Representing and Reasoning with Modular Ontologies

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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_at_cs.iastate.edu
• July 10, 2007

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Outline

• Introduction
• Motivation, desiderata and state-of-the-art of
  modular ontologies
• Representing Modular Ontology
• Using Package-based Description Logics (P-DL)
• Reasoning with Modular Ontology
• Distributed reasoning in P-DL using tableau
  algorithm
• Privacy-Preserving Reasoning with Hidden
  Knowledge
• Collaborative Building of Modular Ontologies

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From Web to Semantic Web
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Semantic Web
Figure courtesy of Tim Berners-Lee, AAAI 2006
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A Very Very Short DL Primer

• Description Logics (DL)
• a knowledge representation formalism to describe
  ontologies
• the foundation for web ontology languages, e.g.,
  OWL
• Ontology example
• A Dog is an Animal
• A Dog eats some DogFood
• goofy is a Dog

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DL Families

• ALC
• ? (disjunction) Child Boy ? Girl
• ? (conjunction) Mother Female ? Parent
• ? (existential restriction) Parent ?
  hasChild.Human
• ? (value restriction) Human ? ? hasBrother.Man
• ? (negation) Boy ? ?Girl
• SHOIQ
• SALCtransitive role Trans(hasSibling)
• H (role hierarchy) hasBrother ? hasSibling
• O (nominal, i.e., concept that has single
  instance) Sun, France
• I (inverse role) hasChild hasParent-
• Q (qualified number restriction) Human ? (2
  hasParent.Human)

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From Web Pages to Ontologies
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Distributed, Modular Ontologies

• Distributed ontology modules
• Are produced by autonomous participants
• Are limited in their scope
• Represent different points of view
• Have (potentially) partially overlapping domains
• Lack global semantics
• Need contextualized semantics
• Need selective or partial knowledge reuse
• Need distributed inference algorithms without
  forcing ontology integration
• Should facilitate network effect

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Analogy Paper Writing
Citation is not copypaste, hence does not
result in a single, combined document
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Modular Ontology Languages State-of-the-art
overview
1998 2002 2003
2004 2005
2006 2007
C-OWL
CTXML
DDL
DDL with Role ??Concept Mapping
DFOL
P-DL
DL
ALCPC
SHOIQP
OWL
E-Connections
C? (SHOIN(D))
C?(SHIF(D))
IHNs
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Ontology Reuse in OWL Syntactic Importing

• The OWL primitive intended to support ontology
  reuse is owlimport
• One can use owlimport to copy-and-paste an
  ontology into another

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Analogy Paper Writing in OWL fashion
copypaste

• no partial reuse
• loss of context

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DDL

• Distributed Description Logics (DDL) Borgida
  Serafini, 2002
• Allows bridge rules between concepts across
  ontology modules
• Bridge rules between roles are similar
• Semantics given by domain relations

(onto)
(into)
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DDL Semantics Problem with Bridge Rules

• DDL bridge rules are not compositional
• r13 cannot be inferred from r12 and r23
• Knowledge is not transitively reusable!

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DDL Semantics Problem with Bridge Rules

• DDL bridge rules do not preserve concept
  unsatisfiability across modules

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E-Connections

• E-connections allow multiple links between two
  local domains Grau, 2005
• Links can be used to construct local concepts

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E-Connections Grau, 2005

• A concept cannot be declared in an ontology as a
  subclass of a foreign concept
• A property cannot be declared as sub-relation of
  a foreign property
• An individual cannot be declared as an instance
  of a foreign concept
• A pair of individuals cannot instantiate a
  foreign property
• The use of E-Connections semantics with
  owlimports syntax leads to several difficulties

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Section summary

• OWL
• No localized or contextualized semantics,
• No partial reuse.
• DDL
• Allows inter-module concept inclusions (but not
  inter-module roles)
• In general, does not support transitive knowledge
  reuse or preservation of unsatisfiability
• E-Connections
• Allows inter-module roles (but not concept
  inclusions)
• Presents strong expressivity limitation
• P-DL aims to overcome these limitations

