On the Semantics of Linking and Importing in Modular Ontologies

Jie Bao. ISWC 2006 . Supported by the US NSF (0219699, 0639230) and NIH (GM 066387) 1.

Iowa State University Department of Computer ScienceArtificial Intelligence Research Laboratory

On the Semantics of Linking and Importing in Modular Ontologies

Jie Bao, Doina Caragea and Vasant Honavar

Artificial Intelligence Research Laboratory, Department of Computer Science,

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

{baojie, honavar}@cs.iastate.edu

5th International Semantic Web Conference (ISWC 2006)



Outline

• Background

• Semantics of DDL

• Semantics of E-connections

• Semantics of P-DL

• Summary



Semantic Web

Visualising the Semantic Web by Juan C. Dürsteler



No Unique Point of View



Modular Ontologies

• Modular ontologies also support– Collaborative ontology building– Distributed knowledge management– Scalable reasoning– Selective knowledge reuse



Modular Ontology Languages

• Linking approach: DDL (Distributed Description Logics) and C-OWL[Bouquet etal. ISWC 2003], E-Connections [Grau etal. ISWC 2004]

• Importing approach: P-DL (Package-based Description Logics)

O1 O2

O1 O2

1:Dog 2:Petvv

1:Dog 1:Dog 2:Petvv1:Dog



Outline

• Background




• Summary



DDL

I1Dog

Pet I2Animal I1

r12

[Borgida and L. Serafini, 2002]

• Models correspondences between concepts– 1: Animal 2:Pet (onto)– 1: Dog 2:Pet (into)vv

• Semantics given by “domain relations”



Bridge Rule Composition Problem

DDL domain relations are not composable: • r13 cannot be inferred from r12 and r23 – not transitively reusable• Similar problem also exists with composing ontology alignments

[Zimmermann & Euzenat; ISWC 2006 ]

Chickenm1 Birdm2

vv

Animalm3

vvChicken Animal ?vv



Inter-module Unsatisfiability Problem

Flym1

Birdm1

Penguinm2

Bird Penguin

~Fly Penguin



Why?

r12

Domain relations can not be seen as identity relations

• Observation 1: DDL implicitly assumes disjoint domains



Why?

• Observation 2: Bridge rules are not reducible to subsumption relations:

• Example: into rules

[Borgida & Serafini, CoopIS 2002]

BI2

AI1

(R.B)I1

r(AI1) BI2: all A’s instances are mapped to a subset of B via Rij

r(AI1)



DDL Bridge Rules vs. Subsumption

For a bridge rule to simulate subsumption

it should preserve properties of subsumption• Transitivity

• Non-emptiness

• Transfer of (Un)satisfability

Domain relations of DDL are not

9R¡ :C9R¡ :C D DC

should be ??

R=R+R=R+

R v ? £ ?R v ? £ ?

9R¡ :F lyu 9R¡ :: F ly9R¡ :F lyu 9R¡ :: F ly



A (Partial) Solution

• Requiring domain relations to be bijective (one-to-one) solves the inter-module unsatisfiability problem[Serafini et al IJCAI 2005]

• DDL alone currently does not provide such a semantics• Bridge rules still cannot be composed

r12



Outline

• Background




• Summary



E-Connections

• Allow multiple “link” relations between two local domains

• Links can be used to construct local concepts

[Grau, 2005]

PetOwner

Pet

PetOwner

Petowns



E-connections vs. DDL

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

with Inverse links



Limitations of E-Connections

• Local domains are explicitly disjoint• Hence, E-connections present difficulty with

– The use of foreign concepts or roles– Inter-module concept subsumption or role

subsumption– Instantiation of external concepts or roles

[Grau, 2005]



Outline

• Background




• Summary



P-DL

• Package-based Description Logics• A package contains

– a local signature (local terms)– an external signature (imported terms)

[Bao et al, CTS 2006, ASWC 2006]



Semantics of P-DL: Main Intuition

• Importing as “citation”

• Package 2 cites package 1 for the definition of ‘1:Dog’– Interpretation of ‘1:Dog’ is shared.– Citation does not mean global complete agreement, e.g.

on Cats.

P1 P2

1:Dog 2:PetDog 1:Dogvv



P-DL Semantics

• Domain relations are transitive (compositionally consistent)

r13=r12 O

r23

• Local domains can be partially overlapping

• The interpretations of ‘1:Dog’ in all packages are identical

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)



Inference in P-DL

²

²importee

importer consequences

• Each package witness consequences from its own point of view



Inference via Witness

• Inter-module subsumption is transitive: A Q witnessed by P4

• The importing relation is directional: A D witnessed by P2

but not by P1

• Overlap between local models is only partial: interpretation of E and F in P1’s model may not be shared

• Different packages can witness different consequences

A BC D E F

1B CC P

2B,C

B C

3

B,C

P Q

4P

v

v



Distributed Reasoning

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



DDL, E-connections vs. P-DL

• DDL and E-connections can be reduced to P-DL with concept importing– DDL bridge rules subsumption between imported and local

concepts– E-Connections links roles with imported concepts in ranges

• Is DDL + E-connections = P-DL?– No– One-to-one domain relations can be simulated by DDL

+ E-connections– Transitivity of domain relations – necessary for

compositional consistency - is unique to P-DL



Outline

• Background




• Summary



Summary

• Disjoint local domains lead to several limitations of DDL and E-Connections

• Importing with partially overlapped local domains– Supports semantic import

• Supports contextualized knowledge and partial reuse• Supports transitive reuse of knowledge

– Avoids some DDL inference problems • bridge rule composition problem • inter-module unsatisfiability problem

– Supports modeling scenarios of DDL and E-Connections



Ongoing and Future Work

• Federated Reasoning:– ALC + acyclic concept importing[Bao etal, CRR 2006]

– ALC + cyclic concept importing + parallel tableau search[Bao & Honavar, WI 2006]

– SHOIQ + free concept/role importing (ongoing)• Tools

– COB Editor (collaborative ontology building for life science)

– WikiOnt 2 (wiki-based modular ontology editor)



Thanks



owl:imports

• owl:imports = syntactic “copy and paste”

O1

imports O1

O2

• The complete loss of ontology contexts• No partial reuse



Desiderata: Exact Reasoning

vv

Integrated ontology Modular ontology

Dog Animal vvDog Animal



Desiderata: Directional Knowledge Transfer

PeopleDog

O1 O2



Desiderata: Localized Semantics

Local Semantics

PeoplePet

O1 O2



Desiderata: Transitive Reuse

Dogvv

vvDog Animal

Pet Animalvv

O1 O2 O3



Mapping Approach

• Distributed Description Logics (DDL): simulate inter-module concept subsumption using bridge rules

• E-Connections allow roles to link concepts in different modules

Pet

ownsPetOwner Pet

Dog

vv

vv



Importing Approach

• owl:imports: syntactic “copy and paste”

• Package-based Description Logics (P-DL): semantic importing

O1

imports O1

O1

imports 1:xx x



P-DL Semantics

A concept is (distributed) satisfiable iff it is satisfiable in the integrated ontology (reasoning exactness)

• Let #(.) be the reduction from P-DL to DL, e.g.,

• Let I(P) be the importing transitive closure of a package P.

• A concept C said satisfiable witnessed by P – if there is a (distributed) model of C, P and I(P)– Iff #(C) is satisfiable in #(P,I(P))

Technology

On the Semantics of Linking and Importing in Modular Ontologies