RE: [MathML4] Multiple Formats for Presentation and Semantics

Math Working Group,
MathML Refresh Community Group,

I put together some discussion notes on these MathML4 and related Web technology topics. Attached is a PDF version. I hope this brainstorming is useful to the MathML4 endeavor and, in the event of interest, I could open a Google Documents document of this content.


Presentation and Semantics

<math id="eq1">

<presentation>

<annotation-xml encoding="application/xhtml+xml">...</annotation-xml>

<annotation-xml encoding="application/svg+xml">...</annotation-xml>

<annotation encoding="image/png" src="data:..." />

<annotation-xml encoding="MathML-Presentation">...</annotation-xml>

</presentation>

<semantics>

<annotation-xml encoding="application/openmath+xml">...</annotation-xml>

<annotation-xml encoding="MathML-Content">...</annotation-xml>

</semantics>

</math>

Presentation, Semantics and Metadata

<math id="eq1">

<presentation>

<annotation-xml id="eq1-p-xhtml" encoding="application/xhtml+xml">...</annotation-xml>

<annotation-xml id="eq1-p-svg" encoding="application/svg+xml">...</annotation-xml>

<annotation id="eq1-p-png" encoding="image/png" src="data:..." />

<annotation-xml id="eq1-p-mathmlp" encoding="MathML-Presentation">...</annotation-xml>

</presentation>

<semantics>

<annotation-xml id="eq1-s-om" encoding="application/openmath+xml">...</annotation-xml>

<annotation-xml id="eq1-s-mathmlc" encoding="MathML-Content">...</annotation-xml>

</semantics>

<metadata>

<annotation-xml encoding="application/rdf+xml">...</annotation-xml>

<annotation encoding="application/json+ld">...</annotation>

</metadata>

</math>

Multiple Notations

Expression �metadata� could be utilized to describe and interrelate multiple �presentation� annotations, e.g. to describe �presentation� annotations as utilizing distinct notations. With ontology for describing �presentation� annotations� notations in �metadata�, one or more JavaScript libraries could be authored to facilitate navigating notation, e.g. selecting which notations are displayed for expressions in documents.

<math id="eq1">

<presentation>

<annotation-xml id="eq1-p-n1" encoding="MathML-Presentation">...</annotation-xml>

<annotation-xml id="eq1-p-n2" encoding="MathML-Presentation">...</annotation-xml>

<annotation-xml id="eq1-p-n3" encoding="MathML-Presentation">...</annotation-xml>

</presentation>

<semantics>

<annotation-xml id="eq1-s" encoding="MathML-Content">...</annotation-xml>

</semantics>

<metadata>

<annotation-xml encoding="application/rdf+xml">...</annotation-xml>

</metadata>

</math>



Should, instead, notation be an attribute on �presentation� annotations?

<math id="eq1">

<presentation>

<annotation-xml notation="Notation 1" encoding="MathML-Presentation">...</annotation-xml>

<annotation-xml notation="Notation 2" encoding="MathML-Presentation">...</annotation-xml>

<annotation-xml notation="Notation 3" encoding="MathML-Presentation">...</annotation-xml>

</presentation>

<semantics>

<annotation-xml id="eq1-s" encoding="MathML-Content">...</annotation-xml>

</semantics>

</math>

Multiple Presentation Formats and Multiple Notations

This example shows a combination of multiple presentation formats with multiple notations.

<math id="eq1">
<presentation>
<annotation-xml notation="Notation 1" encoding="application/xhtml+xml">...</annotation-xml>
<annotation-xml notation="Notation 2" encoding="application/xhtml+xml">...</annotation-xml>
<annotation-xml notation="Notation 3" encoding="application/xhtml+xml">...</annotation-xml>
<annotation-xml notation="Notation 1" encoding="application/svg+xml">...</annotation-xml>
<annotation-xml notation="Notation 2" encoding="application/svg+xml">...</annotation-xml>
<annotation-xml notation="Notation 3" encoding="application/svg+xml">...</annotation-xml>
<annotation notation="Notation 1" encoding="image/png" src="data:..." />
<annotation notation="Notation 2" encoding="image/png" src="data:..." />
<annotation notation="Notation 3" encoding="image/png" src="data:..." />
<annotation-xml notation="Notation 1" encoding="MathML-Presentation">...</annotation-xml>
<annotation-xml notation="Notation 2" encoding="MathML-Presentation">...</annotation-xml>
<annotation-xml notation="Notation 3" encoding="MathML-Presentation">...</annotation-xml>
</presentation>
<semantics>
<annotation-xml encoding="application/openmath+xml">...</annotation-xml>
<annotation-xml encoding="MathML-Content">...</annotation-xml>
</semantics>
</math>

Internationalization

For scenarios where natural language is utilized in the �presentation� annotation content, a BCP47 language attribute can adorn annotation markup and �presentation� annotations can also be described in expression �metadata�.

<math id="eq1">
<presentation>
<annotation-xml id="eq1-p-l1" lang="en" encoding="MathML-Presentation">...</annotation-xml>
<annotation-xml id="eq1-p-l2" lang="fr" encoding="MathML-Presentation">...</annotation-xml>
</presentation>
<semantics>
<annotation-xml id="eq1-s" encoding="MathML-Content">...</annotation-xml>
</semantics>
<metadata>
<annotation-xml encoding="application/rdf+xml">...</annotation-xml>
</metadata>
</math>

Multimodality

�Presentation� annotations can include multimodal content, e.g. SSML or audio, and �presentation� annotations can also be described in expression �metadata�.

