Package-based Description Logics – Preliminary Results

International Semantic Web Conference (ISWC) 2006. Doctoral Consortium Track, Nov 5, 2006 Athens, GA 1

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

Package-based Description Logics – Preliminary Results

Jie Bao, Doina Caragea, Vasant Honavar

Artificial Intelligence Research LaboratoryComputer Science Department

Iowa State University Ames, IA USA 50011

Email: [email protected]



Outline

• Motivation

• Language Features

• Semantics

• Reasoning

• Applications

• Conclusions



Modular Ontologies

• What is modular ontology?– An ontology that contains a set of smaller,

(semantically) connected component ontologies

• Why modular ontology ?– A Distributed Semantic Web– Collaborative Ontology Building (COB)– Selective Ontology Reuse– Large Ontology Storage and Reasoning



Berners-Lee, T., Hendler, J., and Lassila, O. (2001).The semantic web. Scientific American, 284(5):34-43.

A Distributed Semantic Web



A COB Example

Swine

Cattle Chicken

Horse

Each group works on an ontology module for a particular species (according to the group’s best expertise)

Collaborative building of an animal trait ontology that involves multiple research groups across the world



Ontology Languages Needed

• Has localized semantics– Allows distributed reasoning

• Supports fine-grained ontology organizational structure – Allows partial ontology reuse– Supports selective knowledge hiding

• Enables collaborative and scalable tools



Modular Ontology Languages Today

OWL

2002 2003 2004 2005 2006

C-OWLC-OWLCTXWL

E-ConnectionsE-Connections

Our approach

DDL based

? ?

(E-connection can also work other logics e.g. modal logic)

P-DL

(to be discussed at the WoMO workshop)



Modular Ontology Languages Today (2)

• E-Connections– Connects DL modules with

special types of roles called “links”

PetOwner

Petowns

• Distributed Description Logics (DDL) & C-OWL

– Allows “bridge rules” between concepts across ontology modules

PetAnimal

Dog

(onto)

(into)



Expressivity Comparison

[Baot et al. ASWC 2006]



Open problems

• How to obtain stronger expressiveness?

• How to enable distributed reasoning without required global knowledge?

• How to ensure the reasoning exactness w.r.t. standard reasoning with integrated ontology?

• How to create modular ontologies?



Outline

• Motivation


• Semantics

• Reasoning

• Applications

• Conclusions



Package

• Packages of an ontology– Are defined in subsets of the same

decidable DL,e.g., SHOIQ– May contain both local terms and

imported terms;

• Each term has a home package• P :Package extension

– PC: Package extension with only concept name importing

– E.g., SHOIQP= SHOIQ +P ALCPC = ALC + PC

General Pet

Wild Livestock

Animal ontology

PetDogPet

DogGeneral



Package: Example

O1 (General Animal) O2 (Pet)

It uses ALCP, but not ALCPC



Ongoing work: Scope Limitation

• SLM of an ontology term or axiom t– is a boolean function that

defines the visible scope of a term or axiom.

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

anywhere

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

P3

P1

P2

public

private

P1

P2

public

private



Outline

• Motivation


• Semantics

• Reasoning

• Applications

• Conclusions



Localized Semantics

O1 O2

AnimalI

CarnivoreI

DogI

fooI

DogI

PetIPetDogI

x

eatsI

1

1

1

2

2

2

22

DogFoodI 2

AnimalI2



Semantics of Importing

O1 O2importing

AnimalI

CarnivoreI

DogI

x fooI

DogI

PetIPetDogI

x

eatsI

1

1

1

2

2

2

22

DogFoodI 2

AnimalI2

Image domain relation



Global Interpretations

AnimalI

CarnivoreI

DogI

I

PetDogI

x

PetI

eatsI

g

g

g

g

g

g

fooIg

DogFoodI g

• The (conceptual) global interpretation for the (virtually) integrated ontology• It can be combined from local interpretations



Partially Overlapped ModelΔI1 ΔI2

x x’

CI1 CI2

r12

ΔI3

r13 r23

x’’CI3

x

CI

Global interpretation obtained from localInterpretations by merging shared individuals

bijective(one-to-one)

Transitive(Compositional consistent)



P-DL Semantics Features

• Localized Semantics– Local “top” concepts are not the same– Each package explains the world based on its

transitive importing closure (local point of view).

• Stronger expressivity– Supports both inter-module concept subsumption and

inter-module role usage.

• Decidable (when all modules are from the same decidable DL)

• Solves some reasoning diffculities in other approaches



Outline

• Motivation


• Semantics

• Reasoning

• Applications

• Conclusions



Reasoning for Modular Ontology

• Major Consideration: should not require the integration of ontology modules.– High communication cost– High local memory cost– May violate module autonomy, e.g., privacy

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



Distributed Reasoning

Stan: Hey, Chef. Is Kyle’s new home far from us?

Chef: Hello there, children! Where does Kyle move to?

Cartman: San Francisco, I guess.

Chef: • We are in South Park, Colorado; • San Francisco is in California; • Colorado is far from California.

Stan: So they are far from us. Too Bad.



