C-OWL: contextualizing ontologies

1
C-OWL contextualizing ontologies

• Fausto Giunchiglia
• October 22, 2003
• 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

5
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

7
A Global Semantics for OWL

• Index OWL Ontologies lti, Oigt 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 lti, Oigt such that the language of
  every Oi contains all the other foreign languages

8
A Global Semantics for OWL (conted)

• (OWL interpretation). An OWL interpretation for
  the OWL space lti, Oigt is a pair I lt?I, (.)Igt,
  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!

9
A Global Semantics for OWL (conted)

• (OWL axiom and fact satisfiability). I satisfies
  a fact or an axiom ø 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
  lti, Oigt, 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

11
Example 1 directionality

• Need to keep track of source and target ontology
• Example
• Construct O2 by importing O1 and adding it some
  new axiom
• 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.

12
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

13
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 since Ferrari produces only petrol
  engines

14
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

15
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

16
Exampe 1 Directionality

• Consider all (local) ontologies as part of a 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

17
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 lti, Oigt is a family I
  Ii, where each Ii lt?Ii, (.)Iigt, 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

19
Example 3 adding context mappings to syntax

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

20
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 the pair
• OWL space lti, Oigt (of local ontologies)
• family Mij of (context) mappings from i to j,
  for any pair i,j
• (Interpretation for context spaces). It is the
  pair
• I, where I is an OWL interpretation with holes
  and local domains and
• rij, the domain relation from i to j, is a subset
  of ?Ii x ?Ii

21
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

22
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 (!!)

23
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)

24
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?

25
Context mappings (conted)

• (Satisfiability of bridge rules)
• A interpretation for a context space is a model
  for it if all the bridge rules are satisfied