[Om3] Tracking OpenMath symbol usage using RDF and Sindice [Re: Notes of CD discussion?]

[Christoph LANGE]

Dear all,

  to recapitulate it for the list, I asked the developers of the Semantic Web
indexer Sindice (http://www.sindice.com) how we could use their service to
track the usage of OpenMath symbols.  Richard Cyganiak answered my question
(http://forum.sindice.com/showthread.php?p=108).

@Richard, thanks for your help!  This Cc to you is FYI.  I'll continue to
discuss the Sindice-related aspects in the Sindice forum.

The way to go is to provide this information in RDF: pure RDF/XML, or RDFa
embedded into HTML.  Sindice crawls the web on its own but can also be
instructed ("pinged") to index the pages we want it to index.

Now for us the questions are:

1. what do we want to be tracked?
   a. the usage of a symbol in a formula?  (e.g. in an FMP, Example, or in any
      other mathematical document)
   b. additional information about a symbol, such as a type signature or a
      notation definition?
   c. anything else?
2. where does the information occur?
   a. in the annotation-xml of MathML formulas on HTML pages?
   b. in pure OpenMath documents (CDs or OMOBJs)?

(2a+1a) is easiest: we just postprocess the XHTML+MathML document and add RDFa
links to the symbols used in a formula.  Should this be done on document level
("symbol S occurs somewhere in this XHTML+MathML document" -- easy) or on
formula level ("symbol S occurs exactly in this formula in a document" -- a
bit harder)?

Example:

<div id="formula">
  <math>
    <semantics>
      <mi>a</mi>
      <mo>+</mo>
      <mi>b</mi>
      <annotation-xml>
        <OMOBJ>
	  <OMA>
	    <OMS cd="arith1" name="plus"/>
	    <OMV name="a"/>
	    <OMV name="b"/>
	  </OMA>
	</OMOBJ>
      </annotation-xml>
    </semantics>
  </math>
  <span rel="omo:usesSymbol" 
resource="http://www.openmath.org/cd/arith1#plus"/>
  <!-- using a property from my OpenMath ontology to establish the link,
       assuming "omo" as namespace prefix for the ontology -->
</div>

Note that I wrapped the formula into an artificial HTML div, as RDFa is not
specified for MathML and therefore likely not to be supported by Sindice, but
I asked (see the forum linked above).

(2a+1b) is not hard either, if notations are defined in some "standard" way.
In the worst case, the author of a notation definition would have to establish
an RDFa-like link to the symbol manually, but if the HTML page is generated
from a notation dictionary, it would be easy for me to auto-create that RDFa
link.

(2b) would be possible, too, but more work: We would have to provide the RDF
links from the OpenMath formulae or content dictionaries to the symbols used
in separate RDF/XML files to be indexed by Sindice.

Cheers,

Christoph

-- 
Christoph Lange, DERI Galway/Jacobs Univ. Bremen, http://kwarc.info/clange


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