Reasoning with Expressive Description Logics

1
Reasoning with Expressive Description Logics
Logical Foundations for the Semantic Web

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

2

• Talk Outline

• Introduction to Description Logics
• The Semantic Web Killer App for (DL) Reasoning?
• Semantic Web Background
• Ontology Languages for the Semantic Web
• Reasoning with OWL
• OileEd Demo (if time)
• Description Logic Reasoning
• Research Challenges

3
Summary 1

• DLs are family of object oriented KR formalisms
  related to frames and Semantic networks
• Distinguished by formal semantics and inference
  services
• Semantic Web aims to make web resources
  accessible to automated processes
• Ontologies will play key role by providing
  vocabulary for semantic markup
• OWL is a DL based ontology language designed for
  the Web
• Exploits existing standards XML, RDF(S)
• Adds KR idioms from object oriented and frame
  systems
• W3C recommendation and already widely adopted in
  e-Science
• DL provides formal foundations and reasoning
  support

4
Summary 2

• 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
• Reasoning with full OWL language
• (Convincing) demonstration(s) of scalability
• New reasoning tasks
• Development of (more) high quality tools and
  infrastructure

5
Introduction to Description Logics
6
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 (relationships) and individuals
• Distinguished by
• Formal semantics (typically model theoretic)
• Decidable fragments of FOL
• Closely related to Propositional Modal Dynamic
  Logics
• Provision of inference services
• Sound and complete decision procedures for key
  problems
• Implemented systems (highly optimised)

7
DL Architecture
Knowledge Base
Tbox (schema)
Man Human u Male Happy-Father Man u 9
has-child Female u
Interface
Inference System
Abox (data)
John Happy-Father hJohn, Maryi
has-child John 6 1 has-child
8
Short History of Description Logics

• Phase 1
• Incomplete systems (Back, Classic, Loom, . . . )
• Based on structural algorithms
• Phase 2
• Development of tableau algorithms and complexity
  results
• Tableau-based systems for Pspace logics (e.g.,
  Kris, Crack)
• Investigation of optimisation techniques
• Phase 3
• Tableau algorithms for very expressive DLs
• Highly optimised tableau systems for ExpTime
  logics (e.g., FaCT, DLP, Racer)
• Relationship to modal logic and decidable
  fragments of FOL

9
Latest Developments

• Phase 4
• Mature implementations
• Mainstream applications and Tools
• Databases
• Consistency of conceptual schemata (EER, UML
  etc.)
• Schema integration
• Query subsumption (w.r.t. a conceptual schema)
• Ontologies and Semantic Web, Grid and e-Science
• Ontology engineering (design, maintenance,
  integration)
• Reasoning with ontology-based markup (meta-data)
• Service description and discovery
• Commercial implementations
• Cerebra system from Network Inference Ltd

10
Semantic WebKiller App for DL Reasoning?
11
History of the Semantic Web

• Web was invented by Tim Berners-Lee (amongst
  others), a physicist working at CERN
• His vision of the Web was much more ambitious
  than the reality of the existing (syntactic) Web
• This vision of the Web has become known as the
  Semantic Web

a plan for achieving a set of connected
applications for data on the Web in such a way as
to form a consistent logical web of data
an extension of the current web in which
information is given well-defined meaning, better
enabling computers and people to work in
cooperation
12
Scientific American, May 2001
Beware of the Hype!

• Realising the complete vision is too hard for
  now (probably)
• Can make a start by adding semantic annotation to
  web resources
• Already seeing exciting applications of
  technology in e-Science

13
Where we are Today the Syntactic Web

• A place where computers do the presentation
  (easy) and people do the linking and interpreting
  (hard)
• Why not get computers to do more of the hard
  work?