Federated Reasoning for P-DL

Basic strategy• Use multiple local reasoners, each

for a single package• Each local reasoner creates and

maintains a local tableau based on (only) local knowledge

• A local reasoner may query other reasoners if its local knowledge is incomplete

• Global relation among tableaux is created by messages

(1)

(2)(3)

(4)



T3

x

ALCPC Expansion Example

• P1: 1:A 1:B• P2: 1:B 2:C• P3: 2:C 3:D• Query: if A D

(witnessed by P3)

L3(x)={A⊓

D, C D⊔A,C, D}

r(x,C)

x x

r(x,A)

T2 T1

L2(x)={B C⊔C, B}

L1(x)={A B⊔A, B }

r(x,B)

(x)

(x) (x)

Transitive Subsumption Propagation

Messages:• m(x,C): if copy of x has label C• r(x,C): add C into the label of x (or its copy) • Message Target: C’s home package reasoner

, B



ALCPC Expansion Example (2)

x1

{A1}

x1

{B1}

{A3}

x4

Local Reasonerfor package A

Local Reasonerfor package B

{A2}

x2

rA

{B2}x3

rB

{B3}

x4

rB

x1

{A1,B1}

{A2}

{A3,B3}

{B2}x2 x3

x4

The (conceptual) global tableau

rA rB

rB



More complex situations

[Bao & Honavar, WI2006]

• Cyclic name importing

• Asynchronous parallel reasoning

[Bao etal, (to be submitted)]

• Role, nominal importing

• Component languages in SHOIQ



Ongoing: Concealable Reasoning

• A reasoner should not expose hidden knowledge

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

QueriesYes

Unknown



Outline

• Motivation


• Semantics

• Reasoning

• Applications

• Conclusions



Collaborative Ontology Building

Ontology modularity facilitates collaborative building

• Each package can be independently developed

• Multiple users can concurrently edit the ontology on different packages

• Ontology can be only partially loaded• Unwanted interactions are minimized by

limiting term and axiom visibility


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

Pig Package

Cattle Package

Chicken Package

http://sourceforge.net/projects/cob/



WikiOnt 2 (under development)

A Wiki-based Ontology Editor with GUI

Will be on http://sourceforge.net/projects/wikiont/



Outline

• Motivation


• Semantics

• Reasoning

• Applications

• Conclusions



Main Contributions

• Investigate the requirement and formal semantics of modular ontologies

• Present a formal modular ontology language, P-DL, that can overcome many limitations in existing approaches– Stronger expressivity– Solve some inference difficulties

• Present a federated reasoning algorithm for P-DL that can – strictly avoid integration of ontology modules– handle reasoning tasks not solvable in existing approaches

• Apply the notion of modular ontology in collaborative ontology building



Ongoing work

• Reasoning with OWL (SHOIQ) + Package extension

• Reasoning with selectively hidden knowledge

• The implementation of the distributed reasoner (based on Pellet)

• WikiOnt 2



PublicationsLanguage Features• 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.

Semantics• 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.

http://boole.cs.iastate.edu:9090/popeye/Wiki.jsp?page=Academic.Basic.CV.Publication



Publications

Reasoning5. Bao, J.; Caragea, D.; and Honavar, V. (2006) A tableau-based federated

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

6. Bao, J.; Caragea, D.; and Honavar, V. (2006) A distributed tableau algorithm for package-based description logics. In the 2nd International Workshop On Context Representation And Reasoning (CRR 2006).

Collaborative Ontology Building7. Bao, J.; and Honavar, V. (2004) Collaborative ontology building with

WikiOnt - a multi-agent based ontology building environment. In Proc. of 3rd International Workshop on Evaluation of Ontology-based Tools, at ISWC 2004, pages 37–46.

8. Bao, J.; Hu, Z.; Caragea, D.; Reecy, J.; and Honavar, V. (2006) Developing frameworks and tools for collaborative building of large biological ontologies. In The 4th International Workshop on Biological Data Management (BIDM’06). 191-195.



References (Related Work)DDL:9. A. Borgida and L. Serafini. Distributed description logics: Directed domain

correspondences in federated information sources. InCoopIS/DOA/ODBASE, pages 36-53, 2002.

10. P. Bouquet, F. Giunchiglia, and F. van Harmelen. C-OWL: Contextualizing ontologies. In Second International Semantic Web Conference, volume 2870 of Lecture Notes in Computer Science, pages 164-179. Springer Verlag, 2003.

11. L. Serafini, A. Borgida, and A. Tamilin. Aspects of distributed and modular ontology reasoning. In IJCAI, pages 570-575, 2005

12. L. Serafini and A. Tamilin. Local tableaux for reasoning in distributed description logics. In Description Logics Workshop 2004, CEUR-WS Vol 104, 2004.

13. L. Serafini and A. Tamilin. Drago: Distributed reasoning architecture for the semantic web. In ESWC, pages 361-376, 2005.

E-Connections:14. B. C. Grau. Combination and Integration of Ontologies on the Semantic Web. PhD

thesis, Dpto. de Informatica, Universitat de Valencia, Spain, 2005.15. O. Kutz, C. Lutz, F. Wolter, and M. Zakharyaschev. E-connections of abstract

description systems. Artif. Intell., 156(1):1-73, 2004.



Thanks!



SLM: exampleA schedule ontology

Hidden: details of the activity

Visible: there is an activity

[CTS06 Paper] a.k.a [1]

Package Package Hierarchy Scope Limitation



DL Interpretation - Example

Interpretation: In any world (or called model) 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



Messages

y y{C?}T1 T2

y y{C}

C(y)T1 T2



Tableau ExpansionTableau Expansion for ALCPC with acyclic concept importing

More expressive extensions in action: SHOIQ + P

Documents

Package-based Description Logics – Preliminary Results