OWL: A Description Logic Based Ontology Language - PowerPoint PPT Presentation

1 / 51
About This Presentation
Title:

OWL: A Description Logic Based Ontology Language

Description:

Title: Ontologe Reasoning: the Why and the How Author: Ian Horrocks Last modified by: Svetlana Vinnik Created Date: 3/5/2005 1:50:41 PM Document presentation format – PowerPoint PPT presentation

Number of Views:239
Avg rating:3.0/5.0
Slides: 52
Provided by: IanHor8
Category:

less

Transcript and Presenter's Notes

Title: OWL: A Description Logic Based Ontology Language


1
OWL A Description Logic Based Ontology Language
  • Ian Horrocks
  • lthorrocks_at_cs.man.ac.ukgt
  • Information Management Group
  • School of Computer Science
  • University of Manchester

2
Talk Outline
  • Introduction to Description Logics
  • Introduction to Ontologies
  • Introduction to Ontology Languages
  • Ontology Reasoning
  • Why do we want it?
  • How do we do it?
  • Current Work and Research Challenges
  • Summary

3
Introduction to Description Logics
4
What Are Description Logics?
  • A family of logic based Knowledge Representation
    formalisms
  • Descendants of semantic networks and KL-ONE
  • Describe domain in terms of concepts (classes),
    roles (properties, relationships) and individuals
  • Distinguished by
  • Formal semantics (typically model theoretic)
  • Decidable fragments of FOL (often contained in
    C2)
  • Closely related to Propositional Modal Dynamic
    Logics
  • Closely related to Guarded Fragment
  • Provision of inference services
  • Decision procedures for key problems
    (satisfiability, subsumption, etc)
  • Implemented systems (highly optimised)

5
DL Basics
  • Concepts (unary predicates/formulae with one free
    variable)
  • E.g., Person, Doctor, HappyParent, (Doctor t
    Lawyer)
  • Roles (binary predicates/formulae with two free
    variables)
  • E.g., hasChild, loves, (hasBrother hasDaughter)
  • Individuals (constants)
  • E.g., John, Mary, Italy
  • Operators (for forming concepts and roles)
    restricted so that
  • Satisfiability/subsumption is decidable and, if
    possible, of low complexity
  • No need for explicit use of variables
  • Restricted form of 9 and 8 (direct correspondence
    with ? and )
  • Features such as counting can be succinctly
    expressed

6
The DL Family (1)
  • Smallest propositionally closed DL is ALC (equiv
    modal K(m))
  • Concepts constructed using booleans
  • u, t, ,
  • plus restricted quantifiers
  • 9, 8
  • Only atomic roles
  • E.g., Person all of whose children are either
    Doctors or have a child who is a Doctor
  • Person u 8hasChild.(Doctor t 9hasChild.Doctor)

7
The DL Family (2)
  • S often used for ALC extended with transitive
    roles (R)
  • Additional letters indicate other extensions,
    e.g.
  • H for role hierarchy (e.g., hasDaughter v
    hasChild)
  • O for nominals/singleton classes (e.g., Italy)
  • I for inverse roles (e.g., isChildOf
    hasChild)
  • N for number restrictions (e.g., gt2hasChild,
    63hasChild)
  • Q for qualified number restrictions (e.g.,
    gt2hasChild.Doctor)
  • F for functional number restrictions (e.g.,
    61hasMother)
  • S role hierarchy (H) inverse (I) QNR (Q)
    SHIQ
  • SHIQ is the basis for W3Cs OWL Web Ontology
    Language
  • OWL DL ¼ SHIQ extended with nominals (i.e.,
    SHOIQ)
  • OWL Lite ¼ SHIQ with only functional restrictions
    (i.e., SHIF)

8
DL Semantics
  • Semantics given by standard FO model theory

Interpretation domain ?I
Interpretation function I
Individuals iI 2 ?I John Mary Concepts CI µ
?I Lawyer Doctor Vehicle Roles rI µ ?I
?I hasChild owns
(Lawyer u Doctor)
9
DL Knowledge Base
  • A TBox is a set of schema axioms (sentences),
    e.g.
  • Doctor v Person,
  • HappyParent Person u 8hasChild.(Doctor t
    9hasChild.Doctor)
  • An ABox is a set of data axioms (ground facts),
    e.g.
  • JohnHappyParent,
  • John hasChild Mary
  • A Knowledge Base (KB) is just a TBox plus an ABox

