Modularizing OWL Ontologies

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Modularizing OWL Ontologies

• Bernardo Cuenca Grau, Bijan Parsia, Evren Sirin
  and Aditya Kalyanpur
• University of Maryland, College Park

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Multiplicity in Web ontologies

• Key features of the Web
• Mostly global identifers
• URIs/IRIs
• Identifer-based information manipulation
• HTTP GET and POST/PUT
• Distributed representations
• - Representations are (somewhat) modular
• Progressive disclosure and graceful degradation
• How do we get these things into OWL?

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URIs in OWL Ontologies

• Three key modalities of URI use
• URIs as data (mention)
• URIs as identifiers (use)
• URIs as values of owlimports (use)
• owlimports supports transclusion
• The transclusion is flat
• I.e., an include imported axioms just asserted
• HTML has these modalities

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owlimports

• Problems with owlimports
• Does not support information hiding or filtering
• None of the imported axioms retain their context.
• No effective difference between copying and
  pasting locally the imported ontology.
• OWL gives us either ALL or NOTHING

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owlimports(2)

• Without inclusion, nothing gets in
• There are (conditional) effects
• If you import or merge, same URIs get merged
• With inclusion, everything gets in
• Even things which are intuitively irrelevant
• NCI You want Gene, you also get Belief System
• The resulting ontologys logic gets complex
• The resulting ontology itself is very complex

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Modularity in Web Ontologies

• Knowledge sharing and re-use crucial research
  issues.
• Modularity, worthy the name, should provide
  advantages in the following aspects
• Maintenance and Evolution
• Understandability for Humans
• Knowledge Re-use and sharing
• Processability

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E-Connections The Basics

• An E-Connection is a knowledge representation
  language defined as a combination of other
  logical formalisms.

C()(L1,,Ln)
DLs Modal Logics Spatial Logics Temporal Logics
Component logics
New Constructors and axioms
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E-connections Combined KBs

• A Combined KB is a set of ontologies written in
  the language of an E-Connection
• Each component ontology can be written in any of
  the component logics
• Each component ontology is interpreted in a
  different logical context

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OWL Ontology (SHION(D))
Spatial KB (RCC8)
Temporal KB (Interval Temporal Logic)
Region1 DC R2. R3 EC R2. R4 PPTP R2. .
Person sub Animal Pets sub Animal Cars Trees
States Countries
T1 before T2. T3 overlaps T4.
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E-connections Connected KBs

• Components are disjoint, but related
• through links
• Individuals in the source are linked to
  individuals in the target
• Concepts can be defined in terms of the links
• A class can be defined as all those individuals
  who are linked to a specific set of individuals
  in another component
• That other set might be defined in terms of links!

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Example Applications

• A set of independently developed KBs that are now
  required to inter-operate.
• An organization wants to represent knowledge
  about intuitively disjoint, but connected
  domains.
• Migration from a monolithic to a distributed
  representation.
• Understanding of an ontology by humans.
• Reuse of the knowledge about a given domain
  within an ontology.

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What can we gain?

• Expressivity Decidability
• Description Logic with temporal or spatial logic
• Expressivity practical algorithms
• ex C(SHIQ,SHOQ,SHIO) merges to SHOIQ
• Modularity Even in C(SHIF)!
• Ability to integrate ontologies as reusable
  modules
• Ability to split up large ontologies

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IntegrationPeople and Pets example
owns
ownedBy
owns
lovesToPlayWith
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owns
DogOwner
ownedBy
Person
Unhappy PetOwner
owns
lovesToPlayWith

• DogOwner Person ? ?owns.Dog
• (owns is a link)

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owns
DogOwner
ownedBy
Person
Unhappy PetOwner
owns
lovesToPlayWith
UnhappyPetOwner Person ? ?owns.(UnfriendlyPet
)
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owns
DogOwner
ownedBy
Person
Unhappy PetOwner
owns
lovesToPlayWith
UnhappyCat Cat ? ?ownedBy.(DogOwner) ownedBy
inverseOf(owns)
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Families of E-Connection Languages

• Two ways of defining new combination languages

C()(L1,.,Ln)
Fix the component languages. Vary the
expressivity of links
Fix the expressivity of links. Vary the
combination languages
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Extensions of E-Connections

