Ontology in Philosophy

D1 - 09/01/2009

Adding Semantic to Web Data and ServicesPart 2 – DL Knowledge base Reasoning

Doctoral School, St Etienne January 2009

Alain Léger FT R&D Orange Labs ResearchDR Knowledge Processing (KRR)Manager Industry Area IST NoEs OntoWeb et Knowledgeweb (2000 -2007)Associated DR CNRS Lyon I - LIRIS

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Plan Cours 1 (5 janv 09 13:30 – 17:15 / 6 janv 09 8:00 – 11:45)

• Why adding semantics to the Web ? (1h30)

CIntroduction

CTake Away and References

• Foundations of Semantic Web (2h15)

CIntroduction to Description Logics

CStandards Inferences and Tableau

• From XML, RDF to OWL (2h45)

CXML, RDF, RDF-S

COWL

• Applications and Roadmap (1h)

CApplication Scenarios

CVisions prospectives et verrous technologiques

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Ontologies

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a philosophical discipline—a branch of philosophy thatdeals with the nature and the organisation of reality

• Science of Being (Aristotle, Metaphysics, IV, 1)

• Tries to answer the questions:What characterizes being?Eventually, what is being?

• How should things be classified ?

Ontology the key ingredient: Origins and History

Ontology in Philosophy

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Classification: An Old Problem

Les représentations du Système figuré : novembre 1750 et juin 1751, publié dans l'Encyclopédie ou Dictionnaire raisonné des sciences, des arts et métiers,Par une Société de gens de Lettres … Tome I, 1751

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Machine Intelligence and Turing Test

Dialogues IHMAcquisition de Connaissances

Représentation des connaissances

Raisonnements Automatisés

Traitement automatisé du langage

Emotion

s

The Phaistos Disc (1700 BC) – undecyphered -can perhaps be thought of as the earliest typewritten workdiscovered on the 3rd of July 1908 by L. Pernier, during an excavation he supervised at the Minoan palace of Phaistos in Southern Crete

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• An ontology is an engineering artefact consisting of:CA vocabulary used to describe (a particular view of) some domain

CAn explicit specification of the intended meaning of the vocabulary.

• almost always includes how concepts should be classified

CConstraints capturing additional knowledge about the domain

• Ideally, an ontology should:CCapture a shared understanding of a domain of interest

CProvide a formal and machine manipulable model of the domain

Ontology in Computer Science

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What is a concept?

• Concepts or “classes”:CAre in general language independent (the words ‘university’ and ‘ollscoil’ denote the

same concept)

CAre mental or logical representations of reality

CAre related to other concepts

CDo not need symbols but hold them for means of communication

• A concept has:CIntension, i.e. meaning

CExtension, i.e. a set of objects that the concept refers to

• Ontology is mainly concerned with intension

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Components of an ontology

• ConceptsCCatCDog

• PropertiesCLengthCAge

• ConstraintsCCardinality is at least 1CMaximum value is 300

• AxiomsCCows are larger than dogsCCats cannot eat only vegetation

• RelationshipsCIs aCPart of

Illustration

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Example Ontology (1)

• Vocabulary and meaning (“definitions”)

CElephant is a concept whose members are a kind of animal

CHerbivore is a concept whose members are exactly those animals

who eat only plants or parts of plants

CAdult_Elephant is a concept whose members are exactly those

elephants whose age is greater than 20 years

• Background knowledge/constraints on the domain (“general axioms”)

CAdult_Elephants weigh at least 2,000 kg

CAll Elephants are either African_Elephants or Indian_Elephants

CNo individual can be both a Herbivore and a Carnivore

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Example Ontology (2)

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Implementing or creating ontologies

• Implementation consists in defining all the ontology

components through an ontology definition language

• Generally in two stages:CInformal stage:

• Ontology is sketched out using either natural language descriptions or some diagram technique

CFormal stage:• Ontology is encoded in a formal knowledge representation language, that is machine computable

• Different tools (e.g., Protégé) may help in the implementation• http://protege.stanford.edu/overview/protege-owl.html

Consider

Re-use

Enumerate

Terms

Define

Classes

Determine

Scope

Define

Properties

Define

constraints

Create

Instances

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Example Ontology (Editor Protégé)

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Example Ontology (Editor OilEd)

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Where are ontologies used?

