Modular Ontologies - A Formal Investigation of Semantics and Expressivity Jie 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 1

Outline Desiderata of Modular Ontologies Abstract Modular Ontology (AMO) Semantics & Expressivity Comparison Summary & Conclusion ASWC, Sept 7, 2006, Beijing, China 2

Modularity ASWC, Sept 7, 2006, Beijing, China 3

A Modular Semantic Web Visualising the Semantic Web by Juan C. Dürsteler ASWC, Sept 7, 2006, Beijing, China 4

Modular Ontologies What is modular ontology? Why 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 5

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 6

Modular Ontology Approaches 1998 2002 2003 2004 2005 2006 CTXML C-OWL DFOL DDL Role<->Concept Mapping P-DL OWL P-OWL (Planning) E-Connections CЄ(SHIF(D)) CЄ (SHOIN(D)) IHN+s ASWC, Sept 7, 2006, Beijing, China 7

Requirements Semantic soundness Needed language features Reasoning correctness Module autonomy Needed language features Concept relations Role relations … ASWC, Sept 7, 2006, Beijing, China 8

Localized Semantics Integrated ontology Modular ontology Local Models Materialized Global Model ASWC, Sept 7, 2006, Beijing, China 9

Exact Reasoning Integrated ontology Modular ontology C D C D ASWC, Sept 7, 2006, Beijing, China 10

Directional Semantic Relations D E D E ASWC, Sept 7, 2006, Beijing, China 11

Transitive Reusability C D D E E F C F ASWC, Sept 7, 2006, Beijing, China 12

Decidability C D is answerable in finite steps ASWC, Sept 7, 2006, Beijing, China 13

Language Features Concept Subsumption Concept Construction with Foreign Concepts Concept Construction with Role Restrictions. Role Inclusion Role Inversion Role Construction Transitive Role Nominal Correspondence Trans(1:P), 1:P used in 2 ASWC, Sept 7, 2006, Beijing, China 14

Outline Desiderata of Modular Ontologies Abstract Modular Ontology (AMO) Semantics & Expressivity Comparison Conclusion ASWC, Sept 7, 2006, Beijing, China 15

Multiple observers of a domain Local Points of View agents agents The domain Multiple observers of a domain ASWC, Sept 7, 2006, Beijing, China 16

Abstract Modular Ontology (AMO) Δ 1 Δ 2 DL1 DL2 r13 2 r23 1 r13 1 DL3 Δ 3 Semantics ASWC, Sept 7, 2006, Beijing, China 17

(General) Domain Relations neighbourOf Δ 1 Δ 3 r13 friendOf ASWC, Sept 7, 2006, Beijing, China 18

Image Domain Relation Δ r13 Δ 1 3 ASWC, Sept 7, 2006, Beijing, China 19

Concept Image r13 Agent3: "these objects in my mind state correspond to the concept Leg from agent 1’s mind state" ASWC, Sept 7, 2006, Beijing, China 20

Role Image Δ 1 Δ 3 P r13 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 21

Possible AMO Expressivity Features ASWC, Sept 7, 2006, Beijing, China 22

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: ASWC, Sept 7, 2006, Beijing, China 23

Semantic Soundness Definitions (2) Reusability C D Transitive Reusability Δ 1 Δ 2 Δ 3 (an agent can infer local constraints based on observing constraints in other agents’ points of view) ASWC, Sept 7, 2006, Beijing, China 24

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 Local Models Integrated Model (consensus) ASWC, Sept 7, 2006, Beijing, China 25

Outline Desiderata of Modular Ontologies Abstract Modular Ontology (AMO) Semantics & Expressivity Comparison Conclusion ASWC, Sept 7, 2006, Beijing, China 26

DDL Semantics 1:Dog into 2:Animal 1:Dog onto 2:Hound [Borgida and L. Serafini, 2002] 1:Dog into 2:Animal citation 1:Dog onto 2:Hound implicit domain disjointness ASWC, Sept 7, 2006, Beijing, China 27

Subsumption Propagation Problem Cm1 C into D Dm2 C into E ? D into E Em3 DDL domain relations are not transitively reusable ASWC, Sept 7, 2006, Beijing, China 28

Inter-module Unsatisfiability Problem Flym1 Bird onto Penguin Penguinm2 Birdm1 ~Fly onto Penguin DDL allows arbitrary domain relations: loss of reasoning exactness ASWC, Sept 7, 2006, Beijing, China 29

DDL: Pros & Cons Pros Cons 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 30

E-Connections Local domains are disjoint [Grau, 2005] Local domains are disjoint It allows multiple “link” relations between two local domains Links can be used to construct local concepts ASWC, Sept 7, 2006, Beijing, China 31

E-Connections Semantics R ASWC, Sept 7, 2006, Beijing, China 32

E-Connections: Pros & Cons 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 33

P-DL Semantic Importing [Bao et al., 2006] ASWC, Sept 7, 2006, Beijing, China 34

P-DL Semantics x x’ ΔI1 ΔI2 CI1 CI2 Domain relation: individual correspondence between local domains r12 ΔI3 r13 r23 x’’ CI3 Importing establishes one-to-one domain relations “Copied” individuals are shared Domain relations are compositionally consistent: r13=r12 O r23 Therefore domain relations are transitively reusable. 35

P-DL Semantics (2) r12 r13 r23 ΔI1 ΔI2 ΔI3 CI2 CI1 CI CI3 x x’ x x’’ Global model obtained from local models by merging shared individuals ΔI3 36

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 37

P-DL: Pros & Cons Pros Cons 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 38

Summary: Semantic Soundness ASWC, Sept 7, 2006, Beijing, China 39

Summary: Expressivity ASWC, Sept 7, 2006, Beijing, China 40

Outline Desiderata of Modular Ontologies Abstract Modular Ontology (AMO) Semantics & Expressvity Comparison Conclusion ASWC, Sept 7, 2006, Beijing, China 41

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 42

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 43

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 44

Thanks! ASWC, Sept 7, 2006, Beijing, China 45

Semantic Soundness What 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? r13 y a b x friendOf friendOf ? r13 y a b x friendOf enemyOf a/x b/y friendOf ASWC, Sept 7, 2006, Beijing, China 46