ontologia

(1)

DL Ontologies

Fabio Porto

LNCC - DEXL

eScience 2012

Fábio Porto

Modelagem de Dados e Processos em eScience

Agenda

l

 

Introduction

l

 

DL Language

l

 

Applications

l

 

Conclusion

Fábio Porto

Introduction

l 

Ontologies

– An ontology is a specification of a conceptualization. [Gruber]

– an ontology is a description (like a formal specification of a program) of the concepts and relationships that can exist for an agent or a community of agents;

– enabling knowledge sharing and reuse

– Practically, an ontological commitment is an agreement to use a vocabulary (i.e., ask queries and make assertions) in a way that is consistent (but not complete) with respect to the theory specified by an ontology

(2)

Reference

l

 

The Descrption Logics Handbook: Theory,

Implementation and Applications, Franz

Baader, Diego Calvanese, Deborah

McGuiness, Daniele Nardi, Peter

Patel-Schneider

– 

Available at the library

Fábio Porto

Conceptual Modeling

Domain of

Discourse Mental Model

Knowledge Representation Conceptual Model Languages Fábio Porto

Conceptual Modeling

l

 

Expresses the understanding of a group wrt

a domain of discourse

l

 

Use a formal language to express the

meaning of the elements of a domain

l

 

Allows people to agree upon a formal

interpretation of a domain

l

 

Ideally, one may reason on the definitions in

a conceptual model of a domain

(3)

Fábio Porto

Expressions of Conceptual Models

l

 

Database schema

l

 

Entity-Relationship models

l

 

UML data models

l

 

Logical programming

l

 

Description logics

l

 

First-order, modal logics

Fábio Porto

First-order logic (FOL)

l

 

Elements of a language L FOL :

–

 

Predicate - symbols that range over n-ary

relations:

l R(a1, a2,…, an) , where R is a predicate, ai are terms;

l Ex: Married(man,woman)

–

 

Variables - range over elements of a universe of

discourse;

l Ranging done through ∀, ∃

– ∀ x (Woman); ∃ x(∀ y (cheaper(x,y))

–

 

Function symbols;

–

 

Propositional connectivity's: unary negation (

¬

),

binary: disjunction (

∨

), conjunction(

∧

),

implications(

⇒

), equivalence(≡);

–

 

Constants;

Fábio Porto

FOL (cont.)

l  Terms are built from constants, variables, function symbols;

l  An atom:

–  True or false;

–  R(a1, a2,…, an);

–  Correspond to propositional variables;

l  Formulas are specified by composing atoms with connectives

and quantifiers

(4)

Meaning for FOL formulas

l

 

Interpretation

– 

Gives meaning into a domain to elements of the

language;

– 

(

U,C,P,F)

: universe of discourse (U);

C,F,P

give

meaning to constants, functions and predicates;

– 

different interpretations may be implied by a

certain logical theory;

l

 

An interpretation is finite if its UoD is finite,

typical in databases (CWA);

Fábio Porto

Elements of Conceptual

Representation

l 

Concepts

l 

Concept properties

l 

Relationships (associations, part-whole,

isA(subsumption),inverse, functional dependencies,

…)

l 

Cardinality Constraints

l 

Universal and existential quantification

l 

Relationship properties: transitive, reflexive,

symmetric, equivalence, ..)

l 

Instances

l 

Nominal (Pope, LNCC,…)

l 

Symbols (Top, Bottom, …)

Fábio Porto

Elements of Conceptual

Representation (cont.)

l

 

Functional dependency

l

 

Spatio-temporal relationships

l

 

Datatypes

l

 

Imprecision

(5)

Fábio Porto

Description Logics

l

 

Family of logic-based knowledge

representation formalisms well-suited for the

representation of and reasoning about

– 

Terminological knowledge

– 

Ontologies

– 

Data integration

– 

Conceptual modeling

l

 

Descendant of semantic networks,

frame-based systems, and KL-one

Fábio Porto

Description Logics as a

conceptual representation

language

l

 

