Mathematical Proofs in HTML5 Documents

Math Working Group,
 
Greetings. I would like to describe some ideas about the representation of, the clipboarding of, and the dragging and dropping of <math> objects as well as other mathematical document objects that can each contain multiple <math> element instances along with other hypertext.  Such mathematical document objects can include representations of mathematical proofs.
 
MathML3 includes <annotation> and <annotation-xml> elements which can provide parallel representations of mathematical semantics (http://www.w3.org/TR/MathML3/chapter5.html). The versatile clipboarding and dragging and dropping of mathematics could, then, be a JavaScript topic so as to provide at least as many data formats as are expressed in a contextual document region or selection. Relevant JavaScript API's topics include: clipboarding (http://dev.w3.org/2006/webapi/clipops/clipops.html), drag and drop (http://dev.w3.org/html5/spec/dnd.html), DataTransferItem (http://dev.w3.org/html5/spec/dnd.html#datatransferitem), and DataTransferItemList (http://dev.w3.org/html5/spec/dnd.html#datatransferitemlist). In mathematical articles and textbooks, where hypertext sections or selections may contain or be related to one or more mathematical objects, such as mathematical proof structures or substructures, combinations of structured knowledge and JavaScript can deliver new functionalities.  Structured knowledge, such as representations of mathematical proofs, can be included in HTML5 documents and can be attached to or referenced by HTML5 documents. Some techniques include: 
1. Having entire proofs in <math> elements.  Proof formats could then express semantics in <annotation> or <annotation-xml> elements.  OpenMath content dictionaries could come to exist for mathematical proof structures.
 
2. Having proofs in HTML5 document structure, possibly containing one or more <math> element instances, while utilizing XML attributes from other XMLNS.  Proof structure and semantics can overlay the HTML5 and/or the XML can relate elements to referenced external resources. 3. Having proofs in HTML5 document structure, possibly containing one or more <math> element instances, while utilizing RDFA (http://dev.w3.org/html5/rdfa/).  Proof structure and semantics can overlay the HTML5 and/or the RDFA can relate elements to referenced external resources. 
4. An element from an XMLNS, resembling <semantics>, which can include <annotation>- and <annotation-xml>-like elements, and which can appear in HTML5 documents in the <head> section, or alternatively on any element, while referencing HTML5 document elements by id.
 
5. The use of SMIL3, SMIL timesheets, for example with timesheets.js, to align two or more XML-based documents referring to documents' elements by id's.
  Kind regards, Adam Sobieski

Received on Monday, 2 April 2012 22:54:47 UTC