C-OWL: contextualizing ontologies Pavel Shvaiko October 20, 2004 Paolo Bouquet, Fausto Giunchiglia, Frank van Harmelen, Luciano Serafini, and Heiner Stuckenschmidt
Jan 26, 2016
C-OWL: contextualizing ontologies
Pavel ShvaikoOctober 20, 2004
Paolo Bouquet, Fausto Giunchiglia, Frank van Harmelen, Luciano Serafini, and Heiner Stuckenschmidt
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
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, …)
Pro’s and Contra’s 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
Contextual OntologiesContextual ontology = Ontology + Context mappings
Key idea (in two steps):1. Share as much as possible (OWL import construct)
2. Keep it local whenever sharing does not work (C-OWL context mappings)
Notes: 1. In many (most in the Web?) cases sharing does not work
and produces undesired results (semantic heterogeneity)
2. Using context allows for incremental, piece-wise construction of the Semantic Web (bottom up vs. top down approach)
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
A (restated) Global Semantics for OWLIndex OWL Ontologies: <i, Oi> and their languages
(e.g., i:C, j:E, 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, Oi>}i I such that every Oi is an OWL ontology
A Global Semantics for OWL (cont’ed)(OWL interpretation). An OWL interpretation
for the OWL space {<i, Oi>}i I is a pair I = <∆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!
A Global Semantics for OWL (cont’ed)(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, Oi>}i I, if I satisfies each axiom and fact of Oi,
for any i
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
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 1:B 1:C
In new semantics, we want 1:A 1:D in O2,
but not in O1
Example 1 (cont’ed): Directionality We want to avoid propagation of inconsistency
Example: O1 contains axioms A B and C D O2 contains also axiom 1:B 1:C We want to derive 1:A 1:D in O2 but not in O1
… O2 contains also 1:A(a) and 1: not D(a) O2 is inconsistent
In new semantics, we want to keep O1 consistent
Example 2: Local domainsNeed 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 Ferrari’s production Imports OWCM standard Axiom: engine of a Ferrari is either an F23 or and F34i
Ferrari (WCM:car (1) (WCM:hasEngine).{F23, F34i}) F23F34i
In new semantics, we want to avoid (F23)IFerrari = (Diesel)IWCM or (F34i)IFerrari = (Diesel)IWCM since Ferrari produces only petrol engines
Example 3: Context mappingsNeed 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. Sale:Car and FIAT:Car) may be very different, still describing same real world object (different viewpoints)
Not possible to state relation between two concepts with OWL syntax
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
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
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, Oi>}i I is a family I = {Ii}i I, where each Ii = <∆Ii, (.)Ii>, called the local interpretation of Oi, is either an interpretation of Li on ∆Ii, or a hole
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
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, Oi>}i I a mapping Mij from Oi to Oj is a set of bridge rules from Oi to Oj for some i, j I
Context mappings (cont’ed)
(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 pair1. OWL space {<i, Oi>}i I (of local ontologies)2. family {Mij}i,j I of (context) mappings from i to j, for
each pair i, j I
(Interpretation for context spaces). It is a pair 1. I, where I is an OWL interpretation with holes and local
domains2. rij, the domain relation from i to j, is a subset of ∆Ii × ∆Ij
Examples: Context mappingsFrom example 3: Sale:Car and FIAT:car 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}
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 (!!)
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)
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)?
Shouldn’t the Semantic Web be a Web of Semantic links (e.g., context mappings)? Context mappings useful for: maintaining alignment, propagating info, (semantics driven) navigation, …
Shouldn’t discovering context mappings (e.g., Semantic matching) be one of the core issues in building the Semantic Web?
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
Thank You!