OpenMath workshop 2010

1. Towards OpenMath Content Dictionaries as
Linked Data
OpenMath Workshop 2010
Christoph Lange
Jacobs University, Bremen, Germany
KWARC – Knowledge Adaptation and Reasoning for Content
July 08, 2010
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 1/13

2. Overview
Linked Data
Best practices for publishing and connecting structured data on the
web
easy retrieval of further information
lightweight semantics enables scalable reasoning
as decentral as the web
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 2/13

3. Overview
Linked Data
Best practices for publishing and connecting structured data on the
web
easy retrieval of further information
lightweight semantics enables scalable reasoning
as decentral as the web
. . . just as OpenMath CDs?
Not quite: CDs keep up in principle, but not in practice – so . . .
1 Why make CDs Linked Data aware?
2 And how?
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 2/13

4. The Linked Data principles
1 Use URIs to identify things
2 Use HTTP URIs – can be dereferenced for looking up [information
about] things
3 Provide useful (machine-understandable) information at those
URIs
4 Link to other related things to improve information discovery
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 3/13

5. Linked Open Data
The Semantic Web as it should have been right from the start
ECS
South-
Sem- Wiki-
Surge ampton
LIBRIS Web- company
Radio Central RDF
ohloh
Resex
Doap- Buda-
Music- space Semantic ReSIST
brainz Audio- pest Eurécom
Project
Flickr Web.org
MySpace Scrobbler QDOS SW BME Wiki
exporter
Wrapper
Conference IRIT
Corpus Toulouse
RAE National
BBC BBC Crunch 2001 Science
FOAF SIOC ACM
BBC Later + John Base Revyu Foundation
Jamendo Peel profiles Sites
Playcount TOTP Open-
Data Guides
DBLP
flickr RKB
Project
Pub Geo- Euro- wrappr Explorer
Guten- Virtuoso
Guide names stat Pisa CORDIS
berg Sponger eprints
BBC
Programm
Open
es
Calais
RKB
riese World Linked
ECS
Fact- MDB IEEE New-
South-
Magna- book
ampton castle
Gov- tune RDF Book
Track Mashup
DBpedia
lingvoj Freebase LAAS-
US CiteSeer
CNRS
Census W3C DBLP
IBM
Data WordNet Hannover
UniRef
GEO
UMBEL Species DBLP
Berlin
Reactome
LinkedCT UniParc
Open Taxonomy
Cyc Yago Drug
PROSITE
Daily Bank
Med
Pub GeneID
Homolo Chem
Gene KEGG UniProt
Pfam ProDom
Disea- CAS
Gene
some
ChEBI Ontology
Symbol OMIM
Inter
Pro
UniSTS PDB
HGNC
MGI
PubMed
As of March 2009
The opener the better (but also works in intranets)
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 4/13

6. LOD Applications – Researchers Map
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 5/13

7. Linked Open Data Applications – RelFinder
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 6/13

8. The Need for Mathematical Semantics
Statistical datasets of EU, US, UK being published as Linked Data
ahs:EH100 # ID of this data point
scv:dimension env:isle-of-wight ; # "region" dimension
scv:dimension env:year-2008 ; # "time" dimension
scv:dimension env:geese ; # type of items counted
rdf:value "693"^^xsd:decimal ; # count
scv:dataset ahs2:livestock . # back-reference to dat
Here: count of items (per year and region)
Also in those datasets: growth rates, densities, indices (derived
values!)
How to check derived values, how to compute new ones?
Need mathematical semantics!
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 7/13

9. Semantics of Derived Values
Population
Population Density = Area
# the density is computed by ...
ahs:PD100 sl:computedFrom [
# ... calling OpenMath’s arith1#divide
sl:function <http://www.openmath.org/cd/arith1#divide> ;
sl:arguments
# ... passing the value of the EH100 data point as first argum
[ sl:argPosition "1"^^xsd:int ;
sl:argValue ahs:EH100 ] ,
# ... and the value of the AR100 data point as second argument
[ sl:argPosition "2"^^xsd:int ;
sl:argValue ahs:AR100 ] ].
How to compute?
1 translate RDF to OpenMath object
2 send to SCSCP computation service
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 8/13

10. Non-Standard Derivations
Human Development Index of a country:
1 2 1
HDI = (LE + ALI + GEI + GDP)
3 3 3
Let this be http://example.org statistics # hdi
cd name
cdbase
No standard phrasebook knows this!
Linked Data solution: download definition from CD URI and use it
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 9/13

11. Linked Data Principles in OpenMath
1 Use URIs to identify things – CDBase hardly ever used ⇒ URI
awareness?!
2 Use HTTP URIs – who has control over
http://www.openmath.org/cd (the default CDBase)?
3 Provide useful information at those URIs – URIs are usually
considered names only; if anything, non-semantic HTML is
available from there
4 Link to other related things – ‘‘It is defined in Abramowitz and
Stegun, Handbook of Mathematical Functions, section 4.1’’, but
how about a link to DLMF? To DBpedia?
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 10/13

12. Technical and Conceptual Flaws of OpenMath
It’s not only to blame on the community, but also on the standard. . .
No MIME type specified ⇒ can’t retrieve a CD file from a URI by
HTTP content negotiation – application/openmath+xml?
“It is important to stress that it is not CDs themselves which are
being transmitted, but some ‘mathematics’ whose definitions
are held within the CDs” – discourages publishers of making
machine-understandable CDs available!
weak semantics of FMP (10th anniversary?) – anyway, practice of
RDF-based Linked Data and OpenMath advise to be pragmatic
no way to link OpenMath symbols to anything but other
OpenMath symbols (e. g. DLMF or DBpedia)
Links could be given by FMP or OMATTR ⇒ link target has to be
encoded as OMS ⇒ restrictive cdbase / cd # name schema
(hash vs. slash URIs)
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 11/13

13. Conclusion
Linked Data applications lack mathematical semantics
OpenMath fails to meet Linked Data principles
We need better practices
We need a better specification
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 12/13

14. Future Work
Integrate OpenMath
Computation?
computations right into RDF
queries
OpenMath entailment
regime for SPARQL,
or simply SPARQL extension
functions
Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 13/13