CICM 2011 Systems & Projects

1. Motivation Krextor OpenMath CDs Outlook
Krextor – An Extensible Framework for
Contributing Content Math to the Web of Data
CICM Systems & Projects 2011
Christoph Lange
Universität Bremen, Germany
2011-07-19
Christoph Lange Krextor – An Extensible Framework for Contributing Content Math to the Web of Data 2011-07-19 1

2. Motivation Krextor OpenMath CDs Outlook
Linked [Open] Data
Best practices for publishing and connecting structured data:
easy retrieval of further information
lightweight semantics enables scalable reasoning
as decentral as the Web (“Web of Data”)
Sussex St.
Reading Andrews NDL
Audio- Lists Resource subjects t4gm
MySpace scrobbler Lists
Moseley (DBTune) (DBTune) RAMEAU
Folk NTU SH lobid
GTAA Plymouth Resource
Lists
Organi-
Reading
Lists
sations
Music The Open ECS
Magna- Brainz Music
DB tune Library LCSH South-
(Data Brainz LIBRIS ampton
Tropes lobid Ulm
Incubator) (zitgist) Man- EPrints
Resources
chester
Surge Reading
biz. Music RISKS
Radio Lists The Open ECS
data. John Brainz
Discogs Library PSH Gem. UB South-
gov.uk Peel (DBTune)
FanHubz (Data In- (Talis) Norm- Mann- ampton
(DB cubator) Jamendo datei heim RESEX
Tune)
Popula- Poké- DEPLOY
Last.fm
tion (En- pédia
Artists Last.FM Linked RDF
AKTing) research EUTC (DBTune) (rdfize) LCCN VIAF Book Wiki
data.gov Produc- Pisa Eurécom
P20 Mashup semantic
NHS .uk tions classical web.org
(EnAKTing) Pokedex
(DB
Mortality Tune) PBAC ECS
(En-
AKTing)
BBC MARC (RKB Budapest
Program Codes Explorer)
Energy education OpenEI BBC List Semantic Lotico Revyu OAI
(En- CO2 data.gov mes Music Crunch SW
AKTing) (En- .uk Chronic- Linked Dog
NSZL Base
AKTing) ling Event- MDB RDF Food IRIT
America Media Catalog
ohloh
BBC DBLP ACM IBM
Good- BibBase
Ord- Wildlife (RKB
Openly Recht- win
nance Finder Explorer)
Local spraak. Family DBLP
legislation Survey Tele- New VIVO UF
.gov.uk nl graphis York flickr (L3S) New-
VIVO castle
Times URI wrappr OpenCal Indiana RAE2001
UK Post- Burner ais DBLP
codes statistics (FU
VIVO CiteSeer Roma
data.gov LOIUS Taxon iServe Berlin) IEEE
.uk Cornell
Concept Geo
World data
ESD Fact- OS dcs
Names book dotAC
stan- reference Project
Linked Data NASA (FUB) Freebase
dards data.gov Guten-
.uk
for Intervals (Data GESIS Course-
transport DBpedia berg STW ePrints CORDIS
Incu- ware
data.gov bator) (FUB)
Fishes ERA UN/
.uk
of Texas Geo LOCODE
Uberblic
Euro- Species
The stat dbpedia TCM SIDER Pub KISTI
(FUB) lite Gene STITCH Chem JISC
London Geo KEGG
DIT LAAS
Gazette TWC LOGD Linked Daily OBO Drug
Eurostat Data UMBEL lingvoj Med
(es) Disea-
YAGO Medi some
Care ChEBI KEGG NSF
Linked KEGG KEGG
Linked Drug Cpd
GovTrack rdfabout Glycan
Sensor Data CT Bank Pathway
US SEC Open Reactome
(Kno.e.sis) riese Uni
Cyc Lexvo Path-
totl.net way Pfam PDB
Semantic HGNC
XBRL
WordNet KEGG KEGG
(VUA) Linked Taxo- CAS Reaction
rdfabout Twarql UniProt Enzyme
EUNIS Open nomy
US Census Numbers PRO- ProDom
SITE Chem2
UniRef Bio2RDF
Climbing WordNet SGD Homolo
Linked (W3C) Affy- Gene
Cornetto
GeoData metrix PubMed Gene
UniParc
Ontology
GeneID
Airports
Product
DB UniSTS MGI
Gen
Bank OMIM InterPro
As of September 2010
Christoph Lange Krextor – An Extensible Framework for Contributing Content Math to the Web of Data 2011-07-19 2

