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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
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 2
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 3
Overview Service Integration Knowledge Representation Conclusion & Future
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
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 5
Overview Service Integration Knowledge Representation Conclusion & Future
Looking up Background Knowledge
“What does that mean?”
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 6
Overview Service Integration Knowledge Representation Conclusion & Future
Adapting the Presentation to FamiliarTerminology
“What does that mean?” – here: unfamiliar unit system (imperial vs.metric)
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 7
Overview Service Integration Knowledge Representation Conclusion & Future
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
Overview Service Integration Knowledge Representation Conclusion & Future
Pointing out and Discussing Problems
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 9
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 10
Overview Service Integration Knowledge Representation Conclusion & Future
Document Perspective: XML Markup
XHTML+MathML(+OpenMath)
... is <math><mn>9144</mn><mo>⁢</mo><mo>m</mo>
</math> from city ...
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 11
Overview Service Integration Knowledge Representation Conclusion & Future
Network Perspective: RDF Graphs
Look up Related Information:
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
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 12
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 13
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 14
Overview Service Integration Knowledge Representation Conclusion & Future
SWiM, an Integrated Collaboration Environment
Developed formaintainingmathematical knowledge collectionsChristoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 15
Overview Service Integration Knowledge Representation Conclusion & Future
SWiM, an Integrated Collaboration Environment
Semantic wiki, combining knowledge production and consumption
Editor for documents,formulæ, metadata
Graph-basednavigation
Localized discussionforums
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 16
Overview Service Integration Knowledge Representation Conclusion & Future
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?
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 17
Overview Service Integration Knowledge Representation Conclusion & Future
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
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 19
Overview Service Integration Knowledge Representation Conclusion & Future
Self-explaining Publicationsand Assistive Services
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 20
Overview Service Integration Knowledge Representation Conclusion & Future
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)
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 21
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 22
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 23
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 24
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 25
Overview Service Integration Knowledge Representation Conclusion & Future
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 26
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 27
Knowledge Representation Service Integration
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
……
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 28
Knowledge Representation Service Integration
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
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 30
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 31
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 32
Knowledge Representation Service Integration
MKM Services for Ontology Engineering
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 33
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 34
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 35
Knowledge Representation Service Integration
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
Knowledge Representation Service Integration
Publishing Linked Data for Machines
Machine-comprehensible information under HTTP URIs; links torelated information.
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 37
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 38
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 39
Knowledge Representation Service Integration
Flexibly Eliding and Displaying Reading Aids
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 40
Knowledge Representation Service Integration
Definition Lookup
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 41
Knowledge Representation Service Integration
Unit conversion
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 42
Knowledge Representation Service Integration
RDFa: Generic Navigation and RhetoricalStructure Visualization
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 43
Knowledge Representation Service Integration
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)
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 44
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 45
Knowledge Representation Service Integration
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
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 46
Knowledge Representation Service Integration
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?
Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 47