introduction to description logic and ontology...

Introduction to Description Logic and Ontology Languages

Jidi (Judy) ZhaoOctober 21, 2009

CS6999 Presentation

Talk Outline

• Introduction to Ontologies• Introduction to Description Logic (DL)• Reasoning in DL• Introduction to Ontology Languages: OWL• Extensions of DL and Research Challenges

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What is an ontology?Many definitions have been given:

from Philosophy: “a systematic explanation of being”Neches gives some guidelines: “…defines the basic terms and relations including the vocabulary of a topic area as well as the rules for combining terms and relations to define extensions to the vocabulary.”Gruber, the most quoted: “…an explicit specification of a conceptualization”An ontology defines the concepts used to describe and represent an area of knowledge, as well as relations among them.

Types of OntologiesTop-level Ontologies

The Standard Upper Ontology (SUO): http://suo.ieee.org/

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Types of OntologiesTop-level Ontologies

The Standard Upper Ontology (SUO): http://suo.ieee.org/

WordNet:http://wordnet.princeton.edu/

Sowa’s top-level ontologyCyc’s upper ontology

Domain OntologiesE-commerceMedicineEngineeringEnterpriseChemistry….

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Thing

Living Nonliving

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Methodologies for Ontology Engineering

Building domain ontologies from huge ontologies (SENSUS, Cyc, AKT,…)

OTK (On-To-Knowledge) MethodologyUniv. of Karlsruhe

MethontologyUniv. Politecnica de Madrid

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Methontology: A Methodology for Building Ontologies

Methontology Ontology Development Process Life Cycle(Fernández-López et al., 1997;1999)

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Tools for Ontology EngineeringOilEd from University of Manchester

http://oiled.man.ac.uk/

Ontolingua from KSL (Stanford University) http://www-ksl.stanford.edu

OntoSaurus from ISI (USA) http://www.isi.edu/isd/ontosaurus.html

OntoEdit from Karlsrhue Univ. http://ontoserver.aifb.unikarlsruhe.de/ontoedit/

Protégé from SMI (Stanford University)http://protege.stanford.edu/

WebOnto from KMI (Open University)http://kmi.open.ac.uk/projects/webonto/

WebODE from UPMhttp://webode.dia.fi.upm.es/webODE/

KAON from AIFB and FZI at the University of Karlsruhehttp://kaon.semanticweb.org/

Talk Outline


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Description Logic

Brachman and Levesque [1984] “there is a tradeoff between the expressiveness of a representation language and the difficulty of reasoning over the representations built using that language”.

The more expressive the language, the harder the reasoning.Description Logics

overcome the ambiguities of early semantic networks and framesfirst realized in the system KL-One [Brachman and Schmolze, 1985]

Well-studied and decidable (most DL languages)Tight coupling between theory and practice

Architecture of a DL System

from DL Handbook

DL BasicsConcepts (unary predicates/formulae with one free variable)

E.g., Person, FemaleRoles (binary predicates/formulae with two free variables)

E.g., hasChildIndividuals (constants)

E.g., Mary, John

ConstructorsUniont, IntersectionuExists restriction∃: ∃hasChild.DoctorValue restriction∀: ∀hasChild.DoctorComplement /negation¬: ¬MotherNumber restriction ≥n, ≤nInverse role (-): isChildOf ≡ hasChild–

transitive role (+): hasSisterRole hierarchy : hasDaughter v hasChild

AxiomsSubsumptionv: MothervParentAssertion: Mary: Mother, Mary hasChild John

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What does ∀ R.C and ∃ R.C mean?

FlipCRoverCTabbyBFluffyAFidoA

hasPet

FlipRoverFidoDog

TabbyFluffyCat

A DogLover is someone whose pets are all dogs, in this case {C}DogLover = ∀ hasPet.Dog{p | ∀ a, (p, a) ∈ hasPet → a ∈ Dog}

Also writen more simply as {p | hasPet(p, a) → Dog(a) }

A DogLiker is someone who owns a dog , in this case {A, C}DogLiker = ∃ hasPet.Dog{p | hasPet(p, a) Æ Dog(a) }This slide is from Dr. Bruce Spencer’s slides (2007).