• e-Science, e.g., Bioinformatics

CThe Gene Ontology

CThe Protein Ontology (MGED)

C“in silico” investigations relating theory and data

• Medicine

CTerminologies

• Databases

CIntegration

CQuery answering

• User interfaces

• Linguistics

• The Semantic Web

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Ontology in a nutshell

• “Ontology is an explicit conceptualisation, formal and shared ”

[Gruber 95] [Borst 97]

• Thus, an ontology describes a formal specification of a certain domain:

CShared understanding of a domain of interestCFormal and machine manipulable model of a domain of interest

Aristotle ten categories•Substance. E.g., individual man.

•Quantity. E.g., two cubits.•Quality. E.g., white.

•Relation. E.g., double.•Location. E.g., in the market.

•Time. E.g., today.•Position. E.g., sitting.

•Possession. E.g., wearing shoes.•Doing. E.g., cutting.

•Undergoing. E.g., being cut.

Aristotle was the ontologistof common sense reality

METAPHYSIC : ONTOLOGY and EPISTEMOLOGY

Ontology

« discourse on the being » fondamental questions: « what does exist ? » ; « what is the content of the reality ? » ; « how does the reality work ?» ; « what are the origins of the reality ? » ; « what is the future of the reality ? »

Epistemology

« discourse on the knowledge ». Central question is : « how do we know ? »

LOGIC

Its goal is to infer truths from sound reasoning

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Ontology Technology and Process in a nutshell

To make the Semantic Web working we need:

• Ontology Languages:Cexpressivity

Creasoning support

Cweb compliance

• Ontology Reasoning: Clarge scale knowledge handling

Cfault-tolerant

Cstable & scalable inference machines

• Ontology Management Techniques: Cediting and browsing

Cstorage and retrieval

Cversioning and evolution Support

• Ontology Integration Techniques: Contology mapping, alignment, merging

Csemantic interoperability determination

• and … Applications

NLP Reasonners

Conceptualization Principles

Ontology Re-Use

User

Conceptualization Implemented Model

FormalShared

FormalShared

MethodologyUser

User

User

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Introduction to Description Logics

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What Are Description Logics?

• A family of logic based Knowledge Representation formalismsCDescendants of semantic networks [Brachman 78] and KL-ONE [Brachman&Schmolze 85]

CDescribe domain in terms of concepts (classes), roles (properties, relationships) and individuals

• Characterized by:CFormal semantics (typically model theoretic)

• Decidable fragments of FOL (First Order Logics)

• Closely related to Propositional Modal (nécessaire, contingent, possible)

• Dynamic Logics (comportement dynamique)

• Closely related to Guarded Fragment (Decidable Fragment of FOL)

CProvision of inference services• Decision procedures for key problems (satisfiability, subsumption, etc)

• Implemented systems (highly optimised !)

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DL Basics

• Concepts (unary predicates/formulae with one free variable)Ce.g., Person, Father, Mother

• Roles (binary predicates/formulae with two free variables)Ce.g., hasChild, hasHudband

• Individual names (constants)Ce.g., Alice, Bob, Cindy

• Axioms (axiomatic relations between concepts or roles)Ce.g., Female ⊆ PersonCe.g. HappyFather ⊆ Father Π ≥1 hasChild.Woman Π ≥1 hasChild.Man

• Operators (for forming concepts and roles) CAnd(Π) , Or(U), Not (¬)CUniversal qualifier (∀), Existent qualifier(∃)CNumber restiction : ≤, ≥, = CInverse role (-) : hasParent = hasChild

Ctransitive role (+) : hasBrother(Bob,David), hasBrother(David, Mack) -> hasBrother(Bob,Mack)