10
Introduction to Ontologies
11
See other talk
12
Introduction toOntology Languages
13
The Web Ontology Language OWL
  • 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 DAMLOIL
  • OWL now a W3C recommendation (i.e., a standard)
  • OIL, DAMLOIL and OWL based on Description Logics
  • OWL effectively a Web-friendly syntax for SHOIN

14
OWL RDF/XML Exchange Syntax
E.g., Person u 8hasChild.(Doctor t
9hasChild.Doctor)
  • ltowlClassgt
  • ltowlintersectionOf rdfparseType"
    collection"gt
  • ltowlClass rdfabout"Person"/gt
  • ltowlRestrictiongt
  • ltowlonProperty rdfresource"hasChild"/gt
  • ltowlallValuesFromgt
  • ltowlunionOf rdfparseType" collection"gt
  • ltowlClass rdfabout"Doctor"/gt
  • ltowlRestrictiongt
  • ltowlonProperty rdfresource"hasChil
    d"/gt
  • ltowlsomeValuesFrom
    rdfresource"Doctor"/gt
  • lt/owlRestrictiongt
  • lt/owlunionOfgt
  • lt/owlallValuesFromgt
  • lt/owlRestrictiongt
  • lt/owlintersectionOfgt
  • lt/owlClassgt

15
Class/Concept Constructors
  • C is a concept (class) P is a role (property) x
    is an individual name
  • XMLS datatypes as well as classes in 8P.C and
    9P.C
  • Restricted form of DL concrete domains

16
Ontology Axioms
  • OWL ontology equivalent to DL KB (Tbox Abox)

17
Why Description Logic?
  • OWL exploits results of 15 years of DL research
  • Well defined (model theoretic) semantics

18
Why Description Logic?
  • OWL exploits results of 15 years of DL research
  • Well defined (model theoretic) semantics
  • Formal properties well understood (complexity,
    decidability)

I cant find an efficient algorithm, but neither
can all these famous people.
Garey Johnson. Computers and Intractability A
Guide to the Theory of NP-Completeness. Freeman,
1979.
19
Why Description Logic?
  • OWL exploits results of 15 years of DL research
  • Well defined (model theoretic) semantics
  • Formal properties well understood (complexity,
    decidability)
  • Known reasoning algorithms

20
Why Description Logic?
  • OWL exploits results of 15 years of DL research
  • Well defined (model theoretic) semantics
  • Formal properties well understood (complexity,
    decidability)
  • Known reasoning algorithms
  • Implemented systems (highly optimised)

Pellet
21
Why Description Logic?
  • Foundational research was crucial to design of
    OWL
  • Informed Working Group decisions at every stage,
    e.g.
  • Why not extend the language with feature x,
    which is clearly harmless?
  • Adding x would lead to undecidability - see
    proof in

22
Ontology ReasoningWhy do We Want It?
23
See other talk
24
Why Decidable Reasoning?
  • OWLs expressive power restricted so reasoning is
    decidable
  • Design was motivated by
  • Layered architecture of Semantic Web languages
  • RDF(S) provides basic relational language and
    simple ontological primitives (or this is what
    RDF should be)
  • OWL provides powerful but still decidable
    ontology language
  • Further layers (e.g. RIF) will extend OWL (and
    may be undecidable)
  • W3C requirement for implementation experience
  • Evidence that language can be / is being used in
    practice
  • Should be several implemented systems
  • Users expectations of (automated reasoning)
    systems
  • Should exhibit correct, consistent and
    predictable behaviour
  • And should be quick about it!

25
Ontology ReasoningHow do we do it?
26
Using Standard DL Techniques
  • Key reasoning tasks reducible to KB
    (un)satisfiability
  • E.g., C v D w.r.t. KB K iff K x(C u D) is
    not satisfiable
  • State of the art DL systems typically use (highly
    optimised) tableaux algorithms to decide
    satisfiability (consistency) of KB
  • Tableaux algorithms work by trying to construct a
    concrete example (model) consistent with KB
    axioms
  • Start from ground facts (ABox axioms)
  • Explicate structure implied by complex concepts
    and TBox axioms
  • Syntactic decomposition using tableaux expansion
    rules
  • Infer constraints on (elements of) model

27
Tableaux Reasoning (1)
  • E.g., KB
  • HappyParent Person u 8hasChild.(Doctor t
    9hasChild.Doctor),
  • JohnHappyParent, John hasChild Mary, Mary
    Doctor
  • Wendy hasChild Mary, Wendy marriedTo John

