Representing and Reasoning with Modular Ontologies (2007)

Representing and Reasoning with Modular Ontologies Ph.D. Dissertation Defense Major advisor: Vasant Honavar Jie Bao Artificial Intelligence Research Laboratory Computer Science Department Iowa State University Ames, IA USA 50011 Email: baojie@cs.iastate.edu July 10, 2007

Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

From Web to Semantic Web Ontology: a “PhD Candidate” is a “Student”

Semantic Web Figure courtesy of Tim Berners-Lee, AAAI 2006

A Very Very Short DL Primer ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],concept role individual axioms

DL Families ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

From Web Pages to Ontologies ,[object Object],[Diagram: Joanne Luciano, Predictive Medicine ; Drug discovery demo using RDF, Sideran Seamark and Oracle 10g] ,[object Object]

Distributed, Modular Ontologies ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analogy: Paper Writing Citation is not copy+paste, hence does not result in a single, combined document Recent development in modular ontologies… In this paper, we present two algorithms A and B to … (Alice, 2001) (Bob, 2007) Combining Ontologies Ontology Modularization Recent development in modular ontologies… In this paper, we extend the algorithm A proposed by (Alice,2001) … Same global domain: modular ontologies Multiple independent participants Possible (partial) reuse Contextualized Semantics

Modular Ontology Languages: State-of-the-art overview C Є (SHOIN(D)) OWL 1998 2002 2003 2004 2005 2006 2007 C-OWL CTXML E-Connections P-DL DDL DFOL DDL with Role  Concept Mapping C Є (SHIF(D)) IHN + s DL ALCP C SHOIQP

Ontology Reuse in OWL: Syntactic Importing ,[object Object],[object Object]

Analogy: Paper Writing in OWL fashion copy+paste ,[object Object],[object Object],Recent development in modular ontologies… In this paper, we present two algorithms A and B to … (Alice, 2001) (Bob, 2007) Combining Ontologies Ontology Modularization Recent development in modular ontologies… In this paper, we extend the algorithm A proposed by (Alice,2001) …

DDL ,[object Object],[object Object],[object Object],[object Object],(onto) (into) Pet Animal Dog I 1 Dog Pet I 2 Animal I 1 r 12

DDL Semantics: Problem with Bridge Rules ,[object Object],[object Object],[object Object],1:Chicken 2:Bird 3:Animal Chicken Animal ?

DDL Semantics: Problem with Bridge Rules ,[object Object],1: Fly 1: Bird 2:Penguin Bird Penguin ~Fly Penguin

E-Connections ,[object Object],[object Object],PetOwner Pet PetOwner Pet  owns

E-Connections [Grau, 2005] ,[object Object],[object Object],[object Object],[object Object],[object Object]

Section summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Package-Based Description Logics (P-DL) ,[object Object],O 1 (Animal) O 2 (Pet)

Syntax of P-DL i ,[object Object],[object Object],[object Object],[object Object],P i Male, Female P j 

Semantics of P-DL ,[object Object],People Animals O 1 O 2

Semantics of P-DL ,[object Object],[object Object],[object Object],[object Object],[object Object],P 1 P 2 1:Dog 2:PetDog 1:Dog

Semantics of P-DL ,[object Object],[object Object],[object Object],[object Object],[object Object],x x’ Δ I 1 Δ I 2 1:Dog I 1 1:Dog I 2 r 12 Δ I 3 r 13 r 23 x’’ 1:Dog I 3

Semantics of P-DL ,[object Object],importee importer consequences importer consequences ² ²

Properties of P-DL ,[object Object],[object Object],Integrated ontology Modular ontology Dog Animal Dog Animal

Properties of P-DL ,[object Object],X D E A B A B D E

Properties of P-DL ,[object Object],[object Object],Dog Dog Animal Pet Animal P 1 P 2 P 3 (P j imports P i )

P-DL Families ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

DDL and E-connections vs P-DL ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Section Summary (Details in dissertation Table 4.4) 1,4 Limited Support 2,3 May be simulated using syntactical encoding

Tableau Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],Ontology: Man ⊑ Human Model: Man Human

Tableau Algorithm: Example ,[object Object],[object Object],[object Object],[object Object],Completion Tree (Tableau) Note: the tableau is simplified for demonstration purpose If “Dog” is satisfiable? goofy L(goofy)={Dog, Animal, eats.DogFood } foo L(foo)={DogFood } {eats} pedigree L(pedigree)={Brand } {hasTM} walmart L(walmart)={Supermarket} {soldBy}

Reasoning for Modular Ontology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Federated Reasoning ,[object Object],[object Object],[object Object],What is a “Dog”? “ Dog” is a type of “Animal” Dog Dog ⊑ Animal P 2 P 1

Distributed Tableau ,[object Object],[object Object],[object Object],[object Object],(Virtual) combined tableau for the (conceptual) integrated ontology from all packages

Construction of Distributed Tableau ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],{ other axioms … } O 1 (Animal) O 2 (Pet)

Example ,[object Object],[object Object],R 1  2 (x 1 ,Animal) {Animal} R 1  2 (x 2 ,Animal) Note: the tableau is simplified for demonstration purpose PetDog ⊑ Dog PetDog ⊑  eats.DogFood Dog ⊑ Carnivore Carnivore ⊑ Animal Carnivore ⊑  eats.Animal x 1 {PetDog} Local Reasoner 2 (for package Pet) R 1  2 (x 1 ,Dog) {DogFood} x 2 {eats} {eats} x 2 ’ x 1 {Dog,Carnirvore,Animal} ’ Local Reasoner 1 (for package Animal) R 1  2 (<x 1 ,x 2 >,eats) Expansion for other axioms in P Animal

Section Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Partially Hidden Knowledge Locally visible : Has date Globally visible : Has activity Bob’ schedule ontology

Privacy-Preserving Reasoning ,[object Object],[object Object],Queries Yes Unknown

Privacy-Preserving Reasoning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Collaborative Ontology Building ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The COB Editor Pig Package Cattle Package Chicken Package

Contributions Figure courtesy of Tim Berners-Lee, AAAI 2006 ,[object Object],[object Object],Chapter 3,4 ,[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 5 ,[object Object],[object Object],[object Object],Chapter 6 ,[object Object],[object Object],Chapter 7

Results ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Future Work ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Acknowledgement ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Why not owl:imports? ,[object Object],[object Object]

Hidden Knowledge vs. Incomplete Knowledge ,[object Object],[object Object],[object Object],[object Object],[object Object]

Privacy-Preserving Reasoner ,[object Object],[object Object],[object Object],[object Object],q R A  {Y,N,U} KB q R KB false

Example: Hierarchies unknown YES 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 )

Example: Hierarchies a b c d e Y Y “ unsafe” graph “ safe” graph Reasoning Strategy: Safety Scope: a b c d e

Privacy-preserving reasoning with DL ,[object Object],[object Object],[object Object],[object Object],Hidden knowledge (K h ) Visible knowledge (K v ) Critical visible knowledge (K vc ) C ⊑ D C ⊑  R. D G ⊑ H axioms that contain names in Sig(K h )

Privacy-preserving reasoning with P-DL ,[object Object],[object Object],r(x,Dog), r(x,  Animal)  Dog ⊑ Animal P 1 Dog ⊑ Animal inferred!

Section Summary ,[object Object],[object Object],[object Object]

WikiOnt ,[object Object],[object Object],[object Object]

Representing and Reasoning with Modular Ontologies (2007)

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