Ontology Reasoning: the Why and the How

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Ontology Reasoningthe Why and the How

• Ian Horrocks lthorrocks_at_cs.man.ac.ukgt
• University of Manchester
• Manchester, UK

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Talk Outline

• Ontologies What are they?
• Ontology Reasoning Why do we need it?
• Tools and services for ontology design and
  deployment
• Importance of decidability, soundness and
  completeness
• Ontology Reasoning How do we do it?
• Description Logics
• Tableaux algorithms
• Research Challenges
• Expressive power, scalability etc.
• Summary

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Ontologies What are they?
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Ontology Origins and History

• a philosophical disciplinea branch of
  philosophy that
• deals 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?

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Classification An Old Problem
Extract from Bills of Mortality, published weekly
from 1664-1830s
The Diseases and Casualties this Week

• Aged 54
• Apoplectic 1
• .
• Fall down stairs 1
• Gangrene 1
• Grief 1
• Griping in the Guts 74
• Plague 3880

• Suddenly 1
• Surfeit 87
• Teeth 113
• Ulcer 2
• Vomiting 7
• Winde 8
• Worms 18

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Classification An Old Problem

• On those remote pages it is written that animals
  are divided into
• a. those that belong to the Emperor
• b. embalmed ones
• c. those that are trained
• d. suckling pigs
• e. mermaids
• f. fabulous ones
• g. stray dogs
• h. those that are included in this classification
• i. those that tremble as if they were mad
• j. innumerable ones
• k. those drawn with a very fine camel's hair
  brush
• l. others
• m. those that have just broken a flower vase
• n. those that from a long way off look like flies
  

Attributed to a certain Chinese encyclopaedia
entitled Celestial Empire of benevolent
Knowledge. Jorge Luis Borges The Analytical
Language of John Wilkins
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Ontology in Computer Science

• An ontology is an engineering artifact consisting
  of
• A vocabulary used to describe (a particular view
  of) some domain
• An explicit specification of the intended meaning
  of the vocabulary.
• almost always includes how concepts should be
  classified
• Constraints capturing additional knowledge about
  the domain
• Ideally, an ontology should
• Capture a shared understanding of a domain of
  interest
• Provide a formal and machine manipulable model of
  the domain

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Example Ontology

• Vocabulary and meaning (definitions)
• Elephant is a concept whose members are a kind of
  animal
• Herbivore is a concept whose members are exactly
  those animals who eat only plants or parts of
  plants
• Adult_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)
• Adult_Elephants weigh at least 2,000 kg
• All Elephants are either African_Elephants or
  Indian_Elephants
• No individual can be both a Herbivore and a
  Carnivore

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Example Ontology (Protégé)
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Example Ontology (OilEd)
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Where are ontologies used?

• e-Science, e.g., Bioinformatics
• The Gene Ontology
• The Protein Ontology (MGED)
• in silico investigations relating theory and
  data
• Medicine
• Terminologies
• Databases
• Integration
• Query answering
• User interfaces
• Linguistics
• The Semantic Web

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Ontology Driven User Interface
FRACTURE SURGERY

• Fixation of open fracture of neck of left femur

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Scientific American, May 2001
Beware of the Hype!
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Ontology Reasoning Why do we need it?
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Philosophical Reasons

• Applications such as the Semantic Web aim at
  machine understanding
• Understanding is closely related to reasoning
• Recognising semantic similarity in spite of
  syntactic differences
• Recognising implicit consequences given
  explicitly stated facts

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Practical Reasons

• Given key role of ontologies in many
  applications, it is essential to provide tools
  and services to help users
• Design 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
• Answer queries over ontology classes and
  instances, e.g.
• Find more general/specific classes
• Retrieve individuals/tuples matching a given
  query
• Integrate and align multiple ontologies

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Why Decidable Reasoning?

• OWL constructors/axioms have been restricted so
  reasoning is decidable
• Consistent with Semantic Web's layered
  architecture
• XML provides syntax transport layer
• RDF(S) provides basic relational language and
  simple ontological primitives
• OWL provides powerful but still decidable
  ontology language
• Further layers (e.g. SWRL) will extend OWL
• Will almost certainly be undecidable
• W3C requirement for implementation experience
• Practical algorithms for sound and complete
  reasoning
• Several implemented systems
• Evidence of empirical tractability

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Why Sound Complete Reasoning?

• Important for ontology design
• Ontologists need to have complete confidence in
  reasoner
• Otherwise they will cease to trust results
• Doubting unexpected results makes reasoner
  useless
• Important for ontology deployment
• Many realistic web applications will be agent ?
  agent
• No human intervention to spot glitches in
  reasoning
• Incomplete reasoning might be OK in 3-valued
  system
• But dont know typically treated as no

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System Demonstration (OilEd)
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Ontology ReasoningHow do we do it?
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Use a (Description) Logic

• OWL DL based on SHIQ Description Logic
• In fact it is equivalent to SHOIN(Dn) DL
• OWL DL Benefits from many years of DL research
• Well defined semantics
• Formal properties well understood (complexity,
  decidability)
• Known reasoning algorithms
• Implemented systems (highly optimised)
• In fact there are three species of OWL (!)
• OWL full is union of OWL syntax and RDF
• OWL DL restricted to FOL fragment (¼ DAMLOIL)
• OWL Lite is simpler subset of OWL DL

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OWL Class Constructors

• XMLS datatypes as well as classes in 8P.C and
  9P.C
• Restricted form of DL concrete domains

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RDFS Syntax
E.g., Person u 8hasChild.(Doctor t
9hasChild.Doctor)

