enabling collaboration on semiformal mathematical knowledge by semantic web integration

Overview Service Integration Knowledge Representation Conclusion & Future

Enabling Collaborationon Semiformal Mathematical Knowledge

by Semantic Web Integration

Christoph Lange

Jacobs University, Bremen, GermanyKWARC – Knowledge Adaptation and Reasoning for Content

2011-03-11

Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 1

http://kwarc.info

http://www.jacobs-university.de


http://kwarc.info


Why Mathematics?

Mathematicsubiquitous foundation of science, technology, and engineeringthese have in common:

rigorous style of argumentationsymbolic formula languagesimilar process of understanding results

Mathematical Knowledge

complex structures. . . that have been well studied and understood


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Semiformal Mathematical Knowledge

Informal

x4−4x3+2x2+4x+4 = (x2−√

2±√

4 + 2√7)x+(1±

√4 + 2

√7+

√7)),

(1)whereabove thetwo factorscomefrom takingthe+ signeachtime,or the−

signeachtime. Note factoringa quarticinto two realquadraticsis differentthantrying to find four complexroots.Definition: A function f is analytic on an opensubsetR ⊂ C if f is complexdifferentiableeverywhereonR; f is entire if it is analyticonall of C.

2 Proof of the FundamentalTheoremvia Liouville

Theorem 2.1 (Liouville). If f(z) is analyticandboundedin thecomplex plane,thenf(z) is constant.

Wenow prove

Theorem 2.2 (Fundamental Theorem of Algebra). Let p(z) be a polynomialwith complex coefficientsof degreen. Thenp(z) hasn roots.

Proof. It is sufficient to show any p(z) hasoneroot, for by division we canthenwrite p(z) = (z − z0)g(z), with g of lowerdegree.

Notethatif

p(z) = anzn + an−1z

n−1 + · · ·+ a0, (2)

thenas|z| → ∞, |p(z)| → ∞. This followsas

p(z) = zn ·∣∣∣an +

an−1

z+ · · ·+ a0

zn

∣∣∣ . (3)

Assumep(z) is non-zeroeverywhere.Then 1p(z)

is boundedwhen |z| ≥ R.

Also, p(z) 6= 0, so 1p(z)

is boundedfor |z| ≤ R by continuity. Thus, 1p(z)

isa bounded,entire function, which must be constant. Thus, p(z) is constant,acontradictionwhich impliesp(z) musthave azero(ourassumption).

[Lev]

2

Formalized = Computerized

Semiformal – a pragmatic and practical compromiseanything informal that is intended to or could in principle beformalizedcombinations of informal and formal for both human andmachine audience


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Collaboration in Mathematics

History of collaboration

in the small: Hardy/Littlewoodin the large: hundreds ofmathematicians classifying the finitesimple groups“industrialization” of research

Utilizing the Social Web

research blogs: Baez, Gowers, TaoPolymath: collaborative proofs

Collaboration = creation,formalization, organization,understanding, reuse, application Polymath wiki/blog: P ≠ NP proof

[Pol]Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 4

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http://michaelnielsen.org/polymath1/index.php?title=Deolalikar_P_vs_NP_paper


An Integrated View on a Collaboration Workflow

The author(s):

0 original idea (in one’smind)

1 formalize intostructured document

2 search existingknowledge to buildon

3 validate formalstructure

4 present in acomprehensible way

5 submit for review

The reader(s):

“What does thatmean?”: missingbackground,used to differentnotation

“How does thatwork?”

“What is that goodfor?”

look up backgroundinformation in citedpublications

The reviewer(s):

1 read paper (←Ð)

2 verify claims

3 point out problemswith the paper andits formal concepts


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Looking up Background Knowledge

“What does that mean?”


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Adapting the Presentation to FamiliarTerminology

“What does that mean?” – here: unfamiliar unit system (imperial vs.metric)


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Looking up Related Information“What can I reuse—what is that good for —where/how is it applied?”