Person 8hasChild.(Doctor t 9hasChild.Doctor)
28
Tableaux Reasoning (2)
  • Tableau rules correspond to constructors in logic
    (u, 9 etc)
  • E.g., John(Person u Doctor) --! JohnPerson
    and JohnDoctor
  • Stop when no more rules applicable or clash
    occurs
  • Clash is an obvious contradiction, e.g., A(x),
    A(x)
  • Some rules are nondeterministic (e.g., t, 6)
  • In practice, this means search
  • Cycle check (blocking) often needed to ensure
    termination
  • E.g., KB
  • Person v 9hasParent.Person,
  • JohnPerson

29
Tableaux Reasoning (3)
  • In general, (representation of) model consists
    of
  • Named individuals forming arbitrary directed
    graph
  • Trees of anonymous individuals rooted in named
    individuals

30
Decision Procedures
  • Algorithms are decision procedures, i.e., KB is
    satisfiable iff rules can be applied such that
    fully expanded clash free graph is constructed
  • Sound
  • Given a fully expanded and clash-free graph, we
    can trivially construct a model
  • Complete
  • Given a model, we can use it to guide application
    of non-deterministic rules in such a way as to
    construct a clash-free graph
  • Terminating
  • Bounds on number of named individuals, out-degree
    of trees (rule applications per node), and depth
    of trees (blocking)
  • Crucially depends on (some form of) tree model
    property

31
Ontology ReasoningA Tableaux Algorithm for SHOIQ
32
Motivation for OWL Design
  • Exploit results of DL research
  • Well defined semantics
  • Formal properties well understood (complexity,
    decidability)
  • Known tableaux decision procedures and
    implemented systems
  • But not for SHOIN (until recently)!
  • So why is/was SHOIN so hard?

33
SHIQ is Already Tricky
  • Does not have finite model property, e.g.
  • ITN v 61 edge u 9edge.ITN,
  • R(ITN u 60 edge)
  • Double blocking
  • Block interpreted as infinite repetition

34
SHIQ is Already Tricky
  • Does not have finite model property, e.g.
  • ITN v 61 edge u 9edge.ITN,
  • R(ITN u 60 edge)
  • Double blocking
  • Block interpreted as infinite repetition
  • Termination problem due to gt and 6, e.g.
  • John9hasChild.Doctor u gt2 hasChild.Lawyer
  • u 62 hasChild
  • Add inequalities between nodes generated by gt
    rule
  • Clash if 6 rule only applicable to ? nodes

35
SHOIQ Loss (almost) of TMP
  • Interactions between O, I, and Q lead to new
    termination problems
  • Anonymous branches can loop back to named
    individuals (O)
  • E.g., 9r.Mary
  • Number restrictions (Q) on incoming edges (I)
    lead to non-tree structure
  • E.g., Mary61 r
  • Result is anonymous nodes that act like named
    individual nodes
  • Blocking sequence cannot include such nodes
  • Dont know how to build a model from a graph
    including such a block

36
Intuition Nominal Nodes
  • Nominal nodes (N-nodes) include
  • Named individual nodes
  • Nodes affected by number restriction via outgoing
    edge to N-node
  • Blocking sequence cannot include N-nodes
  • Bound on number of N-nodes
  • Must initially have been on a path between named
    individual nodes
  • Length of such paths bounded by blocking
  • Number of incoming edges at an N-node is limited
    by number restrictions

37
Generate Merge Problem is Back!
  • E.g., KB
  • VMP Person u 9loves.Mary u
    9hasFriend.VMP,
  • John9hasFriend.VMP
  • Mary62 loves
  • Blocking prevented by N-nodes
  • Repeated generation and merging of nodes leads to
    non-termination

38
Intuition Guess Exact Cardinality
  • New Ro?-rule guesses exact cardinality constraint
    on N-nodes
  • VMP Person u 9loves.Mary u
    9hasFriend.VMP,
  • John9hasFriend.VMP
  • Mary62 loves
  • Inequality between resulting N-nodes fixes
    generate merge problem
  • Introduces new source of non-determinism
  • But only if nominals used in a nasty way
  • Usage in ontologies typically harmless
  • Otherwise behaves as for SHIQ

39
Research ChallengesWhat next?
40
Increasing Expressive Power
  • OWL not expressive enough for some applications
  • Constructors mainly for classes (unary
    predicates)
  • No complex datatypes or built in predicates
    (e.g., arithmetic)
  • No variables
  • No higher arity predicates
  • Extensions (of OWL) that have/are being
    considered include
  • (Decidable) extensions to underlying DL
  • Rule language extensions
  • The focus of much research/debate (e.g., W3C RIF
    working group)
  • First order logic (e.g., SWRL-FOL)
  • (Syntactically) higher order extensions (e.g.,
    Common Logic)