CRole hierarchy : hasMother ⊆ hasParent

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The DL Family (Notation)

• Given DL defined by set of concept and role forming operators• Smallest propositionally closed DL is ALC (equiv modal K(m))

CConcepts constructed using u, t, ¬, ∃ and ∀• S often used for ALC with transitive roles (R+)

• Additional letters indicate other extension, e.g.:CH for role inclusion axioms (role hierarchy)

CO for nominals (singleton classes, written {x})

CI for inverse roles

CN for number restrictions (of form 6nR, >nR)

CQ for qualified number restrictions (of form 6nR.C, >nR.C)

• E.g., ALC + R+ + role hierarchy + inverse roles + QNR = SHIQ• Have been extended in many directions

CConcrete domains, epistemic, n-ary, fuzzy, …

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The DL Family (a very few part)

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Concept Description

• Représenter des conceptsCConcepts atomiques et rôlesCConstructeurs de conceptCExemple : classe des mères, i.e. des personnes de sexe féminin ayant au moins un enfant qui est lui-même une personne.

Mère ≡ Personne Féminin ∃aEnfant.Personne

• Une terminologie (ou Tbox) = {définitions de concepts}• Une logique de description = {constructeurs}• Sémantique :

CNotion d’interprétation issue de la théorie des modèlesCConcept = ensemble d’{individus} du dom. Interprétation

Descriptions de concepts complexes

concepts atomiques rôleconstructeursdescription de conceptconcept

défini

définition de concept

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DL Semantics

• Semantics defined by interpretations• An interpretation I = (∆I, .I), where

C ∆I is the domain (a non-empty set)

C.I is an interpretation function that maps:

• Concept (class) name A → subset AI of ∆I

• Role (property) name R → binary relation RI over ∆I

• Individual name i → iI element of ∆I

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DL Semantics (2)

• Interpretation function .I extends to concept (and role)

expressions in the obvious way, e.g.:

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Interpretation Example (homework)

∆ = {v, w, x, y, z}

AI = {v, w, x}

BI = {x, y}

RI = {(v, w), (v, x), (y, x), (x, z)}• ¬ B =

• A u B =

• ¬ A t B =

• ∃ R B =

• ∀ R B =

• ∃ R (∃ R A) =

• ∃ R ¬ (A t B) =

• 6 1 R A =

• > 1 R A =

AI

v

x

yz

w

BI

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Base de Connaissance (KB) : Architecture, syntaxe, sémantique

• Un langage L-KR étant donné, une Base de connaissance K dans Lest définie par K= hT ,AiCT (Tbox) est un ensemble de définitions et d'axiomes (in L) :

• C D (concept inclusion)

• C ≡ D (concept equivalence)• R S (role inclusion)

• … + autres constructeurs selon L-KR

CA (Abox) est un ensemble d'assertions (in L) : • x ∈ D (concept instantiation)• hx,yi ∈ R (role instantiation)

• La sémantique est donnée par interprétation I=(∆I,.I)C∆I est le domaine (non vide)

C.I est une fonction d'interpretation qui fait correspondre :• Concept (classe) nom A → Sous-ensemble AI of ∆I

• Role (propriété) nom R → Relation binaire RI sur ∆I

• Individu (instance) nom i → iI element of ∆I

Knowledge Base

Tbox (schema)

Abox (data)

Man ≡ Human u Male

Happy-Father ≡ Man u ∃ has-child Female u …

John : Happy-FatherhJohn, Maryi : has-child In

fere

nce

Syst

em

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Knowledge Base Semantics

• An interpretation I satisfies (models) an axiom A (I A):

C I C D iff CI ⊆ DI

C I C ≡ D iff CI = D I

CI R S iff RI ⊆ SI

CI R ≡ S iff RI = SI

CI R+ R iff (RI)+ ⊆ RI

CI x ∈ D iff x ∈ DI

CI h x,yI i ∈ R iff (xI ,yI) ∈ RI

• I satisfies a Tbox T (I T ) iff I satisfies every axiom T in I• I satisfies an Abox A (I A) iff I satisfies every axiom A in I• I satisfies an KB K (I K) iff I satisfies both T and A