• Basic E-Connections CI(L1,,Ln)
• Inverses on links
• Extensions with number restrictions
• FanaticPetOwner PetOwner ? 20owns.Pet
• Extensions with Link hierarchies
• lovesToPlayWith ? lovesActivity
• Extensions with Booleans on Links
• FrustratedPetOwner PetOwner ? (owns
  likes).Pet

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Reasoning with E-Connections of DLs

• Depends on
• Which are the component logics
• Expressivity of the links

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Algorithms

• Direct tableau algorithm
• Intuitive extension
• Color the nodes
• Apply standard techniques to source, links, and
  target separately
• Does not perturb optimizations.
• Actually implemented quickly

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Integrating E-Connections in OWL

• ltowlClass rdfID"PetOwner"gt
• ltrdfscommentgtA Person who owns at least
  one petlt/rdfscommentgt
• ltowlintersectionOf rdfparseType"Collect
  ion"gt
• ltowlClass rdfabout"Person"/gt
• ltowlRestrictiongt
• ltowlonPropertygt
• ltowlLinkProperty
  rdfabout"owns"gt
• 
  ltowlforeignOntology rdfresource"pets"/gt
• lt/owlLinkPropertygt
• ltowlonPropertygt
• ltowlsomeValuesFromgt
• ltowlForeignClass
  rdfabout"petsPet"gt
• 
  ltowlforeignOntology rdfresource"pets"/gt
• lt/owlForeignClassgt
• lt/owlsomeValuesFromgt
• lt/owlRestrictiongt
• lt/owlintersectionOfgt
• lt/owlClassgt

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A suprising practical result Automatic
Partitioning of Web Ontologies
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Partitioning Problem

• The task
• Input An OWL ontology
• Output (Intuition) A set of semantically
  coherent modules

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Partitioning Problem (II)

• Issue How to precisely define the output
• What is a module?
• What does exactly mean that a module is
  semantically coherent?

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Intuitions

• A module of an ontology O should be
• a subset of the axioms of O
• semantically self-contained
• reusable
• evolvable
• But what does this mean?
• It should have the same essential meaning
• It should have no extra meaning

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Formalizing the problem

• OWL entities
• Classes, properties, individuals (datatypes,
  etc.)
• Typically with a URI
• As terms
• A subset of O has a vocabulary
• Simply, all the URIs used as identifiers in it
• I.e., all the entities it talks about

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Formalizing the problem

• Semantic Encapsulation
• A subset of O encapsulates an entity if it
  preserves certain essential entailments about it
• A subset of O is strongly encapsulating if it
  encapsulates all the entities in its vocabulary
• Strong encapsulation formalizes
  Self-Containment
• Which entailments (e.g., for classes)?
• Subsumption
• Satisfiabilty
• Instantiation

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Formalizing the Problem

• A module is for an entity in an ontology
• So relative to an ontology
• A module for X in O
• Is a subset of O
• Encapsulates X
• Is strongly encapsulating
• I.e., encapsulates all of the entities in its
  vocabulary
• Is minimal
• No strongly encapsulating encapsulation of X
  encapsulates fewer entities
• Say that 5 times fast!

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Formalizing the problem

• Partitioning Problem (formal)
• Input An OWL Ontology, O
• Output A module for each entity in O

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How to tackle the problem

• Generate an E-Connection, K by
• Dividing the axioms of O into disjoint sets
• Respecting the E-Connection constraints
• Preserve certain key entailments
• With the maximal number of components
• Some axioms must go together
• Disjointness of domains enforces that

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Constraints and Choices

• Recall E-connection is a set of ontologies where
• Each ontology is disjoint
• (share no classes, properties, or individuals)
• There are link relations
• between individuals in different ontologies
• Classes in an ontology can be defined in terms of
  restrictions on link relations.

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The Algorithm in a Nutshell

• Order the axioms, then
• Move the first axiom into a new component
• Find all the related axioms and move them
• Suppose, C ? D moves to the first component
• Suppose the ontology has D ? E
• D ? E must go into the first component
• (Primarily) structural tracing
• Make link relations whenever possible
• Repeat until they original list is empty.
• Surprising Result Obtained partitions are
  natural from a modeling perspective

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From Components to Modules

• Once the E-Connection has been obtained How do
  we get the module for an entity (say, X)?
• Find the component which contains X
• Trace the transitive closure of all the link
  properties of that component
• Import all the found components, converting link
  properties back to object properties
• Thats the module weve found!