14
Hard Work using the Syntactic Web
Find images of Peter Patel-Schneider, Frank van
Harmelen and Alan Rector
Rev. Alan M. Gates, Associate Rector of the
Church of the Holy Spirit, Lake Forest, Illinois
15
Impossible (?) using the Syntactic Web

• Complex queries involving background knowledge
• Find information about animals that use sonar
  but are neither bats nor dolphins
• Locating information in data repositories
• Travel enquiries
• Prices of goods and services
• Results of human genome experiments
• Finding and using web services
• Visualise surface interactions between two
  proteins
• Delegating complex tasks to web agents
• Book me a holiday next weekend somewhere warm,
  not too far away, and where they speak French or
  English

16
What is the Problem?

• Consider a typical web page

• Markup consists of
• rendering information (e.g., font size and
  colour)
• Hyper-links to related content
• Semantic content is accessible to humans, but not
  (easily) to computers
• Requires (at least) NL understanding

17
Solution(?) Add Semantic Markup

• Annotations added to web pages (and other web
  accessible resources)
• Semantics given by ontologies
• Ontologies provide a vocabulary of terms used in
  annotations
• New terms can be formed by combining existing
  ones
• Meaning (semantics) of such terms is formally
  specified
• Need to agree on a standard web ontology language

18
Structure of an Ontology

• Ontologies typically have two distinct
  components
• Names for important concepts in the domain
• 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
• 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

19
A Semantic Web First Steps
Make web resources more accessible to automated
processes

• Extend existing rendering markup with semantic
  markup
• Metadata annotations that describe
  content/funtion of web accessible resources
• Use Ontologies to provide vocabulary for
  annotations
• Formal specification is accessible to machines
• A prerequisite is a standard web ontology
  language
• Need to agree common syntax before we can share
  semantics
• Syntactic web based on standards such as HTTP and
  HTML

20
Ontology Languagesfor theSemantic Web
21
RDF and RDFS

• RDF stands for Resource Description Framework
• It is a W3C candidate recommendation
  (http//www.w3.org/RDF)
• RDF is graphical formalism ( XML syntax
  semantics)
• for representing metadata
• for describing the semantics of information in a
  machine- accessible way
• RDFS extends RDF with schema vocabulary, e.g.
• Class, Property
• type, subClassOf, subPropertyOf
• range, domain

22
RDF Syntax Triples
_yyy
_xxx
 plain litteral 
 lexical datatype
Jean-François Baget
23
RDF Syntax Graphs
_xxx
Jean-François Baget
24
RDFS

• RDFS vocabulary adds constraints on models, e.g.
• 8x,y,z type(x,y) and subClassOf(y,z) ) type(x,z)

25
RDFS

• RDFS allows arbitrary use of schema vocabulary
• Can be used/abused to say very strange things!

26
RDF/RDFS Semantics

• RDF has Non-standard semantics given by RDF
  Model Theory (MT)
• IR, a non-empty set of resources
• IS, a mapping from V into IR
• IP, a distinguished subset of IR (the properties)
• IEXT, a mapping from IP into the powerset of
  IRIR
• Class interpretation ICEXT induced by
  IEXT(IS(type))
• ICEXT(C) x (x,C) 2 IEXT(IS(type))
• RDFS adds constraints on models
• (x,y), (y,z) µ IEXT(IS(subClassOf)) ) (x,z) 2
  IEXT(IS(subClassOf))

27
Problems with RDFS

• RDFS too weak to describe resources in sufficient
  detail
• No localised range and domain constraints
• Cant say that the range of hasChild is person
  when applied to persons and elephant when applied
  to elephants
• No existence/cardinality constraints
• Cant say that all instances of person have a
  mother that is also a person, or that persons
  have exactly 2 parents
• No transitive, inverse or symmetrical properties
• Cant say that isPartOf is a transitive property,
  that hasPart is the inverse of isPartOf or that
  touches is symmetrical
• Difficult to provide reasoning support
• No native reasoners for non-standard semantics
• May be possible to reason via FO axiomatisation