A fragment of first-order logic

– 

Decidable for a large number of variants

l Provides reasoning termination guarantees

– 

Logic-based semantics

l Inference according to the language semantics of subsumption, equivalence,..

l Relationships can be mapped to predicate logic

Fábio Porto

Ontology languages complexity

History

(6)

DL languages

l 

Classic

– Limited + complete

– Restricted the set of constructs such that subsumption can be computed efficiently

- [Brachmanet al., 1991]

l 

Loom and Back

– Expressive + incomplete (I.e. can not detect all subsumptions and instances)

– Expressive language and efficient reasoning

– Incomplete reasoning algorithms

l Loom [MacGregorand Bates, 1987]" l Back [Nebel and von Luck, 1988]

Fábio Porto

DL Languages

l 

Kris = expressive + complete"

– created by identifying combinations of constructs that... "

l are sources of incompleteness "

l require an exponential algorithm to preserve the completeness" –  provide a testbedfor the implementation of reasoning

techniques

–  played an important role as benchmarks for other systems"

–  [Baaderand Hollunder, 1991a]"

Fábio Porto

Description Logics Architecture

Terminology

Professor

⊆

Person

Facts

Professor (Fabio)

Description

(7)

Fábio Porto

Description Logics

Terminology

l 

DatabaseScientist

≡

ComputerScientist

∩

∃

teach.DatabaseTopic

∩

∀

knows.DBMSs

l 

A Database scientist is a computer scientist that

teaches at least on database topic and knows all

DBMSs.

–  The concept DatabaseScientist is defined a set of instances that semantically share the definition

l 

Allows the definition of hierarchies of concepts

–  DatabaseScientist ⊆ Scientist

–  ConceptualModelScientis ⊆ DatabaseScientist

–  ∃ teach.Logics ⊆ ConceptualModelScientis

Fábio Porto

Description Logics -

Assertions

l

 

DatabaseScientist(Fabio)

l

 

ConceptualModelScientist(Spaccapietra)

l

 

Logics(DL)

l

 

Teach (AnaMaria, DL)

Fábio Porto

Satisfiability of the KB

Scientist Database Scientist ConceptualModel Scientist

∃

teach.Logics

Logics(DL) ¬(AnaMaria) Teach(AnaMaria,DL) clash

¬ DatabaseScientist(AnaMaria)

(8)

DL and Ontology languages

l

 

DL is the foundation of various ontology

languages:

– 

OIL semantics is that of

SHIQ

– 

OWL-DL (based on the

SHOIN

variant)

l Decidable

l Worst-case EXPTIME complexity

l Very efficient reasoners FACT++, RACER, Pellet

Fábio Porto

ALC-DL Syntax and Semantics

Fábio Porto

(9)

Fábio Porto

Knowledge Base TBox

Fábio Porto

Knowledge Base ABox

Fábio Porto

SHIQ Extensions

l

 

Role hierarchies

– 

r

⊆

s , {r,s are roles with semantics r

I

_⊆

_s

I

_};

l

 

Equivalence (or sameAs)

– 

A

≡

C , A,C concepts

iff

A

⊆

C

∧

C

⊆

A

l

 

Nominals

– 

Catholic

∩

∃

hasSeen. {Pope}

(10)

Describing Ontologies using SHIQ

l 

Human

⊆

Muggle

∪

Sorcerer

l 

Muggle

⊆

¬

Sorcerer

l 

Human

⊆

∀

hasParent.Human

∩

(

≤

2hasParent.Top)

∩

(≥ 2hasParent.Top)

∩

∀hasParent

–

_.Human

l 

hasParent ⊆ hasAncestor

*

l 

Human ∩ ∃hasAncestor.Sorcerer ⊆ Sorcerer

l 

Parent ≡ Human ∩ ∃hasParent

–

.Top

l 

Grandparent ≡ ∃hasParent

–

.Parent

.

l 

Grandparent ∩ Sorcerer ⊆ ∃hasParent

–

.

