Towards OpenMath Content Dictionaries as Linked Data

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OpenMath workshop 2010

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Towards OpenMath Content Dictionaries as Linked Data

  1. 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. 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. 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. 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. 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. 6. LOD Applications – Researchers Map Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 5/13
  7. 7. Linked Open Data Applications – RelFinder Christoph Lange (Jacobs University) Towards OpenMath Content Dictionaries as Linked Data July 08, 2010 6/13
  8. 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. 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. 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. 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. 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. 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. 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

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