Reasoning with Expressive Description Logics

Ian Horrocks <horrocks@cs.man.ac.uk>University of Manchester

Manchester, UK

Logical Foundations for the Semantic Web

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

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

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

Introduction to Description Logics

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)

DL Architecture

Knowledge BaseTbox (schema)

Abox (data)

Man ´ Human u MaleHappy-Father ´ Man u 9 has-child

Female u …

John : Happy-FatherhJohn, Maryi : has-child

John: 6 1 has-child

Infe

renc

e Sy

stem

Inte

rfac

e

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

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

Semantic Web:Killer App for DL Reasoning?

• 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 …”

• 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!

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?

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

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

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

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

Ontology Languagesfor the

Semantic Web

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

RDF Syntax: Triples

_:xxx

Subject Property Object

ex:subjectex:property

ex:object

_:yyy

« plain litteral »

« lexical »^^datatype

Jean-François Baget

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

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

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

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))

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

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

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)

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

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):

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)

Reasoning with OWL

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?

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

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

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

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”

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

E.g.: Reasoning Support for Ontology Design

E.g.: Reasoning Support for Instance Retrieval

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– …

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

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

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

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

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

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/