The DL Family

Smallest propositionally closed DL is ALCConcepts constructed using boolean operatorst , u , ¬

plus restricted quantifiers∃ , ∀

Only atomic roles

E.g.,Person u ∀hasChild.(Doctor t ∃hasChild.Doctor)

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The DL Family (cont.)S often used for ALC extended with transitive roles (R+)Additional letters indicate other extensions, e.g.:

H for role hierarchyO for nominals (e.g., {Mary, John})I for inverse rolesN for number restrictionsQ for qualified number restrictions (e.g., ≥2hasChild.Doctor)R for limited complex role inclusion axioms, role disjointness

ALC+ transitive role (R+)+role hierarchy (H) +O + I + Q = SHOIQ

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DL SemanticsSemantics given by standard FO model theoryThe vocabulary is the set of names (consist of concepts and roles ) we use in our model of (part of) the world

{Daisy, Cow, Animal, Person, Car, drives, …}An interpretation I is a tuple (ΔI, •I)

ΔI is the domain (a set)•I is a mapping that maps:

Names of objects (individuals/constants) to elements of ΔI

Names of unary predicates (classes/concepts) to subsets of ΔI

Names of binary predicates (properties/roles) to subsets of ΔI ×ΔI

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DL Semantics(adapted from Horrocks 2006)

Interpretation domain ΔIInterpretation function •I

Individuals iI ∈ ΔI

Mary

John

Concepts CI ⊆ ΔI

Teacher

Student

Car

Roles RI ⊆ ΔI × ΔI

hasChild

owns

(Teacher u Student)17

A Knowledge Base (KB) <T,A>=a Tbox + an Abox

A TBox (terminology) is a set of inclusion axioms and equivalence axioms

the vocabulary of an application domaine.g.: { Mother v Person,

GrandMother ≡ Person u ∃hasChild.Parent }

An ABox (Assertion) is a set of assertions about individuals

about named individuals in terms of this vocabularye.g.: {Mary: Mother, Anita hasChild Mary}

DL Knowledge Bases

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Tableau Reasoning (1)Key reasoning tasks

Satisfiability: asat(A), whether the assertions in a KB have a modelInstance checking: C(a)?Concept satisfiability: C?Retrieval: retrieve a set of individuals that instantiate CSubsumption: B v A ?

A subsumes B if every individual of concept B is also of concept A.

Equivalence: A≡B? ⇔ B v A ? And A v B?

Reasoning tasks reducible to KB (un)satisfiability: asat(A)Instance checking: instance(a, C, A) ⇔ ¬asat (A ∪ {a: ¬C})Concept satisfiability: sat(C) ⇔ asat(A ∪ {a:C})Concept subsumption:C v D w.r.t. KB A⇔ A ∪ {¬D u C} is not satisfiable ⇔ ¬asat(A ∪ {a:¬D u C})Retrieval:check each individual in the Abox, reducible to instance checking

DL systems typically use tableau algorithms to decide the satisfiability(consistency) of KB

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CS6795 Semantic Web Techniques21

Tableau Reasoning (2)Tableau algorithms work by trying to construct a concrete example(model) consistent with KB.A KB A is satisfiable iff a fully expanded clash-free graph is constructed.Tableau reasoning contains a set of completion rules operating on constraint sets or tableauClash: a clash is an obvious contradiction, e.g., A(x), ¬A(x)Proof procedure:

start from assertions about individuals (ABox axioms)unfold the TBox so that atomic concepts only appear on the right side of axioms transform all concepts into negation normal form (i.e. negation only occurs in front of atomic concept names):

¬ (C u D) → ¬C t ¬D¬ ∃R.C → ∀ R.¬C

apply completion rules in arbitrary order as long as possiblestops when a clash is foundterminates if no completion rule is applicableA KB is satisfiable iff a clash-free tableau can be derived

completion rules

Tableau Reasoning (3)

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Tableau Reasoning (5): Concept SubsumptionKB:

Reasoning task: mother v woman?

Exercise: Is the concept ¬ woman u mother satisfiable?

Tableau Reasoning (4): asat(A)E.g., KB: {HappyParent≡Person u ∀hasChild.(Doctor t ∃hasChild.Doctor),John:HappyParent, John hasChild Mary,Mary: ¬Doctor, Wendy hasChild Mary, Wendy marriedTo John}

from Harrock, 2006

Person∀hasChild.(Doctor t ∃hasChild.Doctor)

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Tableau Reasoning (6)Some completion rules are nondeterministic (e.g., ∃ , ≤ ).Blocking Strategies are often needed to ensure termination.E.g., KB:

{Person v ∃hasParent.Person,John:Person}

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In general, (representation of) model consists of:

Named individuals forming arbitrary directed graphTrees of anonymous individuals rooted in named individuals

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Similar tableaux expansions can be designed for more expressive DL languages. A tableau algorithm has to meet three requirements:

Soundness: if a complete and clash-free graph is found by the algorithm, we can construct a model.Completeness: Given a model, the algorithm can always find an complete and clash-free graphTermination: the algorithm can terminate in finite steps with specific result.


