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Source: Erica Melis
Educational TechnologiesEducational TechnologiesWS2006WS2006
Knowledge RepresentationKnowledge Representation
Deutsches Forschungszentrum für Künstliche IntelligenzDeutsches Forschungszentrum für Künstliche Intelligenz
2Source: Erica Melis Educational Technologies WS 2006/07
Approximate Plan of the Course Approximate Plan of the Course
18.10. Introduction25.10. XML- Knowledge Representation 8.11. Student Modelling15.11. Web technologies and security22.11. Tutorial Planning and instructional design29.11. Media Principles 6.12. Interactive exercises13.12. Authoring tools, CTAT20.12. Diagnosis: model tracing and domain reasoning 10.1. Diagnosis: constraint based17.1. Tutorial dialogues24.1. Action analysis and Machine Learning techniques31.1. Cognitive tools 7.2. Meta-cognitive support14.2. student projects
3Source: Erica Melis Educational Technologies WS 2006/07
Typical AI-representationsTypical AI-representations
Semantic networks with labelled links: member, isA,hasXXXML/metadata – annotated (varieties) objects and propertiesRDF: relations = labeled links www.dfki.de/~melis/ links# designatedPerson document defines labeled link…ontologiesRDF language refers to URIs (subject property object)rdf:type : specific instance of a category
FramesRDFS: isA link for class (with slots domain, range) and subclass
Logics, decision logics (formal language for subsumption and classification,satisfyability)
OWL, OWL-DL (RDFS+terms for describing properties symm, 1-1) + (class, property-value restrictions e.g. cardinality)Prolog reasoners
4Source: Erica Melis Educational Technologies WS 2006/07
Semantic Networks -- OntologiesSemantic Networks -- Ontologies
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Labelled link ….OWL descriptions…ontologiesLabelled link ….OWL descriptions…ontologies
http:…/melis/index.html http:../melis/pict1.jpg
http://www.dfki.de/melis/links#designatedPerson
:designatedPerson rdf:Property rdfs:domain: Person rdfs:range:Photograph:
<owl:Class rdf:about=“#Feline-Leukemia“> <rdfs:subClassOf rdf:resource=“NCI:Leukemia“/> <rdfs:Restriction> <owl:onProperty rdf:resource=“#NCI:Organism-affected“/> <owl:allValuesFrom rdf:resource=“CYC:cat“/> </rdfs:subClassOf></owl:Class>
6Source: Erica Melis Educational Technologies WS 2006/07
AI Knowledge Representation for ITSsAI Knowledge Representation for ITSs
Frames in Cognitive Tutors
(make-wme composed-cen-insc isa problem key-quantities (angle-KHP-measure arc-KP-measure angle-KQP-measure) key-reasons (angle-KHP-measure ...) questions (question1) given-relational-quantities (central-angle-KHP inscribed-angle-KQP) table composed-cen-insc-table)
Quantity WME ...
Relation WME...
angle-KHP-measure...unit..dimension..labels..
inscribed-angle...inputs (arc-KP-measure)output (angle-KQP-measure)
Problem WME:
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Knowledge Representation for Web-based ITSsKnowledge Representation for Web-based ITSs
Capture domain and educational knowledgeContent, instructionl knowledge, tutorial strategies
Reusability in different contexts
Semantic encoding for functionalitiesautomatic search in documents
automatic manipulation of documents
adaptive presentation of documents
=> automatic processing of documents
requirements
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ReusabilityReusability
Courses for BWL, Mathematics, Engineering
Courses for different learning contexts
Courses by several authors and various formats and languages
Previously: html
10Source: Erica Melis Educational Technologies WS 2006/07
Requirements for Maths Application: SemanticsRequirements for Maths Application: Semantics
Maple
Calculator
Mathematica
MuPadFormula/Expression
Search
Machine readable and interoperable
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Content Representation, GranularityContent Representation, Granularity
Content items• unique ID
Content items• unique ID
Concept Satellite
Definition Assertion
ProofAlgorithm
Axiom ExampleExercise
MotivationElaboration
Relations:• Mathematical dependency• Pedagogical prerequisite
Relations:• Pedagogical dependency
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Mathematical Element TypesMathematical Element Types
D
S
EX
P
T
S S
S
isA
D
D T
XE
Definition
E
Symbol
Example
Theorem
ProofExercise
X
forfor
forforfor
D D
for counter
P
for
S S
for depends on
depends on
Abstract Layer
Content Layer
Satellite Layer
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Standard Metadata and LanguagesStandard Metadata and Languages
Dublin Core (dc)
Learning Object Metadata (LOM)
IMS Global Learning Consortium
OpenMath / OMDoc
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Characterization of LO by MetadataCharacterization of LO by Metadata
DLearning contextschool, university, ..