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Multiple Models -v- Single Model

• DL KB doesn’t define a single model, it is a set of constraints

that define a set of possible modelsCNo constraints (empty KB) means any model is possibleCMore constraints means fewer modelsCToo many constraints may mean no possible model (inconsistent KB)

• In contrast, DBs (and frame/rule KR systems) make

assumptions such that DB/KB defines a single modelCUnique name assumption

• Different names always interpreted as different individuals

CClosed world assumption• Domain consists only of individuals named in the DB/KB

CMinimal models• Extensions are as small as possible

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Example of Multiple Models

KB = {}

KB = {a:C, b:D, c:C, d:E}

KB = {a:C, b:D, c:C, d:E, b:C}

KB = {a:C, b:D, c:C, d:E, b:CD v C}

KB = {a:C, b:D, c:C, d:E, b:CD v C, E v C}

KB = {a:C, b:D, c:C, d:E, b:CD v C, E v C, d:¬ C}

I1:

∆ = {v, w, x, y, z}CI = {v, w, y}DI = {x, y} EI = {z}aI = v bI = xcI = w dI = y

I3:

∆ = {v, w, x, y, z}CI = {v, w, y}DI = {x, y} EI = {z}aI = v bI = ycI = w dI = z

I2:

∆ = {v, w, x, y, z}

CI = {v, w, y}

DI = {x, y} EI = {z}

aI = v bI = x

cI = w dI = z

I4:

∆ = {v, w, x, y, z}

CI = {v, w, x, y}

DI = {x, y} EI = {z}

aI = v bI = x

cI = y dI = y

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Example of Single Model (homework)

KB = {}

KB = {a:C, b:D, c:C, d:E}

KB = {a:C, b:D, c:C, d:E, b:C}

KB = {a:C, b:D, c:C, d:E, b:CE v C}

I:

∆ = {}

I:

∆ = {a, b, c, d}

CI = {a, b, c}

DI = {b} EI = {d}

aI = a bI = b

cI = c dI = d

I:

∆ = {a, b, c, d}

CI = {a, c}

DI = {b} EI = {d}

aI = a bI = b

cI = c dI = d

I:

∆ = {a, b, c, d}

CI = {a, b, c, d}

DI = {b} EI = {d}

aI = a bI = b

cI = c dI = d

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Short History of Description Logics

Phase 1: (early 80's) mostly system development

CIncomplete systems (KL-ONE, Back, Classic, Loom, . . . )

CBased on structural algorithms

Phase 2: (mid-80's) first formal investigation

CDevelopment of tableau algorithms and complexity results

CTableau-based systems for Pspace logics (e.g., Kris, Crack)

CInvestigation of optimisation techniques

Phase 3: (90's) tableau algorithms and thorough complexity analysis

CTableau algorithms for very expressive DLs

CHighly optimised tableau systems for ExpTime logics (e.g., FaCT, DLP, Racer)

CRelationship to modal logic and decidable fragments of FOL

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Recent Developments

Phase 4: (2010's)CMainstream applications and tools

• Databases– Consistency of conceptual schemata (EER, UML etc.)

– Schema integration

– Query subsumption (w.r.t. a conceptual schema)

• Ontologies, e-Science and Semantic Web/Grid– Ontology engineering (schema design, maintenance, integration)

– Reasoning with ontology-based annotations (data)

CMature implementations• Research implementations

– FaCT, FaCT++, Racer, Pellet, …

• Commercial implementations

– Cerebra system from Network Inference (and now Racer)

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Description Logic Reasoning

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Practical Reasons

• Given key role of ontologies in e-Science and Semantic Web, it is essential to provide tools and services to help users:CDesign and maintain high quality ontologies, e.g.:

• Meaningful — all named classes can have instances

• Correct — captured intuitions of domain experts

• Minimally redundant — no unintended synonyms

• Richly axiomatised — (sufficiently) detailed descriptions

CStore (large numbers) of instances of ontology classes, e.g.:

• Annotations from web pages (or gene product data)

CAnswer queries over ontology classes and instances, e.g.:

• Find more general/specific classes

• Retrieve annotations/pages matching a given description

CIntegrate and align multiple ontologies

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Why Decidable Reasoning?

