COWL: contextualizing ontologies

1
C-OWL contextualizing ontologies

• Pavel Shvaiko
• October 20, 2004
• Paolo Bouquet, Fausto
  Giunchiglia, Frank van Harmelen, Luciano
  Serafini, and Heiner Stuckenschmidt

2
The Talk

• Ontologies vs. Contexts
• A (restated) global semantics for OWL
  Intuitions
• Three motivating examples
• A (new) local models semantics for OWL
  Intuitions
• C-OWL extending OWL with (context) mappings

3
Ontologies vs. Contexts

• An Ontology is a model of some domain which is
  supposed to encode a view common to a set of
  different parties
• An ontology is built to be shared
• A Context is a model of some domain which is
  supposed to encode a view of a party
• A context is built to be kept local (where
  local implies not shared)
• A context and an ontology of the same domain are
  likely to be very different (different goals,
  different approach, )

4
Pros and Contras

• Ontologies
• Strengths
• easy exchange of information
• Weaknesses
• consensus must be reached about their contents
• maintenance may become arbitrarily hard
• Contexts
• Strengths
• easy to define and to maintain
• can be constructed with no consensus with the
  other parties
• Weaknesses
• Exchange of information by constructing explicit
  mappings among the elements of the contexts of
  the involved parties

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Contextual Ontologies

• Contextual ontology Ontology Context mappings
• Key idea (in two steps)
• Share as much as possible (OWL import construct)
• Keep it local whenever sharing does not work
  (C-OWL context mappings)
• Notes
• In many (most in the Web?) cases sharing does not
  work and produces undesired results (semantic
  heterogeneity)
• Using context allows for incremental, piece-wise
  construction of the Semantic Web (bottom up vs.
  top down approach)

6
The Talk

• Contexts vs. Ontologies
• A (restated) global semantics for OWL
  Intuitions
• Three motivating examples
• A (new) local models semantics for OWL
  Intuitions
• C-OWL extending OWL with (context) mappings

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A (restated) Global Semantics for OWL

• Index OWL Ontologies and their languages
  (e.g., iC, jE, i?r.C)
• (Local language). A local concept (role,
  individual), Ci (Ri, Oi) is an element of C that
  appears in Oi either without indexes or with
  index equal to i
• (Foreign language) Anything (concept, role,
  individual) which is not local
• (OWL space). An OWL space is a family of
  ontologies i ?I such that every Oi is
  an OWL ontology

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A Global Semantics for OWL (conted)

• (OWL interpretation). An OWL interpretation for
  the OWL space i ?I is a pair I (.)I, such that
• I(i, C) ? ?I for any i ? I and C ? Ci
• I(i, r) ? ?I x ?I for any i ? I and r ? Ri
• I(i, o) ? ?I for any i ? I and o ? Oi
• With ?I domain of interpretation and
• (.)I interpretation function
• Note a global interpretation!

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A Global Semantics for OWL (conted)

• (OWL axiom and fact satisfiability). I satisfies
  a fact or an axiom of Oi according to the rules
  defined in
• P.F. Patel-Schneider, P. Hayes, and I.
  Horrocks. Web Ontology Language (OWL) Abstract
  Syntax and Semantics. Technical report, W3C,
  February 2003.
• An OWL interpretation I satisfies an OWL space
• i ?I, if I satisfies each axiom and fact
  of Oi,
• for any i

10
The Talk

• Contexts vs. Ontologies
• A (restated) global semantics for OWL
  Intuitions
• Three motivating examples
• A (new) local models semantics for OWL
  Intuitions
• C-OWL extending OWL with (context) mappings

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Example 1 Directionality

• Need to keep track of source and target ontology
• Example
• Construct O2 by importing O1 and adding it some
  new axioms
• We want that axioms added to O2 do not affect O1
• O1 contains axioms A B and C D
• O2 contains also axiom 1B 1C
• In new semantics, we want 1A 1D in O2,
• but not in O1

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Example 1 (conted) Directionality

• We want to avoid propagation of inconsistency
• Example
• O1 contains axioms A B and C D
• O2 contains also axiom 1B 1C
• We want to derive 1A 1D in O2 but not in O1
• O2 contains also 1A(a) and 1 not D(a)
• O2 is inconsistent
• In new semantics, we want to keep O1 consistent

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Example 2 Local domains

• Need to give up hypothesis that of single global
  domain of interpretation
• Example
• Car manufacturing ontology OWCM with domain of
  interpretation the totality of cars
• Individual constants Diesel and Petrol for diesel
  engine and petrol engine
• Axiom a car has only one engine which is either
  Diesel or Petrol
• Car (?1) hasEngine.Diesel, Petrol
• Diesel ? Petrol
• Ferrari ontology, OFerrari describing Ferraris
  production
• Imports OWCM standard
• Axiom engine of a Ferrari is either an F23 or
  and F34i
• Ferrari (WCMcar (?1) (WCMhasEngine).F23,
  F34i)
• F23?F34i
• In new semantics, we want to avoid (F23)IFerrari
  (Diesel)IWCM or
• (F34i)IFerrari (Diesel)IWCM since Ferrari
  produces only petrol engines

