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Lecture 16Description Logics
Lecture 16Description Logics
Topics Topics Chunking Overview of Meaning
Readings:Readings: Text 13.5
NLTK book 7.2
March 20, 2013
CSCE 771 Natural Language Processing
– 2 – CSCE 771 Spring 2013
OverviewOverviewLast Time (Programming)Last Time (Programming)
Probabilistic parsing Features and Unification Complexity of Language Meaning representations Projects???
TodayToday Chunking Meaning representations Description Logics Projects???
Readings: Readings: Chapter 17.1 771 Website: Resources
Next Time: SemanticsNext Time: Semantics
– 3 – CSCE 771 Spring 2013
Projects / presentationsProjects / presentations
– 4 – CSCE 771 Spring 2013
Meaning ExamplesMeaning Examples
Copyright ©2009 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
Speech and Language Processing, Second EditionDaniel Jurafsky and James H. Martin
– 5 – CSCE 771 Spring 2013
First Order Predicate LogicFirst Order Predicate Logic
Copyright ©2009 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
Speech and Language Processing, Second EditionDaniel Jurafsky and James H. Martin
– 6 – CSCE 771 Spring 2013
Figure 17.1Figure 17.1
Copyright ©2009 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
Speech and Language Processing, Second EditionDaniel Jurafsky and James H. Martin
– 7 – CSCE 771 Spring 2013
Variables and QuantificationVariables and Quantification
http://en.wikipedia.org/wiki/First-order_logic
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Lambda NotationLambda Notation
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Semantics of First Order LogicSemantics of First Order Logic
• Constant symbolsConstant symbols• domain D
• Predicate symbolsPredicate symbols
• Function symbolsFunction symbols
• TermsTerms• variable is a term• a function applied to terms is a term (no predicates)
• Formulas well-formed formulasFormulas well-formed formulas• predicates, equality, negations, AND, OR, , quantifiers
• Free and bound variablesFree and bound variables
• Interpretation: mapping symbols to real worldInterpretation: mapping symbols to real world
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Forward Chaining -Backward ChainingForward Chaining -Backward Chaining
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ResolutionResolution
C1: A OR BC1: A OR B
C2: C OR not BC2: C OR not B
A or C A or C
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Temporal Logic – Representing timeTemporal Logic – Representing time
http://en.wikipedia.org/wiki/Temporal_logic
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Representing Time/Tense fig 17.5Representing Time/Tense fig 17.5Reichenbaschs’ approachReichenbaschs’ approach
• E – denotes time of the eventE – denotes time of the event
• R denotes reference timeR denotes reference time
• U denotes utterance timeU denotes utterance time
Copyright ©2009 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
Speech and Language Processing, Second EditionDaniel Jurafsky and James H. Martin
– 14 – CSCE 771 Spring 2013
Semantic NetworksSemantic Networks
• Collins and QuillianCollins and Quillian
• Conceptual Graphs – Conceptual Graphs – SowaSowa
http://en.wikipedia.org/wiki/Semantic_network
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Conceptual GraphsConceptual Graphs
http://www.jfsowa.com/http://www.jfsowa.com/
http://www.jfsowa.com/
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KL-ONEKL-ONE
KL-ONE - a frame based KL-ONE - a frame based knowledge representation systemsystem
Frame-based = slot and fillerFrame-based = slot and filler
““The system is an attempt to overcome semantic The system is an attempt to overcome semantic indistinctness in semantic network representations indistinctness in semantic network representations and to explicitly represent conceptual information as and to explicitly represent conceptual information as a structured inheritance network.”a structured inheritance network.”
http://en.wikipedia.org/wiki/KL-ONE
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DAML + OILDAML + OIL
DAML - DAML - The DARPA Agent Markup Language The DARPA Agent Markup Language
DAML+OIL is a successor language to DAML+OIL is a successor language to DAML and and OIL that combines features of both. that combines features of both.
In turn, it was superseded by In turn, it was superseded by Web Ontology Language (OWL).(OWL).