• OWL constructors/axioms restricted so reasoning is decidable

• Consistent with Semantic Web's layered architectureCXML provides syntax transport layer

CRDF(S) provides basic relational language and simple ontologicalprimitives

COWL provides powerful but still decidable ontology language

CFurther layers (e.g. SWRL) will extend OWL

• Will almost certainly be undecidable

• Facilitates provision of reasoning servicesC“Practical” algorithms for sound and complete reasoning

CSeveral implemented systems

CEvidence of empirical tractability

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Why Sound & Complete Reasoning?

• Important for ontology designCOntologists need to have complete confidence in reasoner

COtherwise they will cease to trust results

CDoubting unexpected results makes reasoner useless

• Important for ontology deploymentCMany realistic web applications will be agent ↔ agent

CNo human intervention to spot glitches in reasoning

• Incomplete reasoning might be OK in 3-valued systemCBut “don’t know” typically treated as “no”

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DL Reasoning: Highly Optimised Implementations

• DL reasoning based on tableaux algorithms

• Naive implementation → effective non-termination

• Modern systems include MANY optimisations

• Optimised classification (compute partial ordering)CEnhanced traversal (exploits information from previous tests)

CUse structural information to select classification order

• Optimised subsumption testing (search for models)CNormalisation and simplification of concepts

CAbsorption (simplification) of axioms

CDependency directed backtracking

CCaching of satisfiability results and (partial) models

CHeuristic ordering of propositional and modal expansion

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KB Inférences

• Subsomption : CC T D ssi ≤I T CI ⊆ DI

CStructure la connaissance, calcule le graphe terminologique

• Consistance ou Satisfiable :C concept C ssi ≥I T CI ≠ ∅C ABox ssi ≥I A Toutes les assertions de ABoxCKB K = hT ,Ai ssi ≥I T A Toutes les assertions de TBox et ABox

• Aussi Equivalence C ≡ T D , Instance a :C(a)

• Les problèmes d'inférence sont liés :CC T D ssi ≤I T CI ¬DI

CC est consistant ssi ≤I T CI ⊆ AI 3 ¬AI

CInférences standard se réduisent à un test de satisfiabilité

• Inférences non standard (étudiées systématiquement depuis ~2000)

CApproximations, LCS, MSC, Matching, Unification, Différence, Ré-écriture …

Dites "Standard"

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KB Basic Inference Tasks (2)

• Knowledge is correct (captures intuitions)CDoes C subsume D w.r.t. ontology O? (CI µ DI in every model I of O)

• Knowledge is minimally redundant (no unintended synonyms)CIs C equivalent to D w.r.t. O? (CI = DI in every model I of O)

• Knowledge is meaningful (classes can have instances)CIs C is satisfiable w.r.t. O? (CI ≠ ∅ in some model I of O)

• Querying knowledgeCIs x an instance of C w.r.t. O? (xI ∈ CI in every model I of O)

CIs hx,yi an instance of R w.r.t. O? ((xI,yI) ∈ RI in every model I of O)

• Above problems can be solved using highly optimised DL reasoners

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DL Reasoning: Basics

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Tableau Algorithm (1)

• Tableau Algorithm is the de facto standard reasoning algorithm

used in DL

• Basic intuitions

CReduces a reasoning problem to concept satisfiability problem

CFinds an interpretation that satisfies concepts in question.