Difficultyeasy, medium, difficult
Abstractnessabstract, neutral, concrete
Typical learning time
Fieldmathematics, biology, physics, ..
Representationspeech,images, numbers, …
Competencythink, argue, model solve, ..
Competency levelknowledge, multistep, complex
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Domain MetadataDomain Metadata
DType of item
definition, assertion, difficult
theorygroups, calculus, ..
Relationprerequisite, for, isA, …
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Educational MetadataEducational Metadata
DLearning contextschool, university, ..
Difficultyeasy, medium, difficult
Abstractnessabstract, neutral, concrete
Typical learning time
Fieldmathematics, biology, physics, ..
Representationaudio, symbolic, graphical, numeric, …
Competencythink, argue, model solve, ..
Competency levelknowledge, multistep, complex
18Source: Erica Melis Educational Technologies WS 2006/07
Position of the metadataPosition of the metadata
metadata
item
metadata
item
metadata
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Classification of MetadataClassification of Metadata
●Administrative● General
● Lifecycle
● Rights
●Mathematical● Relation
● Classification
●Application-dependent● Educational
● Publishing
● Formal-maths-calculi
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Administrative Metadata: GeneralAdministrative Metadata: General
●dc:title
●dc:description● dcq:abstract
●dc:creator, dc:contributor● omdoc:role (aut, edt, clb, trl, etc.)
● identifier
●dc:publisher
●dc:source
●dc:language (ISO 639:1988 + ISO 2166-1:1997)
●dc:identifier
21Source: Erica Melis Educational Technologies WS 2006/07
Administrative Metadata: LifecycleAdministrative Metadata: Lifecycle
●dc:date● omdoc:action (new, updated, etc.)
● omdoc:who
●lom:version● previous_version
●lom:status (draft, final, revised, unavaible)
22Source: Erica Melis Educational Technologies WS 2006/07
Example of simple metadata recordExample of simple metadata record
<dc:title> an example of metadata annotation</dc:title>
<dc:creator role=”aut“ identifier=”JD”>John Doe</dc:creator>
<dc:contributor role=”clb” identified=”MW”>
Mary Waters
</dc:contributor>
<dc:date omdoc:action=”new” omdoc:who=”JD”>
2003-03-20 / 23:59:59
</dc:date>
<dc:date omdoc:action=”updated” omdoc:who=”MW”>
2003-03-21 / 00:03:48
</dc:date>
23Source: Erica Melis Educational Technologies WS 2006/07
Administrative Metadata: TechnicalAdministrative Metadata: Technical
●dc:format (mime types)
●dc:type (text, dataset, image etc.)
●lom:size (bytes)
●lom:requirement ● lom:name (technology required)
● resource_of_technology
● lom:minimumversion
● lom:maximumversion
24Source: Erica Melis Educational Technologies WS 2006/07
Example of lifecycle+technical metadataExample of lifecycle+technical metadata
<dc:title> Example of a lifecycle metadata</dc:title>
...