28
From RDF to OWL

• Two languages developed by extending (part of)
  RDF
• OIL developed by group of (largely) European
  researchers (several from EU OntoKnowledge
  project)
• DAML-ONT developed by group of (largely) US
  researchers (in DARPA DAML programme)
• Efforts merged to produce DAMLOIL
• Development was carried out by Joint EU/US
  Committee on Agent Markup Languages
• Extends (DL subset of) RDF
• DAMLOIL submitted to W3C as basis for
  standardisation
• Web-Ontology (WebOnt) Working Group formed
• WebOnt group developed OWL language based on
  DAMLOIL
• OWL language now a W3C Proposed Recommendation

29
OWL Language

• 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
• Semantic layering
• OWL DL ¼ OWL full within DL fragment
• 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)

30
OWL Class Constructors

• XMLS datatypes as well as classes in 8 9 8P.C and
  9P.C
• E.g., 9hasAge.nonNegativeInteger (see work by
  Zhiming Pan)
• Arbitrarily complex nesting of constructors
• E.g., Person u 8hasChild.Doctor t 9hasChild.Doctor

31
RDFS Syntax

• 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

E.g., Person u 8hasChild.(Doctor t
9hasChild.Doctor)
32
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)

33
Reasoning with OWL
34
OWL and Description Logic

• OWL DL corresponds to SHOIN(Dn) Description Logic
• Provides well defined semantics
• Formal properties well understood (complexity,
  decidability)
• Facilitates provision of reasoning services
  (using DL systems)
• Why do we want/need reasoning services for the
• Semantic Web?

35
Philosophical Reasons

• Semantic Web aims at machine understanding
• Understanding closely related to reasoning
• Recognising semantic similarity in spite of
  syntactic differences
• Drawing conclusions that are not explicitly stated

36
Practical Reasons

• Given key role of ontologies in e-Science and
  Semantic Web, 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
• Store (large numbers) of instances of ontology
  classes, e.g.
• Annotations from web pages (or gene product data)
• Answer queries over ontology classes and
  instances, e.g.
• Find more general/specific classes
• Retrieve annotations/pages matching a given
  description
• Integrate and align multiple ontologies

37
Why Decidable Reasoning?

• OWL constructors/axioms 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
• Facilitates provision of reasoning services
• Practical algorithms for sound and complete
  reasoning
• Several implemented systems
• Evidence of empirical tractability

38
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

39
Basic Inference Tasks

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

40
E.g. Reasoning Support for Ontology Design
41
E.g. Reasoning Support for Instance Retrieval
42
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)
• Enhanced traversal (exploits information from
  previous tests)
• Use structural information to select
  classification order
• Optimised subsumption testing (search for models)
• 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

43
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
• Querying
• Matching
• Least common subsumer
• ...
• Tools and Infrastructure
• Support for large scale ontological engineering
  and deployment

44
Summary 1

• DLs are family of object oriented KR formalisms
  related to frames and Semantic networks
• Distinguished by formal semantics and inference
  services
• Semantic Web aims to make web resources
  accessible to automated processes
• Ontologies will play key role by providing
  vocabulary for semantic markup
• OWL is a DL based ontology language designed for
  the Web
• Exploits existing standards XML, RDF(S)
• Adds KR idioms from object oriented and frame
  systems
• W3C recommendation and already widely adopted in
  e-Science
• DL provides formal foundations and reasoning
  support

45
Summary 2

• 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
• Reasoning with full OWL language
• (Convincing) demonstration(s) of scalability
• New reasoning tasks
• Development of (more) high quality tools and
  infrastructure

46
Acknowledgements

• Thanks to the many people who I have worked
  with, in particular
• Dieter Fensel
• Frank van Harmelen
• Peter Patel-Schneider
• Alan Rector
• Uli Sattler

47
Resources

• Slides from this talk
• http//www.cs.man.ac.uk/horrocks/Slides/Sussex
• 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

48
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/