As of September 2010

MusicBrainz

(zitgist)

P20

YAGO

World Fact-book (FUB)

WordNet (W3C)

WordNet(VUA)

VIVO UFVIVO

Indiana

VIVO Cornell

VIAF

URIBurner

Sussex Reading

Lists

Plymouth Reading

Lists

UMBEL

UK Post-codes

legislation.gov.uk

Uberblic

UB Mann-heim

TWC LOGD

Twarql

transportdata.gov

.uk

totl.net

Tele-graphis

TCMGeneDIT

TaxonConcept

The Open Library (Talis)

t4gm

Surge Radio

STW

RAMEAU SH

statisticsdata.gov

.uk

St. Andrews Resource

Lists

ECS South-ampton EPrints

Semantic CrunchBase

semanticweb.org

SemanticXBRL

SWDog Food

rdfabout US SEC

Wiki

UN/LOCODE

Ulm

ECS (RKB

Explorer)

Roma

RISKS

RESEX

RAE2001

Pisa

OS

OAI

NSF

New-castle

LAAS

KISTIJISC

IRIT

IEEE

IBM

Eurécom

ERA

ePrints

dotAC

DEPLOY

DBLP (RKB

Explorer)

Course-ware

CORDIS

CiteSeer

Budapest

ACM

riese

Revyu

researchdata.gov

.uk

referencedata.gov

.uk

Recht-spraak.

nl

RDFohloh

Last.FM (rdfize)

RDF Book

Mashup

PSH

ProductDB

PBAC

Poké-pédia

Ord-nance Survey

Openly Local

The Open Library

OpenCyc

OpenCalais

OpenEI

New York

Times

NTU Resource

Lists

NDL subjects

MARC Codes List

Man-chesterReading

Lists

Lotico

The London Gazette

LOIUS

lobidResources

lobidOrgani-sations

LinkedMDB

LinkedLCCN

LinkedGeoData

LinkedCT

Linked Open

Numbers

lingvoj

LIBRIS

Lexvo

LCSH

DBLP (L3S)

Linked Sensor Data (Kno.e.sis)

Good-win

Family

Jamendo

iServe

NSZL Catalog

GovTrack

GESIS

GeoSpecies

GeoNames

GeoLinkedData(es)

GTAA

STITCHSIDER

Project Guten-berg (FUB)

MediCare

Euro-stat

(FUB)

DrugBank

Disea-some

DBLP (FU

Berlin)

DailyMed

Freebase

flickr wrappr

Fishes of Texas

FanHubz

Event-Media

EUTC Produc-

tions

Eurostat

EUNIS

ESD stan-dards

Popula-tion (En-AKTing)

NHS (EnAKTing)

Mortality (En-

AKTing)Energy

(En-AKTing)

CO2(En-

AKTing)

educationdata.gov

.uk

ECS South-ampton

Gem. Norm-datei

datadcs

MySpace(DBTune)

MusicBrainz

(DBTune)

Magna-tune

John Peel(DB

Tune)

classical(DB

Tune)

Audio-scrobbler (DBTune)

Last.fmArtists

(DBTune)

DBTropes

dbpedia lite

DBpedia

Pokedex

Airports

NASA (Data Incu-bator)

MusicBrainz(Data

Incubator)

Moseley Folk

Discogs(Data In-cubator)

Climbing

Linked Data for Intervals

Cornetto

Chronic-ling

America

Chem2Bio2RDF

biz.data.

gov.uk

UniSTS

UniRef

UniPath-way

UniParc

Taxo-nomy

UniProt

SGD

Reactome

PubMed

PubChem

PRO-SITE

ProDom

Pfam PDB

OMIM

OBO

MGI

KEGG Reaction

KEGG Pathway

KEGG Glycan

KEGG Enzyme

KEGG Drug

KEGG Cpd

InterPro

HomoloGene

HGNC

Gene Ontology

GeneID

GenBank

ChEBI

CAS

Affy-metrix

BibBaseBBC

Wildlife Finder

BBC Program

mesBBC

Music

rdfaboutUS Census

e-science data – with opaque mathematical modelsstatistical datasets – without mathematical derivation rulespublication databases – without mathematical contentChristoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 8

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Pointing out and Discussing Problems


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Collaboration Still has to be Enabled!

