Towards OpenMath Content Dictionaries as Linked Data

Towards OpenMath Content Dictionaries asLinked Data

OpenMath Workshop 2010

Christoph Lange

Jacobs University, Bremen, GermanyKWARC – 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

http://kwarc.info

http://www.jacobs-university.de


http://kwarc.info

Overview

Linked DataBest practices for publishing and connecting structured data on theweb

easy retrieval of further informationlightweight semantics enables scalable reasoningas decentral as the web

. . . just as OpenMath CDs?Not quite: CDs keep up in principle, but not in practice – so . . .

1 Whymake CDs Linked Data aware?2 And how?


http://kwarc.info


Overview

Linked DataBest practices for publishing and connecting structured data on theweb

easy retrieval of further informationlightweight semantics enables scalable reasoningas decentral as the web

. . . just as OpenMath CDs?Not quite: CDs keep up in principle, but not in practice – so . . .

1 Whymake CDs Linked Data aware?2 And how?


http://kwarc.info


The Linked Data principles

1 Use URIs to identify things2 Use HTTP URIs – can be dereferenced for looking up [information

about] things3 Provide useful (machine-understandable) information at those

URIs4 Link to other related things to improve information discovery


http://kwarc.info


Linked Open DataThe Semantic Web as it should have been right from the start

As of March 2009

LinkedCTReactome

Taxonomy

KEGG

PubMed

GeneID

Pfam

UniProt

OMIM

PDB

SymbolChEBI

Daily Med

Disea-some

CAS

HGNC

InterPro

Drug Bank

UniParc

UniRef

ProDom

PROSITE

Gene Ontology

HomoloGene

PubChem

MGI

UniSTS

GEOSpecies

Jamendo

BBCProgramm

es

Music-brainz

Magna-tune

BBCLater +TOTP

SurgeRadio

MySpaceWrapper

Audio-Scrobbler

LinkedMDB

BBCJohnPeel

BBCPlaycount

Data

Gov-Track

US Census Data

riese

Geo-names

lingvoj

World Fact-book

Euro-stat

flickrwrappr

Open Calais

RevyuSIOCSites

Doap-space

Flickrexporter

FOAFprofiles

CrunchBase

Sem-Web-

Central

Open-Guides

Wiki-company

QDOS

Pub Guide

RDF ohloh

W3CWordNet

OpenCyc

UMBEL

Yago

DBpediaFreebase

Virtuoso Sponger

DBLPHannover

IRIT Toulouse

SWConference

Corpus

RDF Book Mashup

Project Guten-berg

DBLPBerlin

LAAS- CNRS

Buda-pestBME

IEEE

IBM

Resex

Pisa

New-castle

RAE 2001

CiteSeer

ACM

DBLP RKB

Explorer

eprints

LIBRIS

SemanticWeb.org

Eurécom

RKBECS

South-ampton

CORDIS

ReSIST ProjectWiki

NationalScience

Foundation

ECS South-ampton

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

http://kwarc.info


LOD Applications – Researchers Map


http://kwarc.info


Linked Open Data Applications – RelFinder


http://kwarc.info


The Need for Mathematical Semantics

Statistical datasets of EU, US, UK being published as Linked Data

ahs:EH100 # ID of this data pointscv:dimension env:isle-of-wight ; # "region" dimensionscv:dimension env:year-2008 ; # "time" dimensionscv:dimension env:geese ; # type of items countedrdf:value "693"^^xsd:decimal ; # countscv:dataset ahs2:livestock . # back-reference to dataset

Here: count of items (per year and region)Also in those datasets: growth rates, densities, indices (derivedvalues!)How to check derived values, how to compute new ones?Need mathematical semantics!


http://kwarc.info


Semantics of Derived ValuesPopulation Density ∶= Population

Area

# the density is computed by ...ahs:PD100 sl:computedFrom [# ... calling OpenMath’s arith1#dividesl:function <http://www.openmath.org/cd/arith1#divide> ;sl:arguments# ... passing the value of the EH100 data point as first argument[ 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 object2 send to SCSCP computation service


http://kwarc.info


Non-Standard Derivations

Human Development Index of a country:

HDI ∶=13(LE +

23ALI +

13GEI + GDP)

Let this be http://example.org´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶

cdbase

/ statistics´¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¶

cd

# hdi°name

No standard phrasebook knows this!Linked Data solution: download definition from CD URI and use it


http://kwarc.info


Linked Data Principles in OpenMath

1 Use URIs to identify things – CDBase hardly ever used⇒ URIawareness?!

2 Use HTTP URIs – who has control overhttp://www.openmath.org/cd (the default CDBase)?

3 Provide useful information at those URIs – URIs are usuallyconsidered names only; if anything, non-semantic HTML isavailable from there

4 Link to other related things – ‘‘It is defined in Abramowitz andStegun, Handbook of Mathematical Functions, section 4.1’’, buthow about a link to DLMF? To DBpedia?


http://kwarc.info


http://www.openmath.org/cd

Technical and Conceptual Flaws of OpenMathIt’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 byHTTP content negotiation – application/openmath+xml?“It is important to stress that it is not CDs themselves which arebeing transmitted, but some ‘mathematics’ whose definitionsare held within the CDs” – discourages publishers of makingmachine-understandable CDs available!weak semantics of FMP (10th anniversary?) – anyway, practice ofRDF-based Linked Data and OpenMath advise to be pragmaticno way to link OpenMath symbols to anything but otherOpenMath symbols (e. g. DLMF or DBpedia)Links could be given by FMP or OMATTR⇒ link target has to beencoded as OMS⇒ restrictive cdbase / cd # name schema(hash vs. slash URIs)


http://kwarc.info


Conclusion

Linked Data applications lack mathematical semanticsOpenMath fails to meet Linked Data principlesWe need better practicesWe need a better specification


http://kwarc.info


Future Work

Integrate OpenMathcomputations right into RDFqueriesOpenMath entailmentregime for SPARQL,or simply SPARQL extensionfunctions

Computation?


http://kwarc.info


Technology

Towards OpenMath Content Dictionaries as Linked Data