3. Motivation Krextor OpenMath CDs Outlook
The Web of [Linked] Data in Science
“What can I reuse — what is that good for — where/how is it applied?”
Sussex St.
Reading Andrews NDL
Audio- Lists Resource subjects t4gm
MySpace scrobbler Lists
Moseley (DBTune) (DBTune) RAMEAU
Folk NTU SH lobid
GTAA Plymouth Resource
Lists
Organi-
Reading
Lists
sations
Music The Open ECS
Magna- Brainz Music
DB tune Library LCSH South-
(Data Brainz LIBRIS ampton
Tropes lobid Ulm
Incubator) (zitgist) Man- EPrints
Resources
chester
Surge Reading
biz. Music RISKS
Radio Lists The Open ECS
data. John Brainz
Discogs Library PSH Gem. UB South-
gov.uk Peel (DBTune)
FanHubz (Data In- (Talis) Norm- Mann- ampton
(DB cubator) Jamendo datei heim RESEX
Tune)
Popula- Poké- DEPLOY
Last.fm
tion (En- pédia
Artists Last.FM Linked RDF
AKTing) research EUTC (DBTune) (rdfize) LCCN VIAF Book Wiki
data.gov Produc- Pisa Eurécom
P20 Mashup semantic
NHS .uk tions classical web.org
(EnAKTing) Pokedex
(DB
Mortality Tune) PBAC ECS
(En-
AKTing)
BBC MARC (RKB Budapest
Program Codes Explorer)
Energy education OpenEI BBC List Semantic Lotico Revyu OAI
(En- CO2 data.gov mes Music Crunch SW
AKTing) (En- .uk Chronic- Linked Dog
NSZL Base
AKTing) ling Event- MDB RDF Food IRIT
America Media Catalog
ohloh
BBC DBLP ACM IBM
Good- BibBase
Ord- Wildlife (RKB
Openly Recht- win
nance Finder Explorer)
Local spraak. Family DBLP
legislation Survey Tele- New VIVO UF
.gov.uk nl graphis York flickr (L3S) New-
VIVO castle
Times URI wrappr OpenCal Indiana RAE2001
UK Post- Burner ais DBLP
codes statistics (FU
VIVO CiteSeer Roma
data.gov LOIUS Taxon iServe Berlin) IEEE
.uk Cornell
Concept Geo
World data
ESD Fact- OS dcs
Names book dotAC
stan- reference Project
Linked Data NASA (FUB) Freebase
dards data.gov Guten-
.uk
for Intervals (Data GESIS Course-
transport DBpedia berg STW ePrints CORDIS
Incu- ware
data.gov bator) (FUB)
Fishes ERA UN/
.uk
of Texas Geo LOCODE
Uberblic
Euro- Species
The stat dbpedia TCM SIDER Pub KISTI
(FUB) lite Gene STITCH Chem JISC
London Geo KEGG
DIT LAAS
Gazette TWC LOGD Linked Daily OBO Drug
Eurostat Data UMBEL lingvoj Med
(es) Disea-
YAGO Medi some
Care ChEBI KEGG NSF
Linked KEGG KEGG
Linked Drug Cpd
GovTrack rdfabout Glycan
Sensor Data CT Bank Pathway
US SEC Open Reactome
(Kno.e.sis) riese Uni
Cyc Lexvo Path-
totl.net way Pfam PDB
Semantic HGNC
XBRL
WordNet KEGG KEGG
Linked Taxo- CAS Reaction
Twarql (VUA) UniProt Enzyme
rdfabout EUNIS Open nomy
US Census Numbers PRO- ProDom
SITE Chem2
UniRef Bio2RDF
Climbing WordNet SGD Homolo
Linked (W3C) Affy- Gene
Cornetto
GeoData metrix PubMed Gene
UniParc
Ontology
GeneID
Airports
Product
DB UniSTS MGI
Gen
Bank OMIM InterPro
As of September 2010
e-science data – with opaque mathematical models
statistical datasets – without mathematical derivation rules
publication databases – without mathematical content
Christoph Lange Krextor – An Extensible Framework for Contributing Content Math to the Web of Data 2011-07-19 3

4. Motivation Krextor OpenMath CDs Outlook
Problem: No Math on the Web of Data
Mathematical Knowledge
document-oriented (e.g. textbook style; “Mizar /article/”)
often using XML – natively, or as an interchange format
Web of Data
network-oriented (links, relations)
usually following the graph-based RDF data model
So how to contribute mathematical knowledge to the Web of Data?
Christoph Lange Krextor – An Extensible Framework for Contributing Content Math to the Web of Data 2011-07-19 4

5. Motivation Krextor OpenMath CDs Outlook
The Krextor XML→RDF library
RDF/XML
OMDoc
+RDFa
Turtle
OWL in OMDoc RXR
+RDFa
? RDFa
XHTML ?
+RDFa generic your format
representation
OpenMath CD
N-Triples
your XML
+RDFa?
input format
your Microformat Java
callback output format
Christoph Lange Krextor – An Extensible Framework for Contributing Content Math to the Web of Data 2011-07-19 5

6. Motivation Krextor OpenMath CDs Outlook
Concrete Example: OpenMath CDs to RDF
OpenMath CD in XML OpenMath CD ontology
= RDF vocabulary
Dictionary Status
status
ContentDic-
Version
tionaryGroup
version
type
System
Signature Content Notation
Dictionary Dictionary contains Dictionary
contains NotationsFor
SignaturesFor
Role
Symbol role Notation
Signature
typesSymbol Definition rendersSymbol Definition
uses uses
Property Symbol Symbol Example
subClassOf
Commented Formal
hasText subprop.
Part Part of hasPart
hasText other
properties
rdfs:Literal
Christoph Lange Krextor – An Extensible Framework for Contributing Content Math to the Web of Data 2011-07-19 6

7. Motivation Krextor OpenMath CDs Outlook
Challenges with OpenMath CDs
Requirement: Utilize CDs as they are (be conservative, compatible)
Example (Linking a Mathematical Property)
eiz −e−iz
sin z = 2i is identified by . . .
http://dlmf.nist.gov/4.14.E1
and “a mathematical property [CMP+FMP] of the
http://www.openmath.org/cd/transc1#sin symbol”
How to link without touching the CD? Standoff RDF!
How to identify the OpenMath property? Group it, give it an ID
How to represent the formula?
Christoph Lange Krextor – An Extensible Framework for Contributing Content Math to the Web of Data 2011-07-19 7