Many collaboration tasks not currently well supported by machines

For other tasks there is (limited) support

creating and formalizing documents – semiformal!?search existing knowledge to build on – semiformal!?computation (recall unit conversion) – but not inside documentspublishing in textbook style – could it bemore comprehensible?adapting notation (e.g. ⋅↝ ×, (nk)↝ C

kn) – not quite on demand

Existing machine services only focus on primitive tasks

Can’t simply be put together, as they . . .

. . . speak different languages

. . . take different perspectives on knowledge


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Document Perspective: XML Markup

XHTML+MathML(+OpenMath)

... is <math><mn>9144</mn><mo>⁢</mo><mo>m</mo>

</math> from city ...


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Network Perspective: RDF Graphs

Look up Related Information:


MusicBrainz

(zitgist)

P20

YAGO


WordNet (W3C)

WordNet(VUA)

VIVO UFVIVO

Indiana

VIVO Cornell

VIAF

URIBurner

Sussex Reading

Lists

Plymouth Reading

Lists

UMBEL

UK Post-codes

legislation.gov.uk

Uberblic

UB Mann-heim

TWC LOGD

Twarql

transportdata.gov

.uk

totl.net

Tele-graphis

TCMGeneDIT

TaxonConcept


t4gm

Surge Radio

STW

RAMEAU SH

statisticsdata.gov

.uk


Lists


Semantic CrunchBase

semanticweb.org

SemanticXBRL

SWDog Food

rdfabout US SEC

Wiki

UN/LOCODE

Ulm

ECS (RKB

Explorer)

Roma

RISKS

RESEX

RAE2001

Pisa

OS

OAI

NSF

New-castle

LAAS

KISTIJISC

IRIT

IEEE

IBM

Eurécom

ERA

ePrints

dotAC

DEPLOY

DBLP (RKB

Explorer)

Course-ware

CORDIS

CiteSeer

Budapest

ACM

riese

Revyu

researchdata.gov

.uk

referencedata.gov

.uk

Recht-spraak.

nl

RDFohloh

Last.FM (rdfize)

RDF Book

Mashup

PSH

ProductDB

PBAC

Poké-pédia

Ord-nance Survey

Openly Local

The Open Library

OpenCyc

OpenCalais

OpenEI

New York

Times

NTU Resource

Lists

NDL subjects

MARC Codes List

Man-chesterReading

Lists

Lotico

The London Gazette

LOIUS

lobidResources

lobidOrgani-sations

LinkedMDB

LinkedLCCN

LinkedGeoData

LinkedCT

Linked Open

Numbers

lingvoj

LIBRIS

Lexvo

LCSH

DBLP (L3S)


Good-win

Family

Jamendo

iServe

NSZL Catalog

GovTrack

GESIS

GeoSpecies

GeoNames

GeoLinkedData(es)

GTAA

STITCHSIDER


MediCare

Euro-stat

(FUB)

DrugBank

Disea-some

DBLP (FU

Berlin)

DailyMed

Freebase

flickr wrappr

Fishes of Texas

FanHubz

Event-Media

EUTC Produc-

tions

Eurostat

EUNIS

ESD stan-dards


NHS (EnAKTing)

Mortality (En-

AKTing)Energy

(En-AKTing)

CO2(En-

AKTing)

educationdata.gov

.uk

ECS South-ampton

Gem. Norm-datei

datadcs

MySpace(DBTune)

MusicBrainz

(DBTune)

Magna-tune

John Peel(DB

Tune)

classical(DB

Tune)


Last.fmArtists

(DBTune)

DBTropes

dbpedia lite

DBpedia

Pokedex

Airports


MusicBrainz(Data

Incubator)

Moseley Folk


Climbing


Cornetto

Chronic-ling

America

Chem2Bio2RDF

biz.data.