∃hasParent

–

_.Sorcerer

l 

A =

{Human(Harry), Sorcerer(Bob), hasParent(Harry,Bob}

Fábio Porto

Basic Inference Problems

Fábio Porto

(11)

Querying DL Ontologies

Fábio Porto

Querying Ontologies issues

l 

Query languages

– DL like; datalog like;

l 

Query object

– Schema – Instances; l 

Query objective

– Individuals; – Validate; l 

Query interpretation

– Proof theoretic; – Model theoretic; Fábio Porto

Preliminaries

l 

Closed X Open world assumption

– Databases – CWA

l A proposition is false if the database can not imply it. – EX:

l Database: worker(John);worker(Charles)

l Query: worker(Mary) -> False – Logic – OWA

l A proposition is false if the theory implies it so. l Worker(Mary)-> unkown

(12)

Queries

l 

What is a query?

– Is a mapping between instances of an input domain to elements of a range;

l Input domain and range specified in the query expression; – In logical terms corresponds to the set of tuples of literals

that satisfies the query;

l 

Conjunctive query

–  Rule based conjunctive queries;

– Conjunctive calculus;

– Algebra;

Fábio Porto

Questions about a query language

l 

Expressivity:

– What type of queries does it support?

– What part of FOL does the query comprise?

l 

Computability:

– Does its evaluation lead to an end (halt on TM) on all possible interpretations?

Fábio Porto

Query languages SW

l

 

Large number of not yet standardized query

languages:

– 

RDF/S – RQL;RDQL, SPARQL(W3C), Triple,

RDFQL

– 

DAML-OIL QL, DQL

– 

OWL-QL (W3C)

– 

DOGMA

– 

SWRL

(13)

Fábio Porto

Querying DL

l

 

Most works on reasoning over DL languages

considers terminology (TBox) definitions;

l

 

Main task is to validate a theory in the

presence of a new axiom;

l

 

Attention now is to develop strategies that

support reasoning on individuals assertions

(ABox);

Fábio Porto

Introduction to DL querying [Horrocks

&Tessaris00]

l

 

Querying assertions (Abox);

– 

Typical queries:

l Instantiation: x:C;

l Realization: most specialized class for instance x;

l Retrieval: C(x);

– 

All three can be resumed to test for satisfiability of

a knowledge base when these new assertions are

added;

Fábio Porto

Answering typical queries

l

 

An assertion X is a logical consequence of a

KB iff:

– 

X is satisfiable by all interpretations of KB;

– 

A simple strategy to evaluate the implication of an

assertion i.r.t a KB

l Test for unsatisfiability of the KB i.r.t the negation of the assertion;

(14)

Example

Man ⊆ Animal

Man(John),Man(Peter),Man(Bill) Brother (John,Peter), Brother(Peter, Bill) Query:

Animal (John) ?

Test for unsatisfiability of negation: ¬Animal(John);

Fábio Porto

Challenge for more expressive queries

l

 

Conjunctive queries of type: q

₁

∧

…

∧

q

n

,

where q

i

is

x:C

or (x,y):R;

l

 

There is no negation expression over roles;

– 

Queries like: brother(john,bill) ??

l

 

How to deal with conjunctive queries in DL

that may include concepts and relations?

Fábio Porto

Use of

one-of

expression

l

 

Intuition:

– 

Role terms may me reified into concepts;

– 

Strategy:

l Transform literals into new concepts;

l Brother(John,Bill) ≡ John:∃Brother.{Bill} (Reification)

l Negate the new concept:

(15)

Fábio Porto

Conjunctive queries with roles and

variables

l

 

Consider the query:

– 

Friend(john,x)

∧

x:Male

∧

holds(x,PhD)

– 

x can not be reified to a set as it may potentially

corresponds to all elements of the domain;

l The top operator would do the work:

– 

Transformed to concept definition:

l John:∃Friend.{Т ∩ Male ∩∃holds.{PhD}}

l Simplified to:

– John:∃Friend.{Male ∩∃holds.{PhD}}

Fábio Porto

l

 

For roles with no literal:

– 

Two scenarios: cycles and paths

– 

Cycles:

l R1(x,y) ∧ R2(y,z) ∧ R3(z,x) – 

Paths:

l R1(x,y) ∧ R2(y,z)

l

 

No correct substitution

l X:∃R1. Т ∧ (y,z):R2

Conjunctive queries with roles and

variables

Functional Dependencies

in OWL ABOX

Jean-Paul Calbimonte (EPFL)

Fabio Porto (LNCC)

(16)

Agenda

l  Introduction

l  Related Work

l  Problem Formulation

l  FD as application level construct

l  FD interpretation

l  Implementation

l  Conclusion

Fábio Porto

Introduction

l  Various works have attested the benefits of using ontologies in

capturing domain semantics

– Especially in data-centric applications

l  Thus, users expect to find at least the same expressivity as found in database schema languages

l  Functional Dependency is an important type of data dependency

– Establishes functional relationships between groups of attributes in

a Relation

l Leads to primary key specification

l But also, query re-writting and query evaluation strategies

l  Is it applicable to ontologies?

Fábio Porto

Preliminaries

l  Ontologies are formalisation of Conceptualisations [Gruber93]

l  O = T ∪ A

– T = Concepts, Roles, Concept constructors, Restrictions,

Hierarchies

– A = instances, axioms about instances

l  Focus in Description Logics semantics

– TBOX and ABOX

l  Web Ontology Language (OWL) - W3C Recommendation

– OWL-DL is one incarnation

l  OWL-DL allows simple Functional Properties

– Restricted to single role

(17)

Fábio Porto

Examples - Fly Ontology snippets

III)

FDs with paths

I)

Classical FDs

II)

FDs as keys

IV)

FDs with explicit function

Fábio Porto

Related Work

l  Borgida and Weddell introduced simple FDs in Classic, polynomial reasoning for subsumption

l  Calvanese et al. showed that unary FD added to DLRfidleads to undecidability, but non-unary FD is EXPTIME

l  Logical implication problem for limited DLFD with

path FD

in the context of ABOX is undecidable [Toman, Weddel 2006]

l  Path FD in non-monotonic constructor is undecidable;

l  [Lutz et al. 2003] added keys to more expressive DL,using key

boxes, satisfiability is shown undecidable, in general case;

l  Other similar studies got to the same conclusions, in the general case.

Fábio Porto

Problem statement

l

 

The desired behavior of path FD is not met in

present ontology languages

l

 

Might be only partially implemented at

type-level TBOX

(18)

Our Approach

l

 

We depart from specifying FD as a concept

construct

– 

No modification to the logical implication algorithm

l

 

FD is defined as an application level

construct

l

 

Defer part of the process to outside the

ontology: constraint validation, views

Fábio Porto

Syntax

€

( fd R : A

" →

" C)

f

Path is a list of ontology roles (or

attributes)

A is the antecedent, is a set of paths

C is the consequent is a single path

R is the root concept

f is a skolem function

Fábio Porto

FD Semantics

A={[r

11

, r

12

,…, r

1n

],…, [r

m1

, r

m2

,…, r

mk

]}

C={[r

c1

, r

c2

,…, r

cv

]}

a

pa

c1

pa

c2

pa

_cn rc,1 rc2 rcn-1

…

b

pb

c1

pb

c2

pb

_cn rc,1 rc2 rcn-1

…

a

p

11

p

12

g

1 r1,1 r12 r1n-1

…

q

m1

q

m2

g

m rm2 rmn-1

…

rm,1

b

p

11

p

12

g

1 r1,1 r12 r1n-1

…

rm2 rmn-1

…

rm,1

=

pa

cn

= pb

cn

(19)