OIL stands for Ontology Inference Layer or Ontology OIL stands for Ontology Inference Layer or Ontology Interchange Language.Interchange Language.
http://www.daml.org/http://en.wikipedia.org/wiki/DAML%2BOIL
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Description LogicDescription Logic
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Ontology fragmentOntology fragment
..
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Ontology refinementOntology refinement
..
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Ontological reasoningOntological reasoning
Reasoning over ontologiesReasoning over ontologies
Challenges for ontology LanguagesChallenges for ontology Languages
• ExpressivityExpressivity
• Computational ComplexityComputational Complexity
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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What Are Description Logics?What Are Description Logics?
A family of logic based Knowledge Representation formalismsA family of logic based Knowledge Representation formalisms Descendants of semantic networks and KL-ONE Describe domain in terms of concepts (classes), roles
(properties, relationships) and individuals
Distinguished by:Distinguished by: Formal semantics (typically model theoretic)
Decidable fragments of FOL (often contained in C2) Closely related to Propositional Modal & Dynamic Logics Closely related to Guarded Fragment
Provision of inference services Decision procedures for key problems (satisfiability, subsumption,
etc) Implemented systems (highly optimised)
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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What Are Description Logics?What Are Description Logics?
A family of logic based Knowledge Representation formalismsA family of logic based Knowledge Representation formalisms Descendants of semantic networks and KL-ONE Describe domain in terms of concepts (classes), roles
(properties, relationships) and individuals
Distinguished by:Distinguished by: Formal semantics (typically model theoretic)
Decidable fragments of FOL (often contained in C2) Closely related to Propositional Modal & Dynamic Logics Closely related to Guarded Fragment
Provision of inference services Decision procedures for key problems (satisfiability, subsumption,
etc) Implemented systems (highly optimised)
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
– 24 – CSCE 771 Spring 2013
What Are Description Logics?What Are Description Logics?
A family of logic based Knowledge Representation formalismsA family of logic based Knowledge Representation formalisms Descendants of semantic networks and KL-ONE Describe domain in terms of concepts (classes), roles
(properties, relationships) and individuals
Distinguished by:Distinguished by: Formal semantics (typically model theoretic)
Decidable fragments of FOL (often contained in C2) Closely related to Propositional Modal & Dynamic Logics Closely related to Guarded Fragment
Provision of inference services Decision procedures for key problems (satisfiability, subsumption,
etc) Implemented systems (highly optimised)
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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DL BasicsDL Basics
ConceptConcept names are equivalent to unary predicates names are equivalent to unary predicates In general, concepts equiv to formulae with one free variable
RoleRole names are equivalent to binary predicates names are equivalent to binary predicates In general, roles equiv to formulae with two free variables
IndividualIndividual names are equivalent to constants names are equivalent to constants
OperatorsOperators restricted so that: restricted so that: Language is decidable and, if possible, of low complexity No need for explicit use of variables
Restricted form of 9 and 8 (direct correspondence with ◊ and [])
Features such as counting can be succinctly expressed
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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DL System ArchitectureDL System Architecture
Knowledge Base
Tbox (schema)
Abox (data)
Infe
ren
ce S
yste
m
Inte
rfaceMan ´ Human u Male
Happy-Father ´ Man u 9 has-child Female u …
John : Happy-Father
hJohn, Maryi : has-child
John: 6 1 has-child
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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The DL FamilyThe DL Family
Given DL defined by set of Given DL defined by set of concept and role forming operatorsconcept and role forming operators
Smallest propositionally closed DL is Smallest propositionally closed DL is ALCALC (equiv modal K (equiv modal K(m)(m))) Concepts constructed using u, t, :, 9 and 8
SS often used for often used for ALCALC with transitive roles ( with transitive roles (RR++))
Additional lettersAdditional letters indicate other extension, e.g.: indicate other extension, e.g.: H for role inclusion axioms (role hierarchy) O for nominals (singleton classes, written {x}) I for inverse roles N for number restrictions (of form 6nR, >nR) Q for qualified number restrictions (of form 6nR.C, >nR.C)
E.g., E.g., ALC ALC + + RR++ + role hierarchy + inverse roles + QNR = + role hierarchy + inverse roles + QNR = SHIQSHIQ
Have been extended in many directionsHave been extended in many directions Concrete domains, fixpoints, epistemic, n-ary, fuzzy, …
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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DL SemanticsDL Semantics
Semantics defined by Semantics defined by interpretationsinterpretations
An interpretation An interpretation I I = (= (II, , ¢¢II), ), wherewhere I is the domain (a non-empty set)
¢I is an interpretation function that maps:Concept (class) name A ! subset AI of I
Role (property) name R ! binary relation RI over I
Individual name i ! iI element of I
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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DL Semantics (cont.)DL Semantics (cont.)