gov.uk

UniSTS

UniRef

UniPath-way

UniParc

Taxo-nomy

UniProt

SGD

Reactome

PubMed

PubChem

PRO-SITE

ProDom

Pfam PDB

OMIM

OBO

MGI

KEGG Reaction

KEGG Pathway

KEGG Glycan

KEGG Enzyme

KEGG Drug

KEGG Cpd

InterPro

HomoloGene

HGNC

Gene Ontology

GeneID

GenBank

ChEBI

CAS

Affy-metrix

BibBaseBBC

Wildlife Finder

BBC Program

mesBBC

Music

rdfaboutUS Census

Point out and Discuss Problems:`

discussion page

knowledgeitems

(OMDoc ontology)on wiki pages

definitionforum1

example

post1: Issue(UnclearWh.Useful)

post7: Decision

post2: Elaboration

post4: Idea(ProvideExample)

post3: Position

post5: Evaluation

exemplifies

hasDiscussion(IkeWiki ontology)

has_container

has_reply

resolvesInto

physical structure(SIOC Core)

argumentativestructure

(SIOC Arg.)

elaborates_on

agrees_with

proposes_solution_for

supports

post6: Position

agrees_with

decides

supported_by


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How to Enable Collaboration?

Integrate a wide range of different services

As they currently speak different languages, . . .first create a unified interoperability layer for knowledgerepresentations (document vs. network perspective)then translate between different representations

Tool: semantic web technology


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Contribution

Building a collaboration environment is not trivial

Collection of foundational, enabling technologiesOMDoc+RDF(a), a unified interoperability layer for representingsemiformal mathematical knowledge (document and networkperspective)Design patterns for integrating services

interactive assistance in published documentstranslations inside knowledge bases

Evaluation of how effectively an integrated environment builtthat way (a semanticwiki for mathematics) supports practicalworkflows


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SWiM, an Integrated Collaboration Environment

Developed formaintainingmathematical knowledge collectionsChristoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 15

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SWiM, an Integrated Collaboration Environment

Semantic wiki, combining knowledge production and consumption

Editor for documents,formulæ, metadata

Graph-basednavigation

Localized discussionforums


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Usability Evaluation of the SWiM Prototype

Integration is feasible, but is the result usable?learnable?effective?useful?satisfying to use?

Can we effectively support maintenance workflows (on theOpenMath CDs)?

Quick local fixing of minor errors(in text, formalization, or presentation)Peer review, and preparing major revisions by discussion

In general: What particular challenges to usability does theintegration of heterogenenous services entail?


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Feedback Statements from Test Users

36understoodconcept

93

positivestatement

95

successfulaction

61negativestatement

52

confusion/uncertainty51

expectationnot met

44

not understoodwhat to do

43dissatisfaction

18 unexpected bug18 not understood concept

Understanding only seemsmarginal, but had a high impact onsuccessfully accomplishing tasks!Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 18

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Interpretation and Consequences

Usability hypotheses largely hold, but:

Users with previous knowledge of related knowledge models orUIs had advantagesLess experienced users frequently taken in by misconceptions;requested better explanations

Users expected a more coherent integration

User interfaces need Semantic Transparency (for learnability):

self-explaining user interfacesfamiliar and consistent terminology (despite XML/RDFheterogeneity under the hood!)

The SWiM user interface is not yet self-explaining


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Self-explaining Publicationsand Assistive Services


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Structures of Mathematical Knowledge (MK)

Goal: design unified interoperability layer for all relevant aspects ofMK

Different degrees of formality: informal, formalized, semiformal

Classification of structural dimensions:

logical/functional: symbols, objects, statements, theoriesrhetorical/document: from chapters down to phrasespresentation: e.g. notation of symbolsmetadata: general administrative ones;applications/projects/peoplediscussions about MK (e.g. about problems)


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Requirements for Representing MK

▼ satisfiesRequirementa▶

Structure Coverage Formal. Linking Comprh.