<math id="eq1">
<presentation>
<annotation-xml lang="en" encoding="MathML-Presentation">...</annotation-xml>
<annotation-xml lang="fr" encoding="MathML-Presentation">...</annotation-xml>
<annotation-xml lang="en" encoding="application/ssml+xml">...</annotation-xml>
<annotation-xml lang="fr" encoding="application/ssml+xml">...</annotation-xml>
<annotation-xml lang="en" encoding="audio/mpeg" src="...">...</annotation-xml>
<annotation-xml lang="fr" encoding="audio/mpeg" src="...">...</annotation-xml>
</presentation>
<semantics>
<annotation-xml encoding="MathML-Content">...</annotation-xml>
</semantics>
</math>

Quality Scores

With quality score attributes, algorithms for selecting content from alternatives can resemble agent-driven or reactive content negotiation (https://en.wikipedia.org/wiki/Content_negotiation).

<math id="eq1">

<presentation>

<annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml>

<annotation-xml q="0.9" encoding="application/svg+xml">...</annotation-xml>

<annotation q="0.9" encoding="image/png" src="data:..." />

<annotation-xml q="1.0" encoding="MathML-Presentation">...</annotation-xml>

</presentation>

<semantics>

<annotation-xml encoding="application/openmath+xml">...</annotation-xml>

<annotation-xml encoding="MathML-Content">...</annotation-xml>

</semantics>

</math>

Remote Content

<math id="eq1">

<presentation>

<annotation-xml encoding="application/xhtml+xml" src="eq1.xhtml" />

<annotation-xml encoding="application/svg+xml" src="eq1.svg" />

<annotation encoding="image/png" src="eq1.png" />

<annotation-xml encoding="MathML-Presentation" src="eq1.mmlp" />

</presentation>

<semantics>

<annotation-xml encoding="application/openmath+xml" src="eq1.om" />

<annotation-xml encoding="MathML-Content" src="eq1.mmlc" />

</semantics>

</math>

Content Negotiation

Using agent-driven or reactive content negotiation over HTTP, URL�s can be provided for �presentation�, �semantics� and �metadata� (https://en.wikipedia.org/wiki/Content_negotiation).

<math id="eq1">

<presentation src="eq1.php?content=presentation" />

<semantics src="eq1.php?content=semantics" />

<metadata src="eq1.php?content=metadata" />

</math>

Toward a Single URL per Mathematical Expression

<math id="eq1" src="eq1.php" />

Extensibility

Are there any other varieties of content for a mathematical expression beyond �presentation�, �semantics� and �metadata�? Might we want to include �other� for extensibility?

<math id="eq1">

<presentation>

<annotation-xml id="eq1-p-xhtml" encoding="application/xhtml+xml">...</annotation-xml>

<annotation-xml id="eq1-p-svg" encoding="application/svg+xml">...</annotation-xml>

<annotation id="eq1-p-png" encoding="image/png" src="data:..." />

<annotation-xml id="eq1-p-mathmlp" encoding="MathML-Presentation">...</annotation-xml>

</presentation>

<semantics>

<annotation-xml id="eq1-s-om" encoding="application/openmath+xml">...</annotation-xml>

<annotation-xml id="eq1-s-mathmlc" encoding="MathML-Content">...</annotation-xml>

</semantics>

<metadata>

<annotation-xml encoding="application/rdf+xml">...</annotation-xml>

<annotation encoding="application/json+ld">...</annotation>

</metadata>

<other rel="http://www.<http://www.semantic.com/example-uri/>example.com/semantic-uri/<http://www.semantic.com/example-uri/>">

<annotation-xml id="eq1-o" encoding="...">...</annotation-xml>

</other>

</math>

Interrelating Expressions and Mathematical Proofs

Is content which interrelates mathematical expressions, e.g. for mathematical proofs, expression �metadata� or is it another variety of content?

Clipboarding

Some preliminary thoughts on clipboarding mathematical expressions include a consideration of multipart MIME. A mathematics expression can map to data of type multipart/related which contains multiple, nested contents of type multipart/alternative (https://en.wikipedia.org/wiki/MIME#Multipart_messages). The root part or the main part of the multipart/related message, the part which references content in the other parts, can be the �metadata� content.

Content Negotiation and Semantic Web Formats

In the section Multiple Notations, it was asked whether mathematical notation should be an attribute on �presentation� annotations.

We could also add �notation� to a list of parameters for local and remote content negotiation: encoding, language, quality and notation. Perhaps, the parameters of content negotiation could be extensible. Adding a parameter for �notation� could be as simple as utilizing a URI in content returned during agent-driven or reactive content negotiation.

�Unfortunately HTTP leaves the format of the list of representations and metadata along with selection mechanisms unspecified.� � https://en.wikipedia.org/wiki/Content_negotiation

If the format of the content returned accompanying an HTTP 300 or 406 during agent-driven or reactive content negotiation were a Semantic Web format, e.g. RDF/XML, then these matters would be tractable. We could readily add �notation� as a content negotiation parameter.

We could specify the use of Semantic Web formats, e.g. RDF/XML (application/rdf+xml), during agent-driven or reactive content negotiation. This would facilitate extensibility in terms of the parameters of content negotiation (adding �notation� to encoding, language and quality).



Best regards,
Adam Sobieski