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Outline

• Introduction
• Motivation, desiderata and state-of-the-art of
  modular ontologies
• Representing Modular Ontology
• Using Package-based Description Logics (P-DL)
• Reasoning with Modular Ontology
• Distributed reasoning in P-DL using tableau
  algorithm
• Privacy-Preserving Reasoning with Hidden
  Knowledge
• Collaborative Building of Modular Ontologies

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Package-Based Description Logics (P-DL)

• P-DL support semantic importing

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Syntax of P-DL

• Contextualized negation
• There is no global negation, but only
  contextualized negation for each package
• Example

i
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Semantics of P-DL

• Localized Semantics

People
Animals
O1
O2
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Semantics of P-DL

• Semantic importing akin to citation
• Package 2 cites package 1 for the definition of
  1Dog
• Interpretation of 1Dog is the same on the
  shared portions of the local domains of packages
  1 and 2
• The two packages need not agree on the
  interpretation of other unrelated concepts (e.g.,
  Cats)
• P-DL supports selective knowledge reuse

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Semantics of P-DL

• Importing establishes one-to-one domain relations
  
• (1Dog)I2 r12(1DogI1)

• Domain relations are composi-tionally consistent
• r13r23 O r12
• More requirements are needed when importing of
  roles and nominals are allowed.

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Semantics of P-DL

• Each package witnesses consequences from its own
  point of view (using its local and imported
  knowledge)

importer
consequences
importee
importer
consequences
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Properties of P-DL

• Exact Reasoning
• extending an ontology in the classic way and in
  the modular way will ensure same inferential
  results.

Integrated ontology
Modular ontology

Dog Animal
Dog Animal
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Properties of P-DL

• Directional Relation

X
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Properties of P-DL

• The preservation of unsatisfiability
• Transitive Reusability

(Pj imports Pi)
Animal
Dog
Pet
P1
P2
P3
Dog Animal
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P-DL Families

• P package extension with importing of any type
  of names (concept, role and nominal)
• P- - acyclic importing if P (directly or
  indirectly) imports Q, then Q cannot (directly or
  indirectly) import P
• PC importing of concept names only
• Examples
• ALCPCBao et al,CRR 2006
• ALCPC-Bao et al,WI 2006
• SHIQPBao et al,ISWC 2007
• SHOIQPBao et al,AAAI 2007

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DDL and E-connections vs P-DL

• P-DL can simulate
• DDL with bridge rules using subsumption between
• imported concepts and local concepts
• imported roles and local roles
• (one-way binary) E-Connections using roles that
  relate a local concept with an imported concept
• DDL, E-Connection or their combination cannot
  simulate P-DL
• One-to-one domain relations cannot be simulated
  by DDL or E-Connections
• P-DL, unlike DDL and E-connections, supports
  transitive reuse of knowledge

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

• Introduction
• Motivation, desiderata and state-of-the-art of
  modular ontologies
• Representing Modular Ontology
• Using Package-based Description Logics (P-DL)
• Reasoning with Modular Ontology
• Distributed reasoning in P-DL using tableau
  algorithm
• Privacy-Preserving Reasoning with Hidden
  Knowledge
• Collaborative Building of Modular Ontologies

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Tableau Algorithm

• Description Logics usually uses the Tableau
  Algorithm Baader Sattler 2001 for reasoning
  tasks.
• A tableau is a representation of a model
• A model for an ontology represents a world which
  satisfies assertions in the ontology.
• Decidable DLs typically have tree models
  Vardi,1996
• Tableau algorithms try to check concept
  satisfiability w.r.t. a KB by constructing a
  tree that is the model of the concept and the KB

Human
Ontology Man ? Human
Model
Man
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Tableau Algorithm Example

• Dog ? Animal
• Dog ? ?eats.DogFood
• DogFood ? ? hasTM.Brand
• DogFood ? ? soldBy.Supermarket

If Dog is satisfiable?
Completion Tree (Tableau)
Note the tableau is simplified for demonstration
purpose
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Reasoning for Modular Ontology

• Major Considerations
• Avoid integrating ontology modules
• Minimize local memory cost
• Respect module autonomy, e.g., privacy
• Question can we reason with P-DL without
• (syntactic level) an integrated ontology ?
• (semantic level) a (materialized) global tableau
  ?