Interpretation function Interpretation function ¢¢II extends to extends to concept (and role)concept (and role) expressionsexpressions in the obvious way, e.g.in the obvious way, e.g.::
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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DL Knowledge BaseDL Knowledge Base
A DL A DL Knowledge baseKnowledge base KK is a pair is a pair hhT T ,,AAii where where T is a set of “terminological” axioms (the Tbox) A is a set of “assertional” axioms (the Abox)
Tbox axiomsTbox axioms are of the form: are of the form:C v D, C ´ D, R v S, R ´ S and R+ v Rwhere C, D concepts, R, S roles, and R+ set of transitive roles
Abox axiomsAbox axioms are of the form: are of the form:x:D, hx,yi:Rwhere x,y are individual names, D a concept and R a role
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Knowledge Base SemanticsKnowledge Base Semantics
An An interpretationinterpretation II satisfies (models) a Tbox axiom satisfies (models) a Tbox axiom AA ( (II ²² AA):):I ² C v D iff CI µ DI I ² C ´ D iff CI = DI
I ² R v S iff RI µ SI I ² R ´ S iff RI = SI
I ² R+ v R iff (RI)+ µ RI
II satisfiessatisfies a Tboxa Tbox TT ( (II ²² T T ) iff ) iff II satisfies every axiom satisfies every axiom AA in in TT
An An interpretationinterpretation II satisfies (models) an Abox axiom satisfies (models) an Abox axiom AA ( (II ²² AA):):I ² x:D iff xI 2 DI I ² hx,yi:R iff (xI,yI) 2 RI
II satisfies an Aboxsatisfies an Abox AA ( (II ²² AA) iff ) iff II satisfies every axiom satisfies every axiom AA in in AA
II satisfies an KBsatisfies an KB KK ( (II ²² KK) iff ) iff II satisfies both satisfies both T T and and AA
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Short History of Description LogicsShort History of Description Logics
Phase 1:Phase 1: Incomplete systems (Back, Classic, Loom, . . . ) Based on structural algorithms
Phase 2: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: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
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Recent DevelopmentsRecent Developments
Phase 4:Phase 4: Mainstream applications and tools
Databases» Consistency of conceptual schemata (EER, UML etc.)» Schema integration» Query subsumption (w.r.t. a conceptual schema)
Ontologies, e-Science and Semantic Web/Grid» Ontology engineering (schema design, maintenance, integration)» Reasoning with ontology-based annotations (data)
Mature implementations Research implementations
» FaCT, FaCT++, Racer, Pellet, … Commercial implementations
» Cerebra system from Network Inference (and now Racer)
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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a philosophical discipline—a branch of philosophy that deals with the nature and the organisation of reality
Science of Being (Aristotle, Metaphysics, IV, 1)Science of Being (Aristotle, Metaphysics, IV, 1)
Tries to answer the questions:Tries to answer the questions: What characterizes being? Eventually, what is being?
How should things be classified?How should things be classified?
Ontology: Origins and HistoryOntology: Origins and History
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Classification: An Old ProblemClassification: An Old Problem
AgedAged 54 54
ApoplecticApoplectic 1 1
……..
