

expressivity limitations of existing approaches

ASWC, Sept 7, 2006, Beijing, China 43

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Conclusions• There is still no language or reasoner support for

both general inter-module concept and inter-module role correspondence

• Local domain disjointedness assumption of DDL and E-Connections may be partially relaxed.– to improve expressivity– to ensure reasoning exactness and transitivity

reusability.

ASWC, Sept 7, 2006, Beijing, China 44

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Open Problems• A consensus on expressive modular

ontology language• A OWL-compatible syntax for modular

ontologies• A reasoner that supports the expressive

modular ontology language– Pellet and DRAGO are complementary to each

other

To be discussed at the Modular Ontology Workshop (WoMo) at ISWC 2006 , Athens, Georgia, USA, Nov 2006.

ASWC, Sept 7, 2006, Beijing, China 45

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Thanks!

ASWC, Sept 7, 2006, Beijing, China 46

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Semantic SoundnessWhat are the logical consequences in an AMO?

What are the possible cause of semantic inconsistencies between two agents?

What is the "objective" way to integrate knowledge of agents?

a b

friendOf

x y

friendOf ?

r13

a b

friendOf

x y

enemyOf

r13

a/x b/y

friendOf

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