Reification, Named Graphs, Embedded RDF XML, Mathematical Semantics and RDFa

Math Working Group,
RDFa Working Group,
Semantic Web Interest Group,
 
Greetings.  I would like to broach for discussion some topics about RDFa-enhanced hypertext documents, reification, named graphs, embedded RDF XML, and mathematical semantics.
 
Reification and Named Graphs

"In Semantic Web languages, such as Resource Description Framework (RDF) and Web Ontology Language (OWL), a statement is a binary relation. It is used to link two individuals or an individual and a value. Applications sometimes need to describe other RDF statements, for instance, to record information like when statements were made, or who made them, which is sometimes called 'provenance' information. As an example, we may want to represent properties of a relation, such as our certainty about it, severity or strength of a relation, relevance of a relation, and so on." (http://en.wikipedia.org/wiki/Reification_(computer_science)#RDF_and_OWL)

Reification in RDF is illustrated in RDF Primer (http://www.w3.org/TR/rdf-primer/) in examples 19 and 20 (http://www.w3.org/TR/rdf-primer/#example19, http://www.w3.org/TR/rdf-primer/#example20) and in RDF 1.1 XML Syntax Specification in example 20 (http://dvcs.w3.org/hg/rdf/raw-file/default/rdf-xml/index.html#example20).

"Named graphs are a key concept of Semantic Web architecture in which a set of Resource Description Framework statements (a graph) are identified using a URI, allowing descriptions to be made of that set of statements such as context, provenance information or other such metadata." (http://en.wikipedia.org/wiki/Named_graph)

While some describe named graphs as a conceptual superset of reification functionality, both features are useful to have with regard to expressiveness in XML-based formats, such as HTML+RDFa; RDFa should include both reification and named graph functionality.

In hypertext documents, graph triples can be reified syntactically in RDFa, with RDFa syntactic sugar, and <script> elements, <metadata> elements, <annotation> and <annotation-xml> elements can each contain RDF XML as well as other semantic formats.

Embedded RDF XML, Mathematical Semantics and RDFa
 

<math>
  <semantics>
    ...
    <annotation-xml encoding="application/ssml+xml">...</annotation-xml>
    ...
    <annotation-xml encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
  </semantics>
</math>


The indicated MathML can be enhanced with RDFa in ways including: (a) RDFa on the <math> element and on the <annotation-xml> element with the RDF XML version of the mathematical semantics, (b) RDFa on the <math> element and the utilization of a collection ontology (e.g. http://purl.org/co/), a collection with the semantics of multipart MIME, multipart/alternative, and RDFa on a number of the indicated <annotation-xml> elements.

An RDFa parser (http://www.w3.org/TR/rdfa-core/#s_model, http://www.w3.org/TR/rdfa-core/#s_rdfaindetail) could process the contents of the <annotation-xml> element in a number of ways including parsing the RDF XML content into the default graph.

Future Directions

Future directions include uses of RDFa on the scales of entire documents, chapters, sections, subsections and across multiple paragraphs.  Argumentation and mathematical proofs are examples of such uses of RDFa in hypertext-based documents, digital books and digital textbooks.  Mathematical proofs, including those in documents with complex document structure, can be processed into RDF graphs from hypertext-based documents, including the semantics of mathematical expressions.

Existing argumentation and proof representation formats include: Argument Interchange Format (AIF), AIF-RDF, Argument Markup Language (AML), Legal Knowledge Interchange Format (LKIF), Open Mathematical Documents (OMDoc), Proof Markup Language (PML), Thousands of Problems for Theorem Provers (TPTP), and Thousands of Solutions for Theorem Provers (TSTP).  Additionally, new formats and ontologies are possible for argumentation, for mathematical proofs, in RDFa-enhanced hypertext-based documents, digital books and digital textbooks.
 
With RDFa, the thesis statements, topic sentences, and supporting sentences in documents can be indicated, as can relationships between claims, evidence, measurement and methodology, enhancing document navigation, enhancing the indexing, search, and retrieval of documents, enhancing content discovery, and enhancing document summarization.

The quoting and citing of referenced materials and the cross-referencing of document elements pertain to argumentation structures in documents. Where documents quote or cite referenced materials, argumentation structures in RDFa may have typed links to referenced materials or to content in referenced materials and where documents cross-reference document elements, argumentation structures in RDFa may have typed links to document elements.



Kind regards,

Adam Sobieski