41
Extend Underlying DL
  • Role box (SROIQ) Horrocks, Kutz Sattler,
    KR-06
  • E.g., hasLocation partOf v hasLocation
  • Reflexive, irreflexive, and antisymmetric roles
  • Basis for OWL 1.1 effort
  • Concrete domains/datatypes Lutz, IJCAI-99 Pan
    et al, ISWC-03
  • E.g., value comparison (income gt expenditure)
  • Custom datatypes (integer gt25)
  • Database style keys Lutz et al, JAIR 2004
  • E.g., make model chassis-number is a key for
    Vehicles
  • Note that role box concrete domains is basis
    for OWL 1.1

42
Rule Language Extensions (to OWL)
  • First Order extension (e.g., SWRL) Horrocks et
    al, JWS, 2005
  • Horn clauses where predicates are OWL classes and
    properties
  • Resulting language is undecidable
  • Reasoning support currently only via FOL theorem
    provers (Hoolet)
  • Hybrid language extensions being investigated
  • Restricting language interaction maintains
    decidability
  • DL extended with Answer Set Programming Eiter et
    al, KR-04
  • DL extended with Datalog rules Motik et al,
    ISWC-04 Rosati, JWS, 2005
  • LP/F-logic rule language
  • Claimed interoperability with OWL via DLP
    subset de Bruijn et al, WWW-05

43
Improving Scalability
  • Optimisation techniques
  • Improve performance of DL reasoners, e.g., Sirin
    et al, KR-06
  • Reduction to disjunctive Datalog Motik et at,
    KR-04
  • Transform DL ontology to DatalogÇ rules
  • Use LP techniques to deal with large numbers of
    ground facts
  • Hybrid DL-DB systems Horrocks et al, CADE-05
  • Use DB to store Abox (individual) axioms
  • Cache inferences and use DB queries to
    answer/scope logical queries
  • Polynomial time algorithms for sub-ALC logics
    Baader et al, IJCAI-05
  • Graph based techniques for subsumption computation

44
Other Reasoning Tasks
  • Querying Calvanese et al, PODS-98, Fikes et al,
    JWS, 2004
  • Retrieval and instantiation wont be sufficient
  • Would like, e.g., DB style conjunctive query
    language
  • May also need what can I say about x? style of
    query
  • Explanation Schlobach Cornet, DL-03 Parsia et
    al, WWW-04
  • To support ontology design
  • Justifications and proofs (e.g., of query
    results)

45
Other Reasoning Tasks
  • Non-Standard Inferences (e.g., LCS, matching,
    ) Küsters, 2001
  • To support ontology integration
  • To support bottom up design of ontologies
  • Design methodologies, e.g., Wolter Lutz,
    KR-06
  • Foundational ontologies, conservative extensions,
    modularisation, etc.

46
Tools and Infrastructure
  • Editors/environments
  • Oiled, Protégé, Swoop, Construct, Ontotrack,

47
Tools and Infrastructure
  • Editors/environments
  • Oiled, Protégé, Swoop, Construct, Ontotrack,
  • Reasoning systems
  • Cerebra, FaCT, Kaon2, Pellet, Racer,

Pellet
48
Summary
  • DLs are a family of logic based KR formalisms
  • Describe domain in terms of concepts, roles and
    individuals
  • DLs have many applications
  • But best known as basis of ontology languages
    such as OWL

49
Summary
  • Reasoning is crucial to use of ontologies
  • E.g., in design, maintenance and deployment
  • Reasoning support via underlying logic
  • E.g., based on DL systems
  • Many challenges remain, including
  • Well founded language extensions
  • Extending range and effectiveness of reasoning
    services

Enough work to keep logic based KR community busy
for many years to come ?
50
Acknowledgements
  • Thanks to my many friends in the DL and ontology
    communities, in particular
  • Alan Rector
  • Franz Baader
  • Uli Sattler

51
Resources
  • Slides from this talk
  • http//www.cs.man.ac.uk/horrocks/Slides/cisa06.pp
    t
  • FaCT system (open source)
  • http//owl.man.ac.uk/factplusplus/
  • Protégé
  • http//protege.stanford.edu/plugins/owl/
  • W3C Web-Ontology (WebOnt) working group (OWL)
  • http//www.w3.org/2001/sw/WebOnt/
  • DL Handbook, Cambridge University Press
  • http//books.cambridge.org/0521781760.htm

52
DL KR, Windermere, 30th May 5th June
Thank you for listening
Any questions?
Write a Comment
User Comments (0)
About PowerShow.com