Fall down stairsFall down stairs 1 1
GangreneGangrene 1 1
GriefGrief 1 1
Griping in the Guts 74Griping in the Guts 74
……
PlaguePlague 3880 3880
……
SuddenlySuddenly 11
SurfeitSurfeit 87 87
TeethTeeth 113 113
……
UlcerUlcer 22
VomitingVomiting 77
WindeWinde 88
WormsWorms 18 18
Extract from Bills of Mortality, published weekly from 1664-1830s
The Diseases and Casualties this Week:
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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An ontology is an engineering artefact consisting of: An ontology is an engineering artefact 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:Ideally, an ontology should: Capture a shared understanding of a domain of interest Provide a formal and machine manipulable model of the
domain
Ontology in Computer ScienceOntology in Computer Science
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Example OntologyExample Ontology
Vocabulary and meaning (“definitions”)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 Background knowledge/constraints on the domain (“general axioms”)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
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Where are ontologies used?Where are ontologies used?
e-Sciencee-Science, e.g., Bioinformatics, e.g., Bioinformatics The Gene Ontology The Protein Ontology (MGED) “in silico” investigations relating theory and data
MedicineMedicine Terminologies
DatabasesDatabases Integration Query answering
User interfacesUser interfaces
LinguisticsLinguistics
The The Semantic WebSemantic Web
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Why Ontology Reasoning?Why Ontology Reasoning?
Given key role of ontologies in many applications, it is essential Given key role of ontologies in many applications, it is essential to provide to provide toolstools and and servicesservices to help users: to help users: Design and maintain high quality ontologies, e.g.:
Meaningful — all named classes can have instancesCorrect — captured intuitions of domain expertsMinimally redundant — no unintended synonymsRichly axiomatised — (sufficiently) detailed descriptions
Answer queries over ontology classes and instances, e.g.:
Find more general/specific classesRetrieve individuals/tuples matching a given query
Integrate and align multiple ontologies
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Why Decidable Reasoning?Why Decidable Reasoning?
OWL is an W3C standard DL based ontology languageOWL is an W3C standard DL based ontology language OWL constructors/axioms restricted so reasoning is decidable
Consistent with Semantic Web's Consistent with Semantic Web's layered architecturelayered 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 “W3C requirement for “implementation experienceimplementation experience”” “Practical” decision procedures Several implemented systems Evidence of empirical tractability
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Why Correct Reasoning?Why Correct Reasoning?
Need to have high level of Need to have high level of confidenceconfidence in reasoner in reasoner Most interesting/useful inferences are those that were
unexpected
Likely to be ignored/dismissed if reasoner known to be unreliable
Many realistic web applications will be Many realistic web applications will be agent agent ↔ ↔ agentagent No human intervention to spot glitches in reasoning
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Use a (Description) LogicUse a (Description) Logic
OWL DL based on OWL DL based on SHIQSHIQ Description LogicDescription Logic In fact it is equivalent to SHOIN(Dn) DL
OWL DL Benefits from many years of DL researchOWL 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 (!)In fact there are three “species” of OWL (!) OWL full is union of OWL syntax and RDF OWL DL restricted to First Order fragment (¼ DAML+OIL) OWL Lite is “simpler” subset of OWL DL (equiv to SHIF(Dn))
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Class/Concept ConstructorsClass/Concept Constructors
CC is a concept (class); is a concept (class); PP is a role (property); is a role (property); xx is an individual name is an individual name
XMLS XMLS datatypesdatatypes as well as classes in as well as classes in 88P.CP.C and and 99P.CP.C Restricted form of DL concrete domains
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RDFS SyntaxRDFS Syntax