CThe interpretation is incrementally constructed as a "Tableau«

• Tableaux algorithms are decision procedures for concept

satisfiability (& subsumption & w.r.t. an ontology)

i.e., algorithms return “SAT” iff input concept is satisfiable

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Tableau Algorithm (2) (basic case)

• given: Wife⊆ Woman, Woman⊆ Person

question: if Wife⊆ Person

• Reasoning processCTest if there is a individual that is a Woman but not a Person, i.e. test the satisfiability of concept C0=(WifeΠ¬Person)CC0(x) -> Wife(x), (¬Person)(x)CWife(x)->Woman(x)CWoman(x) ->Person(x)CConflict!CC0 is unsatisfiable, therefore Wife⊆ Person is true with the given ontology.

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Tableau Algorithm (3) (General Process)

• Transform C into negation normal form(NNF), i.e. negation

occurs only in front of concept names.

• Denote the transformed expression as C0, the algorithm

starts with an ABox A0 = {C0(x0)}, and apply consistency-

preserving transformation rules (tableaux expansion) to the

ABox as far as possible.

• If one possible ABox is found, C0 is satisfiable.

• If not ABox is found under all search pathes, C0 is

unsatisfiable.

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Tableau Algorithm (4) (Exemple 2)

From Naouel Karam, ISIMA, Tutorial 2005, Postdam

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Current Research (1)

• Extending Description LogicsCExisting DL systems implement (at most) SHIQCOWL extends SHIQ with datatypes and nominals (SHOIN(Dn))

CComplex roles, finite domains, concrete domains, fuzzyness, …

CFuture OWL extensions (e.g., with “rules”) (undecidable such as SWRL ?)

• Integrating with other logics/systemsCE.g., Answer Set Programming

• Alternative reasoning techniquesCAutomata based algorithms

CTranslation into datalogCGraph based algorithms (for sub ALC languages)

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Current Research (2)

• Improving ScalabilityCVery large ontologies

CVery large numbers of individuals

• Other reasoning tasks (non-standard inferences)CMatching, LCS, explanation, querying, …

• Implementation of tools and InfrastructureCMore expressive languages (such as SHOIN)

CNew algorithmic techniques

CTools to support for large scale ontological engineering

• Editing, visualisation, etc.

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Complexité DLs

"DL – Basics, Applicatioions and more", I. Horrocks and U. Sattler, ECAI 2002, http://dl.kr.org

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Moteurs d'inférence

Fournier-Vigier P., Master 2005, Sherbrooke, Canada

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Summary (1)

• DLs are family of object oriented KR formalisms related to frames and

Semantic networks

CCharacterized by formal semantics and inference services

• An Ontology is an engineering artefact consisting of:

CA vocabulary of terms

CAn explicit specification their intended meaning

• Ontologies play a key role in many applicationsCe-Science, Telecommunications, Banking, Medicine, Databases, Semantic Web, etc.

• OWL is a DL based ontology language designed for the WebCExploits existing standards: XML, RDF(S)

CAdds KR idioms from object oriented and frame systems

CW3C recommendation and already widely adopted in e-Science

CDL provides formal foundations and reasoning support

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Summary (2)

• Reasoning is important becauseCUnderstanding is closely related to reasoning

CEssential for design, maintenance and deployment of ontologies

• Reasoning support based on DL systemsCSound and complete reasoning

CHighly optimised implementations

• Challenges remainCReasoning with full OWL language

C(Convincing) demonstration(s) of scalability

CNew reasoning tasks

CDevelopment of (more) high quality tools and infrastructure

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Remerciements

• Une pensée toute particulière à tous ceux à qui j'ai emprunté, et ils

sont nombreux !

• Et à ceux qui m'ont emprunté … ☺

Merci !

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Annexe

Travail à faire

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A Faire pour la semaine prochaine

• Lire les deux premiers chapitres du livre DL Handbook

(Baader et al.)*

• Faire les petits exercices de compréhension des

Interprétations de KB (cf. slides 26-30-31)

• Revoir les exemples de l’algorithme Tableau de résolution de problème SAT pour le test de subsomption C v D

• * Je peux les envoyer par courriel à l’un d’entre vous qui se

chargera des les distribuer.