S.L.* S.R S.N S.M S.D F.R F.C L.A L.→ L.← C.S C.H

O S T

MathML 3 ++ – – – – – – ++ + + + + – +OpenMath 2 Objects ++ – – – – – – + # # – + – #

OpenMath 2 CDs ++b # # – – # – # # – – – – #OMDoc 1.2/STEX ++b ++ + ++ + # – ++ + # – + – –MathLang ++ ++ – – – – – ++ + – – # # –

DocBook 5 ++b – – – – +d – – – – + + – –TEI P5 ++c – – – – # – ++ + + – + – –DITA 1.1 ++c – – – – +d – – – + + + – –EPUB 2.0.1/DTBook 3 ++c – – – – + – – – – – + – –CNXML 0.7/CollXML/mdml ++b + – – – # – – – – – + – –

Formalized languages ++ ++ # – + – – # # – – – + –

RDF(a) 1.1 (depends on vocabulary) # + ++ ++ ++ # +

OMDoc 1.3/1.6 ++b ++ ++ ++ ++ ++e – ++ + ++e ++e ++e #e +e


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OMDoc+RDF(a) as an Interoperability Layer forExchanging and Reusing MK

1 Translate OMDoc to RDF

formalize conceptual model as an ontologyreused existing ontologies for rhetorics, metadata, etc.specified an XML→RDF translation for identifiers and structures

2 Embed RDFa into OMDoc

extend OMDoc beyond mathematicsembed arbitrary metadata into mathematical documents


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Creating an RDF Resource from an XML Node<theory name="group"><symbol name="op"><type>

M ×M→ M</type>

</symbol></theory>

<http://ma.th/group>rdf:type omdoc:Theory ;omdoc:homeTheoryOf<http://ma.th/group#symbol> .

<http://ma.th/group#symbol>rdf:type omdoc:Symbol ;omdoc:declaredType ... .

. . . /group

Theory

. . . /group#op

symbol

rdf:type homeTheoryOfrdf:type

Algorithm:Require: b, p, u, T , P ∈ U, n is an XML node,T is the URI of an ontology class or empty, P is the URI of an ontology property or empty

Ensure: R ∈ U × U × (U ∪ L) is an RDF graphR← ∅if u = ε then {if no explicit URI is defined by the rule, . . . }

u← mint(b, n) {. . . try to mint one, using built-in or customminting functions (configurable per extraction module)}end ifif u ≠ ε then {if we got a URI, . . . }

if T ≠ ε thenR← R ∪ {⟨u, rdf ∶type, T⟩} {make this resource an instance of the given class}

end ifif P ≠ ε then

R← R ∪ add_uri_property(�, p, P, u) {create a link (e.g. of a type like hasPart) from the parent subject to this resource}end iffor all c ∈ πNS($n/ ∗ ∣$n/@∗) do {from each element and attribute child node (determined using an XPath evaluation functionreturning a nodeset) . . . }

R← R ∪ extract(b, c, u) {. . . recursively extract RDF, using the newly created resource as a parent subject}end for{i.e. the recursion terminates for nodes without children}

end ifreturn R


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The OMDoc Ontology (simplified)

MathKnowledgeItem

StatementTheory

Type

ConstitutiveStatement

NonConstitutiveStatement

Import

SymbolDefinition

Axiom

Example AssertionProof

NotationDefinition

subClassOf

otherproperties

dependsOn,hasPart,verbalizes

imports,metaTheory

importsFrom

homeTheory

hasTyp

e

proveshasDefinition exemplifies

render

sSymbol


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Multi-step Dependencies

Logical well-formedness:o∶hasDefinition ○ o∶usesSymbol⊑ o∶hasOccurrenceOfInDefinition⊑ o∶wellFormedNessDependsOn⊑ o∶dependsOn

Validity of a proof:o∶hasStep ○ o∶stepJustifiedBy⊑ o∶validityDependsOn ⊑ o∶dependsOn

Dependency of published documents on notation definitions:o∶usesSymbol ○ o∶hasNotationDefinition⊑ o∶possiblyUsesNotationDefinition⊑ o∶presentationDependsOn ⊑ o∶dependsOn