Fábio Porto

Key Semantics

A={[r

11

, r

12

,…, r

1n

],…, [r

m1

, r

m2

,…, r

mk

]}

a

p

11

p

12

g

1 r1,1 r12 r1n-1

…

q

m1

q

m2

g

m rm2 rmn-1

…

rm,1

b

p

11

p

12

g

1 r1,1 r12 r1n-1

…

q

m1

q

m2

g

m rm2 rmn-1

…

rm,1

=

a = b

(fdk R : A

→

Id)

Fábio Porto

FD with explicit function

Semantics

A={[r

11

, r

12

,…, r

1n

],…, [r

m1

, r

m2

,…, r

mk

]}

C={[r

c1

, r

c2

,…, r

cv

]}

a

pa

c1

pa

c2

pa

_cn rc,1 rc2 _r cn-1

…

b

pb

c1

pb

c2

pb

_cn rc,1 rc2 rcn-1

…

a

p

11

p

12

g

1 r1,1 r12 r1n-1

…

q

m1

q

m2

g

m rm2 rmn-1

…

rm,1

b

p

11

p

12

g

1 r1,1 r12 r1n-1

…

q

m1

q

m2

g

m rm2 rmn-1

…

rm,1

=

fde = (A, R, C, f)

pa

cn

= pb

cn

∧ pa

cn

= f(g

1

,…,g

n

),

Fábio Porto

FD interpretations

l

 

Depending on application and FD type, FDs

may be interpreted as:

– 

Constraints

l Add hurting instances to witness concepts

– 

New assertions (i.e. sameas )

l Add sameas axioms to instances resulting from key

validation

– 

Views

l Return values corresponding to explicit function FD computation

(20)

Extended Knowledge Base

l K=(T, A, FD ,C ,C_A,V) l T is a finite set of standard TBox axioms,

l A is a finite set of standard ABox assertions,

l FD is a finite set of functional dependency definition instances, where each

FD definition can be classified as: l  FDa is a finite set of assertion FDs fdai

l  FDc is a finite set of constraint FDs fdci

l  FDv is a finite set of view FDs fdvi

l C is a finite set of constraint witness classes wfdci, with fdci ∈FDc

l CA is a finite set of assertions hurting some FDc constraint and expressed as

witness facts, i.e. instances of wfdci .

l V is a finite set of view definitions

l V={v1≡ fdv1, …, vn≡ fdvn}, where fdvi ∈FDv

Fábio Porto

Implementation

l

 

FD specification as a OWL class

– 

Independent of the type of FD inforcement

l

 

Re-write FD specification as rules in SWRL

– 

According to specified mappings (see paper)

l

 

Run the SWRL rules in proteg

é

Fábio Porto

FD & instance specification

in OWL

(21)

Fábio Porto

SWRL rule mapped from owl FD

€

fdtax: (A,C,Ticket, ftax)

A = {belongsToFlight,departsFrom}, belongsToFlight,arrivesAt { }, hasPassenger,belongsToGroup { } " # $ % $ & ' $ ( $ C ={{hasPrice,hasTax}} Fábio Porto

Conclusion

l

 

The extension of ontologies with functional

dependencies is important in producing more

expressive ontologies

l

 

Path FDs as part of concept type definition

has been shown to lead to undecidability of

logical implication on subsumption

Fábio Porto

Conclusion

l

 

We specify a practical solution:

– 

FD’s specified as an application class

– 

Re-written as SWRL rules and applied to ABOX

– 

Interpreted as: constraints, new assertions, views

– 

Extend traditional Knowledge base with new

interpretations

– 

Prototype implementation in proteg

é

l

 

We intend to apply the approach in biological

domain

(22)

Obrigado !!!