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Federated Reasoning

• There are multiple local reasoners, one for each
  package
• Each local reasoner only knows and uses local
  knowledge
• A reasoner may ask another reasoner (by messages)
  about the meaning of imported names .

What is a Dog?
Dog is a type of Animal
Dog
P2
P1
Dog ? Animal
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Distributed Tableau

• Distributed tableau
• each local tableau is a fragment of the virtual
  global tree
• thus, each local tableau is a forest
• a node may be shared among local tableaux
  (indicated by domain relations)

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Construction of Distributed Tableau

• Developed algorithms ALCPC, ALCPC-, SHIQP
• Basics of the algorithm
• Intra-tableau expansion rules e.g., if C?D?
  L(x), then C,D lt L(x)
• Inter-tableau expansion rules e.g., if C ?
  L(x), C is defined in another package P, then
  send a reporting message r(x,C) to the reasoner
  of P.
• Termination is guaranteed using suitable
  blocking rules.
• The algorithm is proven to be sound and complete.

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Example

• Check if PetDog is satisfiable as witnessed by O2

other axioms
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Example

• Each local reasoner maintains a local tableau.
• Connections between local tableaux is created by
  a set of messages.

Dog ? Carnivore Carnivore ? Animal
PetDog ? Dog
PetDog ? ?eats.DogFood
Carnivore ? ?eats.Animal
R1?2(x1,Animal)
Animal
R1?2(x2,Animal)
Note the tableau is simplified for demonstration
purpose
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Section Summary

• Distributed reasoning algorithms have been
  designed for P-DL
• Federated no integration of all ontology modules
  is required
• Peer-to-peer each local reasoner only requires
  local knowledge
• Parallel subtasks in reasoning can be explored
  concurrently by multiple reasoners
• Message-based the overall reasoning process is
  enabled by messages exchanged between local
  reasoners.
• Algorithms available for ALCPC-, ALCPC, SHIQP

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Outline

• Introduction
• Motivation, desiderata and state-of-the-art of
  modular ontologies
• Representing Modular Ontology
• Using Package-based Description Logics (P-DL)
• Reasoning with Modular Ontology
• Distributed reasoning in P-DL using tableau
  algorithm
• Privacy-Preserving Reasoning with Hidden
  Knowledge
• Collaborative Building of Modular Ontologies

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Partially Hidden Knowledge
Globally visible Has activity
Locally visible Has date
Bob schedule ontology
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Privacy-Preserving Reasoning

• A reasoner should not expose hidden knowledge
• However, such hidden knowledge may still be
  (indirectly) used in safe queries.

Yes
Queries
Unknown
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Privacy-Preserving Reasoning

• Practical algorithms designed for
• Hierarchical ontologies. (e.g. biological
  ontologies)
• Description Logics (e.g. SHIQ)
• Open for P-DL
• Applications
• Privacy protection in medical information system
• Secure web service
• Query answering in p2p applications

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Outline

• Introduction
• Motivation, desiderata and state-of-the-art of
  modular ontologies
• Representing Modular Ontology
• Using Package-based Description Logics (P-DL)
• Reasoning with Modular Ontology
• Distributed reasoning in P-DL using tableau
  algorithm
• Privacy-Preserving Reasoning with Hidden
  Knowledge
• Collaborative Building of Modular Ontologies

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Collaborative Ontology Building

• Ontology modularity facilitates collaborative
  building
• Each package can be independently developed
• Different curators can concurrently edit the
  ontology on different packages
• Ontology can be only partially loaded
• Unwanted interactions are minimized by limiting
  term and axiom visibility
• Prototypes
• COB-Editor Bao et al, BIDM 2006
• WikiOnt Bao Honavar, EON 2004

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The COB Editor
Pig Package
Cattle Package
Chicken Package
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WikiOnt 2 (Ongoing)
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Contributions
Figure courtesy of Tim Berners-Lee, AAAI 2006
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Results

• Presentations
• Academic Conferences AAAI-07, RR-07 (Web
  Reasoning and Rule System), WI-06 (Web
  Intelligence), ISWC-06(International Semantic Web
  Conference), ASWC-06 (Asian Semantic Web
  Conference, Best Paper)
• Industrial Conferences SemGrail (Microsoft)
  2007, Semantic Technology Conference 2007
• Funding
• Results of this study formed the basis of
  proposals on modular ontologies that were funded
  by NSF (IIS-0639230) and ISU CIAG (Center for
  Integrated Animal Genomics)
• Community Involvement
• 4 workshop organization efforts on related topics
  (SWeCka 2006,2007, Modular Ontologies (WoMo)
  2006,2007)

