Lecture 16 Description Logics Topics Chunking Overview of MeaningReadings: Text 13.5 NLTK book 7.2...

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

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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

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Projects / presentationsProjects / presentations

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Meaning ExamplesMeaning Examples

Speech and Language Processing, Second EditionDaniel Jurafsky and James H. Martin

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First Order Predicate LogicFirst Order Predicate Logic

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Figure 17.1Figure 17.1

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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

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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)

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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

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DL System ArchitectureDL System Architecture

Knowledge Base

Tbox (schema)

Abox (data)

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

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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, …

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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

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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.::

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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

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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

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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

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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)

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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

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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:

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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

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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

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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

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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

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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))

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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):

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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)

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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

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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

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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

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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)

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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.

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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

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