reasoning with expressive description logics ian horrocks university of manchester manchester, uk...
TRANSCRIPT
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Reasoning with Expressive Description Logics
Ian Horrocks <[email protected]>
University of Manchester
Manchester, UK
Logical Foundations for the Semantic Web
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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
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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
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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
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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 (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)
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DL Architecture
Knowledge Base
Tbox (schema)
Abox (data)
Man ´ Human u Male
Happy-Father ´ Man u 9 has-child Female u …
John : Happy-Father
hJohn, Maryi : has-child
John: 6 1 has-child
Infe
ren
ce S
yste
m
Inte
rface
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Short History of Description LogicsPhase 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
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Latest DevelopmentsPhase 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
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Semantic Web:Killer App for DL Reasoning?
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• 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
History of 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 …”
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• 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
Scientific American, May 2001:
Beware of the
Hype!
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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?
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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
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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
, e.g., Barn Owl
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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
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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
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Ontology Languagesfor the
Semantic Web
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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
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RDF Syntax: Triples
_:xxx
Subject Property Object
ex:subjectex:property
ex:object
_:yyy
« plain litteral »
« lexical »^^datatype
Jean-François Baget
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RDF Syntax: Graphs
_:xxx
« Ian Horrocks »
ex:name
ex:Person
rdf:type
« University of Manchester »
ex:Organisation
ex:name
rdf:type
_:yyyex:member-of
Jean-François Baget
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RDFS• RDFS vocabulary adds constraints on models, e.g.:
– 8x,y,z type(x,y) and subClassOf(y,z) ) type(x,z)
ex:Personrdf:typeex:John
ex:Animalrdfs:subClassOf
ex:Person
ex:Animalrdf:type
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RDFS• RDFS allows arbitrary use of schema vocabulary
– Can be used/abused to say very strange things!
rdfs:subClassOfrdfs:subPropertyOf
rdf:type
ex:Personrdf:type
ex:Person
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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 IR£IR
• 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))
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Problems with RDFS• RDFS too weak to describe resources in sufficient detail
– No localised range and domain constraints
• Can’t say that the range of hasChild is person when applied to persons and elephant when applied to elephants
– No existence/cardinality constraints
• Can’t 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
• Can’t 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
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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 DAML+OIL– Development was carried out by “Joint EU/US Committee on Agent
Markup Languages”
– Extends (“DL subset” of) RDF
• DAML+OIL submitted to W3C as basis for standardisation– Web-Ontology (WebOnt) Working Group formed
– WebOnt group developed OWL language based on DAML+OIL
– OWL language now a W3C Proposed Recommendation
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OWL Language• Three species of OWL
– OWL full is union of OWL syntax and RDF
– OWL DL restricted to FOL fragment (¼ DAML+OIL)
– 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)
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OWL Class Constructors
• XMLS datatypes as well as classes in 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
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RDFS Syntax
<owl:Class> <owl:intersectionOf rdf:parseType=" collection"> <owl:Class rdf:about="#Person"/> <owl:Restriction> <owl:onProperty rdf:resource="#hasChild"/> <owl:toClass> <owl:unionOf rdf:parseType=" collection"> <owl:Class rdf:about="#Doctor"/> <owl:Restriction> <owl:onProperty rdf:resource="#hasChild"/> <owl:hasClass rdf:resource="#Doctor"/> </owl:Restriction> </owl:unionOf> </owl:toClass> </owl:Restriction> </owl:intersectionOf></owl:Class>
E.g., Person u 8hasChild.(Doctor t 9hasChild.Doctor):
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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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Reasoning with OWL
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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?
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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
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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
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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
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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 “don’t know” typically treated as “no”
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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
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E.g.: Reasoning Support for Ontology Design
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E.g.: Reasoning Support for Instance Retrieval
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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
– …
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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– Querying– Matching– Least common subsumer– ...
• Tools and Infrastructure– Support for large scale ontological engineering and deployment
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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
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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
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AcknowledgementsThanks to the many people who I have worked with, in particular:
– Dieter Fensel
– Frank van Harmelen
– Zhiming Pan
– Peter Patel-Schneider
– Alan Rector
– Uli Sattler
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Resources• Slides from this talk
– http://www.cs.man.ac.uk/~horrocks/Slides/ICIIP
• 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/~horrocks/Publications/