Reasoning on Dynamically Built

Reasoning Space with Ontology

Modules

Fabio Porto

École Politechnique Fédéral de Lausanne Database Laboratory Switzerland Fábio Porto

Outline

l

 

Introduction

l

 

Preliminaries

l

 

General Framework

l

 

Reasoning space

l

 

Reasoning algorithm

(23)

Fábio Porto

Introduction

l

 

Ontologies are increasingly used as explicit

models of the conceptualization of underlying

information sources;

l

 

Different ontologies:

– 

representing partially intersecting domains

– 

same domain observed from different

perspectives

l

 

Applications require reasoning over such

autonomously developed ontologies

Fábio Porto

Multiple ontology scenarios

l  In e-science:

– In order to study colon carcinoma disease, a biologist would conjointly use its own ontology with others such as:

l medical ontology (UMLS), anatomical ontology(mouse ontology,

HUMAT), Pharmacogenomics (PharmGKB) and GO; l  In e-business:

– In automatic web service discovery within a virtual travel agency: l Location ontology, currency ontology, flight ontology, date ontology

Fábio Porto

Overall picture

Group ontology

O1 _O2

(24)

Context

l  User group agrees on a common ontology but trusts on information defined on other ontologies;

l  Autonomously developed ontologies:

– Partially intersect;

– Represented through different logical languages;

– Require mappings among ontologies models; – May include contradictions;

l  Current reasoners:

– Consider ontologies forming a single logical model;

– Need different ontologies to be aligned; l  Centralized Reasoning:

– Transferring large ontologies to a central site is costly;

Fábio Porto

Problem Statement

l

 

Given a set of autonomously developed

ontologies linked by mapping

correspondences to a group ontology,

conceive a reasoning strategy compatible

with current centralized reasoners

l

 

Contribution

– 

Strategy to dynamically build a reasoning space

based on: a query, an ontology space and

correspondences;

Fábio Porto

Preliminaries

l 

Ontologies expressed in

SHIQ:

–  Distinct sets of concepts, roles and individuals;

– ^, ¨ are concepts and, if C,B are concepts, then ¬C, ( C * B), (C ! B) are concepts;

–  An ontology O is modeled by an interpretation I.

l I=(ΔI, (·I))

l Concept names are interpreted as subsets of ΔI

l Complex expressions are interpreted according to the

following equations: – ! I₌_ΔI_;_⊥I₌_∅;_{( C}_!_B)I_{= (C}I_!_BI_{); ( C}_!_B)I_{= (C} I_!_BI_); – ¬C I₌_ΔI_{\ C}I l Knowledge Base: – ( C ! B), ( R ! S), a:C, <a,b>:R l Interpretation – ( C ! B) iff ( C I_⊆_BI₎ – a:C iff aI_∈_CI

(25)

Fábio Porto

General Framework

l  Ontology Space OS={O1, O2,…, On}, where Oi is an ontology;

l  Ontology Module Mid=<id,D,L,Ob,Cid,OS>

–  C correspondences(bridge rules in c-owl):

l Oi:C ≡ Oj:D; Oi:C ⊆ Oj:D ;Oi:C ⊆ Oj:D ; Oi:R ≡ Oj:S l Oi:v ≡ Oj:t;

– Where C, D are concepts; R, S are roles and v,t are instances Peer Pi=<Mi,S> l  Query: l  Q= q1 ∧ q2 ∧ … ∧ qt. [Horrocks,Tessaris 2000] –  qi,1≤ i ≤ t, is a term : x:C or <x,y>:R –  qi is satisfied by O iff O! qi l  Boolean queries: –  C⊆ D

l  Peer: P=<M,Reasoner,query rewriter>

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Reasoning Space

l

 

Virtual ontology built to answer a query Q

with

relevant entities

from OS

– 

RS

⊆

{OS

∪

C}

l

 

How to compute relevant entities (Q,OS)?

– 

Relevant entity

e

in O

_i

l ei∈ Oi is relevant to Q iff

∃

ej inqj ,term of, Q, such that

– ei∩ej≠ ∅ C1 C2 CN R1 RS ei ej qi Oj C1 C2 CN R1 ei RS´ Fábio Porto

Reasoning Space

l

 

Virtual ontology built to answer a query Q

with

relevant entities

from OS

– 

RS

⊆

{OS

∪

C}

l

 

How to compute relevant entities (Q,OS)?