. . . and their transitive closures


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Knowledge Representation Service Integration

Conclusion and Future Work

Contribution of this thesis:

building blocks for managing mathematical knowledgeknowledge representation interoperability layercollaborative services

methods and techniques for integrating them

Planetary: e-Math on the Web

supporting scientists incollaboratively gaining newknowledge

contributing legacy MKcollections to the Web of Data


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Self-explanation with System Ontologies

System ontologies in Planetary: structural ontologies, workflowontologies, argumentation ontology

Customizable in the environment (= mathematical documents)

“The ontology is the API”

Self-explaining user interface via ontology documentation

`

discussion page

knowledgeitems

(OMDoc ontology)on wiki pages

definitionforum1

example

post1: Issue(UnclearWh.Useful)

post7: Decision

post2: Elaboration

post4: Idea(ProvideExample)

post3: Position

post5: Evaluation

exemplifies

hasDiscussion(IkeWiki ontology)

has_container

has_reply

resolvesInto

physical structure(SIOC Core)

argumentativestructure

(SIOC Arg.)

elaborates_on

agrees_with

proposes_solution_for

supports

post6: Position

agrees_with

decides

supported_by

Position

Decision

Issue

Inappropriatefor Domain

Wrong Incomprehensible

subClassOf

Idea

ProvideExample

Keep asBad Example

Delete

subClassOfproposes_solution_for

agrees_with/disagrees_with

agrees_with/disagrees_with

decides decides

supported_by

OntologyEntity

resolves_into

Math. Know-ledge Item

Theorem Example

subClassOf

subClassOf

SIOCargumentationmodule (partly shown)

Domain-specificargumentationclasses (partly shown)

OMDoc ontology

……


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Structural Coverage of RDF VocabulariesStructures Logical/functional Rhet. Notation Metadata Discussion

Objects Stmts. Theories

N3 Vocabularies + # – – – – –OpenMath CD # # # – – # –HELM + + # – – – –MoWGLI + ++ # – – + –MathLang DRa – + – – – – –PML – ++a – – – – –SALT – – – ++ – – +OntoReST – – – ++ – – –DILIGENT – – – – – – +DCMI Terms – – – – – ++ –

OMDocb # ++ + –c + –d –OpenMath CDe # # # – + # –SIOC Argumentationf – – – – – – ++

a proofs onlyb contribution of this thesisc intentionally delegated to SALTd intentionally delegated to DCMI Terms, ccREL, the OpenMath CD ontology,and other vocabularies

e contribution of this thesis: a modernized ontology, which I have developedfor the purpose of maintaining OpenMath CDs

f contribution of this thesisChristoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 29

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Translate OMDoc to RDF

formalized OMDoc’s conceptual model as an ontology

abstracted from XML schema, generalized (e.g. dependencies)comprehensible for services (via RDF semantics)annotation vocabulary for XHTML+RDFa published from OMDoc

reused existing ontologies for rhetorics, metadata, etc.specified an XML→RDF translation for:

identifiers of structural concepts (peculiarities of URI formats)the structures and relations themselves


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Embed RDFa into OMDoc

extend OMDoc beyond mathematics:coherently express all mathematical and related knowledge inthe same languageembed arbitrary metadata into mathematical documentslink mathematical documents to related external resources


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Write Expressive RDF Vocabularies in OMDocImplementation and alignment of this structural ontology require:

selectively use more expressivity“just” OWL DL does not capture all concepts of interestmetadata inheritance, applicability of problem/solution types toprimary knowledge, etc. require first- or second-order logicOMDoc supports heterogeneous formalization!

comprehensive and comprehensible documentationfor developers and end usersreuse existing ontologies, or adapt and integrate them(modularity!)