<owl:Class><owl:Class> <owl:intersectionOf rdf:parseType=" collection"><owl:intersectionOf rdf:parseType=" collection"> <owl:Class rdf:about="#Person"/><owl:Class rdf:about="#Person"/> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasChild"/><owl:onProperty rdf:resource="#hasChild"/> <owl:toClass><owl:toClass> <owl:unionOf rdf:parseType=" collection"><owl:unionOf rdf:parseType=" collection"> <owl:Class rdf:about="#Doctor"/><owl:Class rdf:about="#Doctor"/> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasChild"/><owl:onProperty rdf:resource="#hasChild"/> <owl:hasClass rdf:resource="#Doctor"/><owl:hasClass rdf:resource="#Doctor"/> </owl:Restriction></owl:Restriction> </owl:unionOf></owl:unionOf> </owl:toClass></owl:toClass> </owl:Restriction></owl:Restriction> </owl:intersectionOf></owl:intersectionOf></owl:Class></owl:Class>
E.g., Person u 8hasChild.(Doctor t 9hasChild.Doctor):
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Ontologies / Knowledge BasesOntologies / Knowledge Bases
OWL ontologyOWL ontology equivalent to a DL Knowledge Base equivalent to a DL Knowledge Base
OWL ontology consists of a set of OWL ontology consists of a set of axioms and factsaxioms and facts Note: an ontology is usually thought of as containing only
Tbox axioms (schema)---OWL is non-standard in this respect
Recall that a DL KB Recall that a DL KB KK is a pair is a pair hhT T ,,AAii where where T is a set of “terminological” axioms (the Tbox) A is a set of “assertional” axioms (the Abox)
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Ontology/Tbox AxiomsOntology/Tbox Axioms
Obvious Obvious FO/Modal Logic equivalencesFO/Modal Logic equivalences E.g., DL: C v D FOL: x.C(x) !D(x) ML: C!D
Often distinguish two kinds of Tbox axiomsOften distinguish two kinds of Tbox axioms “Definitions” C v D or C ´ D where C is a concept name General Concept Inclusion axioms (GCIs) where C may be
complex
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Ontology Facts / Abox AxiomsOntology Facts / Abox Axioms
Note: using Note: using nominalsnominals (e.g., in (e.g., in SHOINSHOIN), can reduce ), can reduce Abox axioms to concept inclusion axiomsAbox axioms to concept inclusion axioms equivalent to equivalent to
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Recent DevelopmentsRecent Developments
Algorithms for NExpTime logics such as SHOIQAlgorithms for NExpTime logics such as SHOIQ
Increased expressive power (roles, keys, etc.)Increased expressive power (roles, keys, etc.)
Graph based algorithms for Polynomial logicsGraph based algorithms for Polynomial logics
Automata based algorithmsAutomata based algorithms
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Current ResearchCurrent Research
ExtendingExtending Description Logics Description Logics Complex roles, finite domains, concrete domains, keys,
e-connections, … Future OWL extensions (e.g., with “rules”)
IntegratingIntegrating with other logics/systems with other logics/systems E.g., Answer Set Programming
Alternative Alternative reasoning techniquesreasoning techniques Automata based algorithms Translation into datalog
Graph based algorithms (for sub ALC languages)
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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Current ResearchCurrent Research
ImprovingImproving Scalability Scalability Very large ontologies Very large numbers of individuals
Other reasoning tasks (Other reasoning tasks (non-standard inferencesnon-standard inferences)) Matching, LCS, explanation, querying, …
Implementation Implementation of tools and Infrastructureof tools and Infrastructure More expressive languages (such as SHOIN) New algorithmic techniques Tools to support for large scale ontological engineering
Editing, visualisation, etc.
http://www.cs.man.ac.uk/~horrocks/Slides/lpar04.ppt
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SummarySummary
DLs are a family of DLs are a family of logic based Knowledge logic based Knowledge Representation formalismsRepresentation formalisms Describe domain in terms of concepts, roles and
individuals
An An OntologyOntology is an is an engineering artefact consisting of: engineering artefact consisting of: A vocabulary of terms An explicit specification their intended meaning
Ontologies play a Ontologies play a key rolekey role in many applications in many applications e-Science, Medicine, Databases, Semantic Web, etc.
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SummarySummary
Reasoning is importantReasoning is important Essential for design, maintenance and deployment of
ontologies
Reasoning supportReasoning support based on DL systems based on DL systems Tableaux decision procedures Highly optimised implementations
Many exciting challenges remainMany exciting challenges remain