<dc:type>dataset</dc:type>
<lom:size>251245230123213</lom:size>
<lom:requirement lom:name=”COQ” rdf:resource=”http://pauillac.inria.fr/coq/distrib-eng.html”>
<lom:minimumversion>7.2.0</lom:minimumversion>
<lom:maximumversion>7.3.1</lom:maximumversion>
</lom:requirement>
25Source: Erica Melis Educational Technologies WS 2006/07
Administrative Metadata: RightsAdministrative Metadata: Rights
●dc:rights● cc:permissions (reproduction, distribution, derivative works)
● cc:prohibitions (commercial_use)
● cc:requirements (notice, attribution, copyleft)
● copyright_holder
26Source: Erica Melis Educational Technologies WS 2006/07
MathematicalMathematical Metadata: Metadata:
●dc:subject (controlled vocabulary)● MathClassificationScheme (LSCH, MSC, DDC, CCS)
●dc:keyword (uncontrolled vocabulary)
●relation● kind (requires, for, etc.)
● omdoc:entailed-by
● omdoc:entails
● omdoc:equivalent
27Source: Erica Melis Educational Technologies WS 2006/07
Application-Dependent Metadata: EducationalApplication-Dependent Metadata: Educational
●dc:relation (prerequisite..)
●lom:difficulty (easy, medium, etc.)
●am:abstractness (concrete, neutral, abstract)
●lom:learning_context (higher_education, etc.)
●lom:field (mathematics, engineering, etc.)
●am:competence_level
●am:competency (model, compute, argue...)
28Source: Erica Melis Educational Technologies WS 2006/07
Markup-LanguagesMarkup-Languages
Presentation-oriented markup: markups are processed to create layout
e.g. LaTeX, HTML
Semantic/Structure-oriented markup: markups describe ‘semantics‘, ´logic structure‘ and ‘relations‘
of content
e.g. XML based languages OpenMath, OMDoc used in ActiveMath
29Source: Erica Melis Educational Technologies WS 2006/07
XMLXML
eXtensible Markup Language
Goal: machine-readable structured documents
Technically:XML defines grammar rules to interpret documents as trees
consisting of elementsBasic rules are shared by all XML dialectsFor concrete XML dialect: define further rules for specifying a
subset of trees as admisable (e.g., by DTD = Document Type Definition)
Platform independence
XML is standard for a family of languages of similar structure
30Source: Erica Melis Educational Technologies WS 2006/07
XMLXML
• XML defines tags and attributes
XML related to family of tools
More Modules:
• Xlink for extending XML by Hyperlinks • XPointer/XFragments for references in an XML-document• XSL für Style Sheets• DOM for standard functions for processing XML or HTML-files
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Ontologisches XMLOntologisches XML
32Source: Erica Melis Educational Technologies WS 2006/07
Example XML DocumentExample XML Document
<?xml version='1.0' encoding='UTF-8' standalone='no'?><!DOCTYPE family SYSTEM 'family.dtd'><family id="f1"> <member role="father" sex="male"> <name> John </name> <surname> Doe </surname> <date-of-birth> <day> 29 </day> <month> 02 </month> <year> 1978 </year> </date-of-birth> <character> mild </character> <hobby> chess </hobby> <hobby> collecting butterflies </hobby> <hobby> watching soap operas </hobby> </member> ...</family>
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Example DTD (family.dtd)Example DTD (family.dtd)
<!ELEMENT family (member)*>
<!ATTLIST family id ID #REQUIRED>
<!ELEMENT member (name,surname?,date-of-birth,character,hobby*)>
<!ATTLIST member role (father|mother|child|grandfather|grandmother|dog|cat) #REQUIRED sex (male|female) #REQUIRED>
<!ELEMENT name (#PCDATA)>
<!ELEMENT surname (#PCDATA)>
<!ELEMENT date-of-birth (day,month,year)>
<!ELEMENT character (#PCDATA)>
<!ELEMENT hobby (#PCDATA)>
<!ELEMENT day (#PCDATA)>
<!ELEMENT month (#PCDATA)>
<!ELEMENT year (#PCDATA)>
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Automatic ProcessingAutomatic Processing
XML document describes structure of contentAutomatic processing by XSL transformations
(XSL = eXtensible Stylesheet Language)