Software for DL Reasoning

Pellet

KAON2 CEL

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Efficiency of Tableau Reasoning

I can’t find an efficient algorithm, but neither can all these famous people.

NP-Complete Cartoons, http://max.cs.kzoo.edu/~kschultz/CS510/ClassPresentations/NPCartoons.html

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Traditional Ontology LanguagesOntolingua and KIFLOOMOKBCF-logic

Ontology Markup LanguagesSHOERDF and RDF SchemaOILDAML+OILOWL

Ontology Languages

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Semantic Web led to requirement for a “web ontology language”

set up Web-Ontology (WebOnt) Working Group

WebOnt developed OWL language OWL based on earlier languages OIL and DAML+OILOWL now a W3C recommendation

OIL, DAML+OIL and OWL based on Description Logic

The Web Ontology Language OWL

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OWLThree species of OWL

OWL full is the union of OWL syntax and RDFOWL DL restricted to FOL fragment (is equivalent to SHOIN(Dn) DL)OWL Lite is an “easier to implement” subset of OWL DL

OWL DL Benefits from many years of DL research

Well defined semanticsFormal properties well understood (complexity, decidability)Known reasoning algorithmsImplemented systems (highly optimised)

Adapted from ENC 2004 Tutorial by Peter F. Patel-Schneider33

OWL RDF/XML Exchange Syntax

<owl:Class><owl:intersectionOf rdf:parseType=“collection">

<owl:Class rdf:about="#Person"/><owl:Restriction>

<owl:onProperty rdf:resource="#hasChild"/><owl:allValuesFrom>

<owl:unionOf rdf:parseType=“collection"><owl:Class rdf:about="#Doctor"/><owl:Restriction>

<owl:onPropertyrdf:resource="#hasChild"/>

<owl:someValuesFromrdf:resource="#Doctor"/>

</owl:Restriction></owl:unionOf>

</owl:allValuesFrom></owl:Restriction>

</owl:intersectionOf></owl:Class>

E.g., Person u ∀hasChild.(Doctor t ∃hasChild.Doctor):

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Class/Concept Constructors

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Ontology Axioms

OWL ontology equivalent to DL KB (Tbox + Abox)

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Talk Outline


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Extensions of DL

Combinations of DL and Logic Programs (LP)Uncertainty extension of DLConcrete domain constraintsModal, epistemic, and temporal operatorsOpen world vs. close world…..

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Venn Diagram of DL, LP, and FOC

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Motivation(1)

DL cannot represent “more than one free variable at a time”.(1) A rule involving multiple variables. E.g.,Man(?X) ∧ Woman(?Y)

→PotentialFriendshipBetween(?X,?Y).(2) Chaining to derive values of Properties. E.g.,Father(?X,?Y) ∧ Father(?Y,?Z)→ Grandfather(?X,?Z). (not allowed in

SHOIN)

Work(?X, ?Y) ∧ Live(?X, ?Z) ∧ Loc(?Y,?W) ∧ Loc(?Z,?W)→HomeWorker(?X).

Motivation(2)

•Horn Logic cannot represent a (1) disjunction or (2) existential in the head.•(1) State a subclass of a complex class expression which is a disjunction. E.g.,

(Human u Adult) v (Man t Woman)•(2) State a subclass of a complex class expression which is an existential. E.g.,

Radio v∃hasPart.Tuner

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Different approaches1. Approaches reducing description logics to logic programs

A. DLPB. OWL 2 RL

2. Homogeneous approachesA. OWL RulesB. SWRL

3. Hybrid approaches accessing description logic through queries in logic programsA. AL-Log

Uncertainty extension of DLHandling uncertain knowledge is becoming a critical research direction for the (Semantic) Web.knowledge on the Web is often uncertain and imprecise. E.g., many concepts needed in business domain ontology modeling lack well-defined boundaries or, precisely defined criteria of relationship between conceptsDomain modeling and Ontology reasoning

Quantify degree of an individual belonging to a classQuantify degree of subsumption between a class and its subclasses

Concept mapping between ontologiesQuantify degree of alignment between classes of two ontologies

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URW3 Situation Report: uncertainty ontology

URW3

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Probability, Possibility and Fuzzy logic

Probabilistic Description Logic:Statistical informatione.g. John is a student with the probability 0.6 and a teacher with the probability 0.4

Fuzzy Description Logic:Express vagueness and imprecisione.g. John is tall with the degree of truth 0.9

Possibilistic Description Logic:Particular rankings and preferencese.g. John prefers an ice cream to a beer

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Research Challenges

Syntax and SemanticsDecidabilityReasoning algorithms for possible extensionsSoundness and completenessComplexity/efficiencyEffective methods for reasoning under uncertainty

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Questions?

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