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Example 3 Context mappings

• Need to state that two elements of two
  ontologies, though being extensionally different,
  are contextually related
• Example
• OFIAT describes cars from manufacturer point of
  view
• OSale describes cars from car vendor point of
  view
• OFIAT and OSale are largely independent and
  different
• Two concepts of car defined in OFIAT and OSale,
  (i.e. SaleCar and FIATCar) may be very
  different, still describing same real world
  object (different viewpoints)
• Not possible to state relation between two
  concepts with OWL syntax

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The Talk

• Contexts vs. Ontologies
• A (restated) global semantics for OWL
  Intuitions
• Three motivating examples
• A (new) local models semantics for OWL
  Intuitions
• C-OWL extending OWL with (context) mappings

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Exampe 1 Directionality

• Consider all (local) ontologies as part of OWL
  space
• Split global interpretation into a family of
  local interpretations, one for each ontology
• Allow for an ontology to be locally inconsistent
  (i.e., not to have a local interpretation)
• Technically Associate inconsistent ontologies
  to a special interpretation, called a hole,
  that verifies any set of axioms

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Example 2 Local Domains

• Associate to each ontology a local domain
• Local domains may overlap (two ontologies may
  refer to the same object)
• Technically An OWL interpretation with local
  domains for the OWL space i ?I is a
  family I Iii ?I, where each Ii (.)Ii, called the local interpretation of Oi, is
  either an interpretation of Li on ?Ii, or a hole

18
The Talk

• Contexts vs. Ontologies
• A (restated) global semantics for OWL
  Intuitions
• Three motivating examples
• A (new) local models semantics for OWL
  Intuitions
• C-OWL extending OWL with (context) mappings

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Example 3 Adding context mappings to syntax

• (Bridge rules). A bridge rule from i to j is a
  statement of one of the five following forms,
• where x and y are concepts, or roles, or
  individuals of the languages Li and Lj
• (Context mapping). Given a OWL space i
  ?I a mapping Mij from Oi to Oj is a set of
  bridge rules from Oi to Oj for some i, j ?I

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Context mappings (conted)

• (Contextual ontology) It is a local ontology
  plus a set of bridge rules (context mappings). We
  sometimes write context meaning contextual
  ontology
• (Context space). A context space is a pair
• OWL space i ?I (of local ontologies)
• family Miji,j ?I of (context) mappings from i
  to j, for each pair i, j ? I
• (Interpretation for context spaces). It is a pair
  
• I, where I is an OWL interpretation with holes
  and local domains
• rij, the domain relation from i to j, is a subset
  of ?Ii ?Ij

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Examples Context mappings

• From example 3 SaleCar and FIATcar describe
  the same set of objects from two different
  viewpoints
• ()
• Domain relation satisfying ()
• rij(CarISale) CarIFIAT
• From example 2
• 
  ()
• Domain relation satisfying ()
• rWCM, Ferrari(Petrol)IWCM ? F23IFerrari ,
  F34iIFerrari

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Context OWL (C-OWL)

• A contextual ontology is a pair
• OWL ontology
• a set of context mappings
• where a mapping is a set of bridge rules with
  the same target ontology
• A context mapping is a 4-tuple
• A mapping identifier (URI)
• A source context containing an OWL ontology
• A target context containing an OWL ontology
• A set of bridge rules from the local language of
  the source ontology to the local language of the
  target ontology
• NOTE mappings are objects (!!)

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Conclusions

• Ontologies share knowledge
• Contexts keep knowledge local (not shared)
• Contextual ontologies share as much as possible,
  keep local whenever necessary
• C-OWL (Context OWL)
• OWL
• Local models semantics
• context mappings (limited, explicitly defined,
  visibility from outside)

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Will C-OWL be of any use?

• How often in the Web we will import ontologies
  and how often we will define context mappings
  (diversity as a defect, or diversity as a
  feature)?
• Shouldnt the Semantic Web be a Web of Semantic
  links (e.g., context mappings)? Context mappings
  useful for maintaining alignment, propagating
  info, (semantics driven) navigation,
• Shouldnt discovering context mappings (e.g.,
  Semantic matching) be one of the core issues in
  building the Semantic Web?

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References

• Project website - ACCORD http//www.dit.unitn.it/
  accord/
• P. Bouquet, F. Giunchiglia, F. van Harmelen, L.
  Serafini, H. Stuckenschmidt C-OWL
  Contextualizing Ontologies. In Proceedings of
  ISWC, 164-179, 2003
• C. Ghidini, F. Giunchiglia Local models
  semantics, or contextual reasoning locality
  compatibility. Artificial Intelligence journal,
  127(3)221-259, 2001
• D.L. McGuinness, F. van Harmelen OWL Web
  Ontology Language Overview. Technical report,
  W3C, http//www.w3.org/TR/owl-features/, February
  2004

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• Thank You!