Result: useful for our ontologies and metadata vocabularies, . . .. . . but also for other ontologies (reimplemented FOAF)existing MKM services become available for ontologyengineering


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MKM Services for Ontology Engineering


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Concrete Workflows and Usage Scenarios

Scenarios I studied:In the OpenMath Content Dictionaries:

Quickly Fixing Minor ErrorsFixing and Verifying NotationsPeer Review and Preparing Major Revisions by Discussion

In Michael Kohlhase’s computer science lecture notes:

Serving Information Needs of Learners and Instructors

In a collection of software engineering documents (contracts,requirements, manuals), and in the Flyspeck collaborative proofformalization effort:

Managing a Project


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Primitive Services that we Need

▼ accom-plishes▶

Creating Formal./Organizing

Under-standing

Reusing Applying

EditingValidatingPublishingInf. Retr.Arguing

quickly fixing minor errorsfixing and verifying notationspeer review and preparing major revisions by discussionserving information needs of learners and instructorsmanaging a project


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A Unified Visual Editing Component

An existing presentation markup (HTML) editor, extended into a versatile reusableediting component for logical and document structures, formulæ, symbolnotation definitions, metadataChristoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 36

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Publishing Linked Data for Machines

Machine-comprehensible information under HTTP URIs; links torelated information.


MusicBrainz

(zitgist)

P20

YAGO


WordNet (W3C)

WordNet(VUA)

VIVO UFVIVO

Indiana

VIVO Cornell

VIAF

URIBurner

Sussex Reading

Lists

Plymouth Reading

Lists

UMBEL

UK Post-codes

legislation.gov.uk

Uberblic

UB Mann-heim

TWC LOGD

Twarql

transportdata.gov

.uk

totl.net

Tele-graphis

TCMGeneDIT

TaxonConcept


t4gm

Surge Radio

STW

RAMEAU SH

statisticsdata.gov

.uk


Lists


Semantic CrunchBase

semanticweb.org

SemanticXBRL

SWDog Food

rdfabout US SEC

Wiki

UN/LOCODE

Ulm

ECS (RKB

Explorer)

Roma

RISKS

RESEX

RAE2001

Pisa

OS

OAI

NSF

New-castle

LAAS

KISTIJISC

IRIT

IEEE

IBM

Eurécom

ERA

ePrints

dotAC

DEPLOY

DBLP (RKB

Explorer)

Course-ware

CORDIS

CiteSeer

Budapest

ACM

riese

Revyu

researchdata.gov

.uk

referencedata.gov

.uk

Recht-spraak.

nl

RDFohloh

Last.FM (rdfize)

RDF Book

Mashup

PSH

ProductDB

PBAC

Poké-pédia

Ord-nance Survey

Openly Local

The Open Library

OpenCyc

OpenCalais

OpenEI

New York

Times

NTU Resource

Lists

NDL subjects

MARC Codes List

Man-chesterReading

Lists

Lotico

The London Gazette

LOIUS

lobidResources

lobidOrgani-sations

LinkedMDB

LinkedLCCN

LinkedGeoData

LinkedCT

Linked Open

Numbers

lingvoj

LIBRIS

Lexvo

LCSH

DBLP (L3S)


Good-win

Family

Jamendo

iServe

NSZL Catalog

GovTrack

GESIS

GeoSpecies

GeoNames

GeoLinkedData(es)

GTAA

STITCHSIDER


MediCare

Euro-stat

(FUB)

DrugBank

Disea-some

DBLP (FU

Berlin)

DailyMed

Freebase

flickr wrappr

Fishes of Texas

FanHubz

Event-Media

EUTC Produc-

tions

Eurostat

EUNIS

ESD stan-dards


NHS (EnAKTing)

Mortality (En-

AKTing)Energy

(En-AKTing)

CO2(En-

AKTing)

educationdata.gov

.uk

ECS South-ampton

Gem. Norm-datei

datadcs

MySpace(DBTune)

MusicBrainz

(DBTune)

Magna-tune

John Peel(DB

Tune)

classical(DB

Tune)


Last.fmArtists

(DBTune)

DBTropes

dbpedia lite

DBpedia

Pokedex

Airports


MusicBrainz(Data

Incubator)