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Future Work

• Modular Ontology Framework
• Understanding modular ontology using DL rules
  RDF modularity
• Extending P-DL
• ABox, Query, Syntax, Interfaces and Views
• Distributed Reasoning
• Implementation, SHOIQ reasoning, optimization
• Privacy-Preserving Reasoning
• P-DL, RDF, medical ontologies
• Applications
• WikiOnt2, Semantic Data Integration (INDUS
  project)

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Acknowledgement

• Major advisor Vasant Honavar
• Modular Ontology Group Giora Slutzki, Doina
  Caragea, George Voutsadakis
• COB-Editor Group LaRon Hughes, Zhiliang Hu,
  Peter Wong, James Reecy,
• Medical Ontology Building Yu Cao, Wallapak
  Tavanapong,
• INDUS Group Doina Caragea, Jyotishman Pathak,
  Neeraj Koul, Jaime Reinoso-Castillo
• Discussion Gary Leavens, Dae-ki Kang,
  Rafael-Armando Jordan, Adrian Silvescu, Kewei Tu,
  Jun Zhang, Feihong Wu, Changhui Yan, Hua Pei, Hua
  Ming, and other members of the AI Lab.
• Non-ISU collaboration Jeff Pan, Yimin Wang,
  Luciano Serafini, Andrei Tamilin, Zhengxiang Pan
  and Jing Mei.
• Research supported by funding from National
  Science Foundation (IIS 0219699,0639230),National
  Institutes of Health (GM 066387), and Center for
  Integrated Animal Genomics, Iowa State
  University, and grants from USDA NAGRP
  Bioinformatics Coordination Project.

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• Backup

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Why not owlimports?

• owlimports does not preserve semantics of
  imported concepts or roles as defined in the
  source ontology (loss of context)
• owlimports does not support partial reuse

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Hidden Knowledge vs. Incomplete Knowledge

• Open World Assumption (OWA)
• An ontology may have only incomplete knowledge
  about a domain
• KB Dog is Animal
• Query if Cat is Animal ? Unknown if
  Cat is not Animal ? Also unknown
• Hidden knowledge can be protected as if it is
  incomplete knowledge

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Privacy-Preserving Reasoner

• A privacy-preserving reasoner should be
• History independent it answers in the same way
  regardless the history of past queries
• Honest it never lies
• History safe answers and visible knowledge
  combined cannot be used to infer hidden knowledge

q
A ?Y,N,U
R
KB
q
R
false
KB
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Example Hierarchies
60
Example Hierarchies
a
Reasoning Strategy
Y
b
c
Safety Scope
d
Y
e
safe graph
unsafe graph
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Privacy-preserving reasoning with DL
G ? H
Visible knowledge (Kv)
C ? ?R.D
Critical visible knowledge (Kvc)
axioms that contain names in Sig(Kh)
C ? D
Hidden knowledge (Kh)

• Critical visible knowledge (Kvc) contains
  existing knowledge about Sig(Kh)
• If we can ensure Kv QY will not give extra
  information about Sig(Kh), other than that Kvc,
  then the reasoner is safe
• Conservative ExtensionGrau etal, 2006 ?a of
  Sig(Kvc), Kvc a iff KvQY a
• Practical algorithm exists for SHIQ (using local
  ontologiesGrau et al, IJCAI 2007)

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Privacy-preserving reasoning with P-DL

• Still an open problem
• Key issue message safety

r(x,Dog), r(x,?Animal)
?
Dog ? Animal inferred!
P1
Dog ? Animal
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Section Summary

• Selective knowledge reuse using partially hidden
  knowledge
• Privacy-preserving reasoning based on the open
  world assumption
• Practical algorithms available for hierarchies
  and DL SHIQ.

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WikiOnt

• A web browser based ontology editor
• Using Wiki script to store ontologies
• With features to support team work, version
  control, page locking, and navigation.