Technically: set of rules describing the transformation of XML tree parts into some output format
Applications:Presentation oriented transformations
e.g., XSL transformation producing HTML e.g., XSL producing LaTeX e.g., XSL producing natural language
Message oriented transformations for data exchange
Advantage: Separation of content (and its structure) and presentation format or data-exchange format
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Example of an XSL Stylesheet
<?xml version="1.0" encoding="iso-8859-1"?><xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" version="1.0"> <xsl:output method="html" /><xsl:template match="family"><html><body><h2> The <xsl:value-of select="member[@role='father']/surname"/> family </h2><xsl:apply-templates /></body></html></xsl:template><xsl:template match="member"><br /><table border="1">...</table>....</stylesheet>
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XSL producing HTMLXSL producing HTML
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XSL producing LaTeXXSL producing LaTeX
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XSL Producing Natural LanguageXSL Producing Natural Language
39Source: Erica Melis Educational Technologies WS 2006/07
MathML
presentation MathML
content MathML
OpenMath
OpenMath Content Dictionaries
OMDoc : the language for mathematical Documents
Semantic XML: examples
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Content MathML and OpenMath
<m:math> <m:apply> <m:times/> <m:ci>a</m:ci> <m:apply> <m:plus/> <m:ci>b</m:ci> <m:ci>c</m:ci> </m:apply> </m:apply></m:math>
<OMOBJ> <OMA> <OMS cd=“arith1“ name=“times“/> <OMV name=“a“/> <OMA> <OMS cd=“arith1“ name=“plus“/> <OMV name=“b“/> <OMV name=“c“/> </OMA> </OMA></OMOBJ>
a∙(b+c)
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OMDoc Language for Mathematics
items of knowledge have typesdefinition
assertion (theorem, lemma, proposition ...)
axiom
proof
example
exercise
items are annotated with metadata
formulas are machine understandable
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ActiveMath Knowledge RepresentationActiveMath Knowledge Representation
Using OMDoc for representing Domain Ontology
Extending OMDoc with educational metadata
Extending the microstructure of exercises
Adding new Elements to the ontology (misconceptions)
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Example OMDoc<definition id="def_diff" for="deriv_symbols/diff"> <metadata> <Title xml:lang="de">Definition der Ableitung bzw. des Differentialquotienten</Title> <Title xml:lang="en">Definition of the derivative, resp., differential quotient</Title> <Title xml:lang="es">Definición de la derivada, resp., cociente diferencial</Title> <Title xml:lang="zh"> 导数及微分的定义 </Title> <extradata>…</extradata> </metadata> <CMP xml:lang="de"> Eine <textref xref="functions_symbols/function">Funktion</textref> $f$ heißt <highlight type="important">differenzierbar an der Stelle $x_0$</highlight> … </CMP> <CMP xml:lang="en"> A <textref xref="functions_symbols/function">function</textref> $f$ is called <highlight type="important">differentiable at $x_0$</highlight> … </CMP> <CMP xml:lang="es"> Una <textref xref="functions_symbols/function">función</textref> $f$ se dice <highlight type="important">diferenciable en $x_0$</highlight> … </CMP> <CMP xml:lang="zh"> 一个 <textref xref="functions_symbols/function"> 函数 </textref> $f$ 被称作 <highlight type="important"> 在 $x_0$ 可微 </highlight> , 如果其 … </CMP> <CMP xml:lang="x-all"> $ap(diff(f),x_0)=lim(x_0,both_sides,lambda(x,(ap(f,x)-ap(f,x_0))/(x-x_0)))$. </CMP></definition>
44Source: Erica Melis Educational Technologies WS 2006/07
Example OMDoc MetadataExample OMDoc Metadata <metadata> <Title xml:lang="de">Definition der Ableitung bzw. des Differentialquotienten</Title> <Title xml:lang="en">Definition of the derivative, resp., differential quotient</Title> <Title xml:lang="es">Definición de la derivada, resp., cociente diferencial</Title> <Title xml:lang="zh"> 导数及微分的定义 </Title>