Moseley Folk


Climbing


Cornetto

Chronic-ling

America

Chem2Bio2RDF

biz.data.

gov.uk

UniSTS

UniRef

UniPath-way

UniParc

Taxo-nomy

UniProt

SGD

Reactome

PubMed

PubChem

PRO-SITE

ProDom

Pfam PDB

OMIM

OBO

MGI

KEGG Reaction

KEGG Pathway

KEGG Glycan

KEGG Enzyme

KEGG Drug

KEGG Cpd

InterPro

HomoloGene

HGNC

Gene Ontology

GeneID

GenBank

ChEBI

CAS

Affy-metrix

BibBaseBBC

Wildlife Finder

BBC Program

mesBBC

Music

rdfaboutUS Census


http://kwarc.info



Arguing about Problems and their Solutions

Extended a genericargumentation ontologyby math-specific problemand solution typesDesigned user assistance:

Discussion forum withtyped posts and repliesProblem-solvingassistance: findsolution proposal withmost positive feedback


http://kwarc.info



Integrated Assistance in Interactive Documents

Reading = understanding + interacting

Integrate services intopublished documents thatassist the reader with

adapting document’sappearance to theirpreferenceslooking up additionalinformation in place

presentation markup+ fine-grained semantic annotations+ scripting support(XHTML+MathML+OpenMath+RDFa, JavaScript)

GUI

menu

mouse

actionobjects Client Services

folding/elision

layers

keybdlookup (e.g. definitions)

computing& rewriting

ontology/definitions

notationcollection

renderer

initially generates

Document

ClientModules

Compu-tational

WebServices

proxy

computeralgebra

… others …

integrated backend(MMT: logics; TNTBase: lecture notes; …)

unit converter

linkeddatasets

Remote Data

Sources

Prerequisite: semantics-preserving transformationsservices hook into fine-grained annotations


http://kwarc.info



Flexibly Eliding and Displaying Reading Aids


http://kwarc.info



Definition Lookup


http://kwarc.info



Unit conversion


http://kwarc.info



RDFa: Generic Navigation and RhetoricalStructure Visualization


http://kwarc.info



Transparent Translations in Knowledge Bases

Knowledge in foreign repositories represented in differentlanguages

Even services operating on the same repository may speakdifferent languages

e.g. semantic XML markup for authoring and publishing . . .. . . and RDF graphs for retrieval and linking

Transparently translate between them!XML to RDFRestricted language (e.g. OWL) to richer language (e.g. OMDoc)Different granularities (e.g. file system vs. fine-grainedknowledge base)


http://kwarc.info



Krextor, an Extensible Library for ExtractingStructures from Semantic Markup

OMDoc+RDFa

OWL in OMDoc+RDFa

XHTML+RDFa

OpenMath CD

your XML+RDFa?

your Microformat

genericrepresentation

RXR

RDF/XML

Turtle

RDFa

your format

N-Triples

Javacallback

??

output format

input format


http://kwarc.info



SWiM, an Integrated Collaboration EnvironmentUse cases specifically considered:

Quickly Fixing Minor ErrorsFixing and Verifying NotationsPeer Review and Preparing Major Revisions by DiscussionManaging a Project

Features:Client for versioned repositories (legacy content)Utilizing dependencies, e.g. for publishingLocal access to the editorArgumentative discussions

Conclusion:Integrating heterogeneous services is feasibleImprovement over wiki state of the artIncubator for new services and system components


http://kwarc.info



Evaluation Techniques and Questions

Content analysis of discussion posts created by domainexperts

Do the user interface and knowledge model allow for exactassociation of problem reports to knowledge items?Does the knowledge model capture common argumentationprimitives?

Community survey: Are the services useful for the OpenMathcommunity?

Supervised experiments with test users:Are the knowledge model and the user interface learnable?Do they effectively support the three workflows?


http://kwarc.info


enabling collaboration on semiformal mathematical knowledge by semantic web integration

Technology

background knowledge

lev semiformal

metric christoph lange

review christoph lange

z z0 gz

an1 z n1

function f

social web research