– 

Relevant entity

e

in O

i

l ei∈ Oi is relevant to Q iff

∃

ej inqj ,term of, Q, such that – ei∩ej≠ ∅ C1 C2 CN R1 RS ei ej qi Oj C1 C2 CN R1 RS‘

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Building Reasoning Space

l

 

Successively extend the Reasoning space by

identifying relevant ontology entities:

– 

Initially assumes RS=local ontology

– 

Apply a reasoning space extension function that

for each ontology in OS, identifies relevant

entities;

l

 

Reason over the current RS

Fábio Porto

Getting relevant entities

Lactation Bodily Process Breast Cancer Disease process Receptor Protein Protein Involved_with Involved_with digestion Stomach Cancer x:Protein ∧ (x,lactation):involved_with ∧ (x,disease):involved_with Fábio Porto

Getting relevant entities

Lactation Bodily Process Breast Cancer Disease process Receptor Protein Protein Involved_with Involved_with digestion Stomach Cancer x:Protein ∧ (x,lactation):involved_with ∧ (x,disease):involved_with

(27)

Fábio Porto

Extending RS

Lactation Bodily Process Breast Cancer Disease process Receptor Protein Protein Involved_with Involved_with x:Protein ∧ (x,lactation):involved_with ∧ (x,disease):involved_with Fábio Porto

General Framework

P2 O2 C21 P3 O3 C 31 x:Protein ∧ (x,lactation):involved_with ∧ (x,disease):involved_with P1 Reasoner O1 C13 C 12 OS Query Rewriter q12 q13 E2 E3

Are there proteins involved in lactation and disease processes?

Fábio Porto

Reasoning space algorithm

reasonspace(query Q,ontology Ob,OS,correspondence C) : answer

{ RS´:= {Ob};RS=∅;

q:= !i=1,t qt ; /* qt terms of query Q */ answer:={evaluate(q,RS)}; q:=q – {satisfied(q)}; While (q ≠∅ and RS ≠ RS’) { RS=RS´; RS´= f(q,RS,OS);

answer:= answer ! {evaluate(q,RS´)}; q:=q – {satisfied(q)}; }

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Related work

l  L. Serafini, A: Tamilin, ´Distributed reasoning services for multiple ontologies´.

Technical Report DIT-04-029, University of Trento, 2004

l  M. Lenzerini,”Data Integration: A Theoretical Perspective”, ACM PODS 2002; l  D. Calvanese, G. De Giacomo, M. Lenzerini, and R. Rosati, Logical foundations

of peer-to-peer data integration, PODS 2004;

l  E. Fancioni, G. Kuper, A. Lopatenko, L. Serafini, A Robust Logical and Computational Characterisation of peer-to-peer Database systems, DBISP2P-2003, co-loacated VLDB2003;

l  K. Alberer, P. Cudré-Mauroux, M. Hauswirth,” GridVine: Building Internet-Scale Semantic Overlay Networks

”, The 3rd International Semantic Web Conference (ISWC2004), Hiroshima, 7-11 Nov 04

l  J.Lin and A. O Mendelzon. Merging databases under constraints, Intl. J. of

Cooperative Information Systems, 7(1):55-76,1988.

l  A. Halevy et al., Z.G. Ives, D. Suciu, I.Tatarinov. Schema mediation in peer data management systems. ICDE 2003.

l  L. Serafini, F. Giunchiglia, J. Mylopoulous, P. Bernstein. Local relational model: A logical formalization of database coordination. In context 2003, 2003.

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Conclusion and Future work

l  Preliminary results on reasoning over autonomously developed distributed ontologies;

l  Present a strategy that:

– Uses current reasoner technology;

– Reduces the cost associated to transferring ontologies; – Identifies contradictions among ontologies;

– Is based on database approach for evaluating distributed queries; l  Future work:

– Use query results to update mapping information;

– Evaluate the approach comparing to distributed reasoning

strategies based on distributed tableau method; – Evaluate quality of results;