<extradata> <relation type="domain_prerequisite"> <ref xref="diffquot_symbols/diff_quot"/> <ref xref="maplimits_symbols/maplimit"/> </relation> <learningcontext value="secondary_education"/> <learningcontext value="higher_education"/> <learningcontext value="university_first_year"/> <field value="all"/> <typicallearningtime value="00:01:00"/> <representation value="verbal"/> <representation value="symbolic"/> <abstractness value="abstract"/> </extradata></metadata>
45Source: Erica Melis Educational Technologies WS 2006/07
OMDoc Knowledge RepresentationOMDoc Knowledge Representation<definition id="monoid/def_monoid" for="monoid"><metadata> <relation type= "domain_prerequisite"> <ref xref= "structures/structure" /> </relation> <Title xml:lang="en">Definition of a monoid</Title> </metadata><CMP xml:lang="en" format="omtext"> A monoid is a <ref xref="structures/def_structure"> structure </ref>
<OMOBJ> <OMA> <OMS cd="elementary" name="ordered-triple"/> <OMV name="M"/> <OMS cd="semigroups" name="times"/> <OMS cd="semigroups" name="unit"/></OMA></OMOBJ>in which<OMOBJ> <OMA> <OMS cd="elementary" name="ordered-pair"/> <OMV name="M"/> <OMS cd="semigroups" name="times"/></OMA> </OMOBJ> is a semi-groupwith <ref xref="semigroups/def_unit">e</ref>
<OMOBJ> <OMS cd="semigroups" name="unit"/> </OMOBJ>. </CMP><FMP><OMOBJ> ... </OMOBJ></FMP></definition>
46Source: Erica Melis Educational Technologies WS 2006/07
Generation of Presentation of MathematicsGeneration of Presentation of Mathematics
Mathematics on the Web is a problemOften only as images
No semantics
ActiveMath:HTML, MathML, (SVG)
Cross-browser: Internet Explorer, Mozilla
Usage of semantics to add invisible information
Authorable appearance
47Source: Erica Melis Educational Technologies WS 2006/07
Math: multiple Output Format - HMTL **Math: multiple Output Format - HMTL **
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Math: XHTML+MathML**Math: XHTML+MathML**
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Math: PDF **Math: PDF **
SVG…
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Maths. Semantics rendered **Maths. Semantics rendered **
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Interactive ExercisesInteractive Exercises
Transition
Condition
Diagnosis
Transition
Condition
Diagnosis
Interaction
Stimulus
Response
Metadata
Interaction
Stimulus
Response
Metadata
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Components of an exerciseComponents of an exercise
Interaction
Stimulus
Response
MetadataTask Definition
• selection• fill_in_blank
• mcq single answer• mcq multiple answer• marking• mapping• ordering• puzzle
•simple blank• blanks in a formula• literal blank• prompt• Item reference
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Fill-in-blank and feedbackFill-in-blank and feedback
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Selection interactivitySelection interactivity
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Selection by marking interactivitySelection by marking interactivity
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Usage of Knowledge RepresentationUsage of Knowledge Representation
Modularity, reusable in different contexts
Efficient Mutli-stage presentation process
Extensible maths symbol presentation
Mutliple output format
Support of multiple languages
Adaptive course generation
Semantic search
Semantic drag and drop
Interoperability of services
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Exercise ArchitectureExercise Architecture
ExerciseManager
Diagnoser
Maxima
Slopert
presentation
user
Feedback
Generator
Learner model
Knowledge Base
Tutorialstrategies
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