Transcript Ontologe Reasoning: the Why and the How

Ontology Reasoning:
the Why and the How
Ian Horrocks <[email protected]>
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 discipline—a 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
…
Suddenly
1
Surfeit
87
Teeth
113
…
Gangrene
1
Ulcer
2
Grief
1
Vomiting
7
Griping in the Guts
74
Winde
8
Worms
18
…
Plague
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3880
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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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
Structured Data Entry
File
Edit
Help
FRACTURE SURGERY
Reduction
Fixation
Open
Open
Closed
Femur
Femur
Tibia
Fibula
Ankle
More...
Humerus
Radius
Ulna
Wrist
More...
Left
Left
Right
Shaft
Neck
Gt Troch
More...
•Fixation of open fracture of neck of left femur
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Scientific American, May 2001:
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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 “don’t know” typically treated as “no”
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System Demonstration (OilEd)
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Ontology Reasoning:
How 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 DAML+OIL)
– 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):
<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>
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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.ppt
• 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/
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