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

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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

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Introduction to Description Logics
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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)

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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

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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)

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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)

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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)
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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

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Introduction to Ontologies
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See other talk
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Introduction toOntology Languages
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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

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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

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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

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Ontology Axioms

• OWL ontology equivalent to DL KB (Tbox Abox)

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Why Description Logic?

• OWL exploits results of 15 years of DL research
• Well defined (model theoretic) semantics

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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.
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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

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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
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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

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Ontology ReasoningWhy do We Want It?
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See other talk
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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!

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Ontology ReasoningHow do we do it?
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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

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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)
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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

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Tableaux Reasoning (3)

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

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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

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Ontology ReasoningA Tableaux Algorithm for SHOIQ
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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?

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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

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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

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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

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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

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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

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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

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Research ChallengesWhat next?
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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)

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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

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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

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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

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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)

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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.

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Tools and Infrastructure

• Editors/environments
• Oiled, Protégé, Swoop, Construct, Ontotrack,

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Tools and Infrastructure

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

Pellet
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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

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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 ?
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Acknowledgements

• Thanks to my many friends in the DL and ontology
  communities, in particular
• Alan Rector
• Franz Baader
• Uli Sattler

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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

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DL KR, Windermere, 30th May 5th June
Thank you for listening
Any questions?