C-OWL: contextualizing ontologies

Fausto GiunchigliaOctober 22, 2003

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 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>} such that the language of every Oi contains all the other foreign languages

A Global Semantics for OWL (cont’ed)(OWL interpretation). An OWL interpretation

for the OWL space {<i, Oi>} 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 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 {<i, Oi>}, 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 axiom 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 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 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

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>} is a family I = {Ii}, 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 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 {<i, Oi>} a mapping Mij from Oi to Oj is a set of bridge rules from Oi to Oj.

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 the pair1. OWL space {<i, Oi>} (of local ontologies)2. family {Mij} of (context) mappings from i to j, for any

pair i,j

(Interpretation for context spaces). It is the pair 1. I, where I is an OWL interpretation with holes and local

domains and 2. rij, the domain relation from i to j, is a subset of ∆Ii x ∆Ii

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?

Context mappings (cont’ed)

(Satisfiability of bridge rules)

A interpretation for a context space is a model for it if all the bridge rules are satisfied