• ltowlClassgt
• ltowlintersectionOf rdfparseType"
  collection"gt
• ltowlClass rdfabout"Person"/gt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"hasChild"/gt
• ltowltoClassgt
• ltowlunionOf rdfparseType" collection"gt
• ltowlClass rdfabout"Doctor"/gt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"hasChil
  d"/gt
• ltowlhasClass rdfresource"Doctor"/gt
  
• lt/owlRestrictiongt
• lt/owlunionOfgt
• lt/owltoClassgt
• lt/owlRestrictiongt
• lt/owlintersectionOfgt
• lt/owlClassgt

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OWL Axioms

• Axioms (mostly) reducible to inclusion (v)
• C D iff both C v D and D v C
• Obvious FOL equivalences
• E.g., C D , ?x.C(x) D(x), C v D ,
  ?x.C(x) !D(x)

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Basic Inference Tasks

• Knowledge is correct (captures intuitions)
• Does C subsume D w.r.t. ontology O? (CI µ DI in
  every model I of O)
• Knowledge is minimally redundant (no unintended
  synonyms)
• Is C equivallent to D w.r.t. O? (CI DI in every
  model I of O)
• Knowledge is meaningful (classes can have
  instances)
• Is C is satisfiable w.r.t. O? (CI ? in some
  model I of O)
• Querying knowledge
• Is x an instance of C w.r.t. O? (xI 2 CI in every
  model I of O)
• Is hx,yi an instance of R w.r.t. O? ((xI,yI) 2 RI
  in every model I of O)
• Above problems can be solved using highly
  optimised DL reasoners

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DL Reasoning Basics

• Tableau algorithms used to test satisfiability
  (consistency)
• Try to build a tree-like model of the input
  concept C
• Decompose C syntactically
• Apply tableau expansion rules
• Infer constraints on elements of model
• Tableau rules correspond to constructors in logic
  (u, t etc)
• Some rules are nondeterministic (e.g., t, 6)
• In practice, this means search
• Stop when no more rules applicable or clash
  occurs
• Clash is an obvious contradiction, e.g., A(x),
  A(x)
• Cycle check (blocking) may be needed for
  termination
• C satisfiable iff rules can be applied such that
  a fully expanded clash free tree is constructed

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DL Reasoning Advanced Techniques

• Satisfiability w.r.t. an Ontology O
• For each axiom C v D 2 O , add C t D to every
  node label
• More expressive DLs
• Basic technique can be extended to deal with
• Role inclusion axioms (role hierarchy)
• Number restrictions
• Inverse roles
• Concrete domains/datatypes
• Aboxes
• etc.
• Extend expansion rules and use more sophisticated
  blocking strategy
• Forest instead of Tree (for Aboxes)
• Root nodes correspond to individuals in Abox

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DL Reasoning Decision Procedures

• Theorem Tableaux algorithms are decision
  procedures for concept satisfiability (
  subsumption w.r.t. an ontology)
• i.e., algorithms return SAT iff input concept
  is satisfiable
• Terminating
• Bounds on out-degree (rule applications per node)
  and depth (blocking) of tree
• Sound
• Can construct a tableau, and hence a model, from
  a fully expanded and clash-free tree
• Complete
• Can use a model to guide application of
  non-deterministic rules and so construct a
  clash-free tree

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DL Reasoning Optimised Implementations

• Naive implementation can lead to effective
  non-termination
• 10 GCIs 10 nodes ? 2100 different possible
  expansions
• Modern systems include MANY optimisations
• Optimised classification (compute partial
  ordering)
• Enhanced traversal (exploits information from
  previous tests)
• Use structural information to select
  classification order
• Optimised satisfiability/subsumption testing
• Normalisation and simplification of concepts
• Absorption (simplification) of axioms
• Dependency directed backtracking
• Caching of satisfiability results and (partial)
  models
• Heuristic ordering of propositional and modal
  expansion

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Research Challenges

• Increased expressive power
• Existing DL systems implement (at most) SHIQ
• OWL extends SHIQ with datatypes and nominals
  (SHOIN(Dn))
• Future (undecidable) extensions such as SWRL
• Scalability
• Very large ontologies
• Reasoning with (very large numbers of)
  individuals
• Other reasoning tasks (non-standard inferences)
• Querying
• Matching
• Least common subsumer
• ...
• Tools and Infrastructure
• Support for large scale ontological engineering
  and deployment

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Summary

• An Ontology is an engineering artifact consisting
  of
• A vocabulary of terms
• An explicit specification their intended meaning
• Ontologies are set to play a key role in many
  applications
• e-Science, Medicine, Databases, Semantic Web,
  etc.
• Reasoning is important because
• Understanding is closely related to reasoning
• Essential for design, maintenance and deployment
  of ontologies
• Reasoning support based on DL systems
• Sound and complete reasoning
• Highly optimised implementations
• Challenges remain
• Expressive power scalability new reasoning
  tasks tools and infrastructure

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Acknowledgements

• Thanks to the many people who inspired me and
  with whom I have had the privilege of
  collaborating, 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/wolter.pp
  t
• FaCT system (open source)
• http//www.cs.man.ac.uk/FaCT/
• OilEd (open source)
• http//oiled.man.ac.uk/
• 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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Select Bibliography

• Ian Horrocks, Peter F. Patel-Schneider, and Frank
  van Harmelen. From SHIQ and RDF to OWL The
  making of a web ontology language. Journal of Web
  Semantics, 2003.
• Franz Baader, Ian Horrocks, and Ulrike Sattler.
  Description logics as ontology languages for the
  semantic web. In Festschrift in honor of Jörg
  Siekmann, LNAI. Springer, 2003.
• I. Horrocks and U. Sattler. Ontology reasoning in
  the SHOQ(D) description logic. In Proc. of IJCAI
  2001.
• All available from http//www.cs.man.ac.uk/horroc
  ks/Publications/