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The Partitioning Graph

• The partitioning graph generated from the
  E-Connection.
• Picture Graph for OWL-S

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Output

• For each entity X in the ontology
• A subset of the axioms and assertions
• which is strongly encapsulating
• and is smaller than the ontology (usually)
• But
• Isnt minimal!

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Advantages of E-modules

• Correctness is ensured
• Partitioning to an E-Connection is a worst-case
  quadratic problem.
• The process is entirely structural
• But the theory of partitioning provides us
  semantic guarantees!
• Results in practice are good

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Some Empirical Results
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The Wines Ontology

• Canonical Example in the OWL Guide
• Contains information about Wines (central
  domain), but also about
• Wines
• Regions
• Wineries
• Grapes

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WINES ONTOLOGY
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Wines Ontology

• Very simple tree-like decomposition.
• Easy to see that wines are central to the ontology

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The NCI Ontology

• Huge ontology about the bio-medical domain.
• Designed around a set of well-defined
  sub-domains, called kinds
• Genes
• Drugs
• Biological processes,

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NCI
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The NCI Ontology

• Nice decomposition
• Components correspond to NCI kinds.
• Large proportion of leaf and independent
  components.
• For every entity, each E-module is strictly
  smaller than the whole ontology.

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OWL-S Ontologies

• Describe Web Services
• Services Core of the ontologies
• Profiles Capabilities of the services
• Processes internal structure of the service
• Grounding concrete message structures

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OWL-S
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OWL-S Ontologies

• Intuitive domains are further decomposed
• Presence of unused information

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NASAs SWEET-JPL

• NASAs terminology in Earth and Environmental
  Sciences
• Ontologies
• EarthRealm ocean, earth, atmosphere,
• Non-Living substances particles, radiation,
• Living substances plants, animals,..
• Physical Processes diffusion, evaporation,
• Physical Properties temperature, pressure,
• Units pounds, miles,
• Time
• Space
• Human Activities Commerce, Research,
• Data Data storage, format,

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NASAs SWEET-JPL
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NASAs SWEET-JPL

• Each ontology within SWEET-JPL models a domain
  which is conceptually disjoint from the rest.
• Intuitive scenario for E-Connections

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NASAs SWEET-JPL
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NASAs SWEET-JPL

• The modularization obtained using owlimports is
  misleading the physically distinct units do not
  correspond to semantically distinct ones.
• There is a significant amount of unused
  information

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GALEN

• Well-known medical ontology
• Composed of
• An upper level domain independent concepts
  (Process, Substance, )
• A domain level domain specific concepts
  (Gene, Research Institution,)

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GALEN
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GALEN

• Claimed to be modular ontology
  normalization criteria.
• Not modular, according to our approach
• Main reason the upper level prevents the
  partitioning

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Limitations

• Certain modeling patterns inhibit partitioning
• They break modularity!
• But for no good reason
• Example Galen
• Slight harmless changes would fix it
• Future work Refactoring advice
• Evolvability
• What happens when you change a module?
• E.g., add an axiom or assertion?
• Current work
• Assess the evolvability of (E-)modules

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More Expressivity

• Generalized links
• In regular E-Connections Links indexed by source
  and target
• So owns to pets and owns to furniture not the
  same!
• Treat each link as indexical wrt source and
  target
• Range and domain of the link are disjoint unions
• A side benefit Transitive links
• We can define expressive transitive (generalized
  link) roles
• Transitive within a domain, across domains, along
  a path of inter and intra domain links
• Better partinomy!

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People Parts
Finger
Not inferred!
People
Hand
Arm
Institutions
Joe
MindLab
UMIACS
All links are partOf. That is, we have one
property
UMD
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Play with it!

• Web form access to E-Conn savvy Pellet
• http//www.mindswap.org/2003/pellet/demo
• Papers, presentations, E-Conns
• http//www.mindswap.org/2004/multipleOnt/
• All the details in my dissertation draft
• http//www.mindswap.org/2004/multipleOnt/papers/Di
  ssertation.pdf
• Swoop support!
• Not just editing, but automated partitioning!
• Just to E-Conns, now. E-modules soon.
• http//www.mindswap.org/2004/SWOOP/