Re: Epistemological Justification via Metadata

Math Working Group,

Here is a quick update on the topic of the uses of metadata for epistemological justifications, i.e., mathematical proofs and argumentation.

I recently opened a WICG issue with some ideas about how to both reference metadata from and attach metadata to document elements (HTML, MathML, SVG) and about ideas regarding ways to use CSS selectors to select and style content for both media resources (images, audio, video) and document elements (HTML, MathML, SVG) based on metadata.

https://github.com/WICG/proposals/issues/141

The gist of the ideas in the issue are:

(1) An attribute, msrc, is broached for referencing metadata from and attaching metadata to document elements:

<math msrc="...">...</math>
<span msrc="...">...<math>...</math>...</span>

where the value of that attribute could be an absolute URL, a relative URL, a local document element reference, or a data URL:

<math id="eq1" msrc="https://www.example.com/m/eq1metadata.xml">...</math>
<math id="eq2" msrc="eq2metadata.xml">...</math>
<math id="eq3" msrc="#elemref">...</math>
<math id="eq4" msrc="data:...">...</math>

(2) A CSS pseudo-class, :meta(), is broached for selecting and styling content based upon its metadata.

math:meta(...)
span:meta(...)

Use case scenarios include selecting and styling media resources, e.g., images, based upon whether they are AI-generated. For example:

img:meta(actions:has(> action:content('c2pa.created')):has(> digitalSourceType:content('trainedAlgorithmicMedia'))) { border-color: blue; }

or

img:meta(actions:has(> action[content='c2pa.created']):has(> digitalSourceType[content='trainedAlgorithmicMedia'])) { border-color: blue; }

These ideas are new – a work in progress – and any feedback is welcomed. Thank you.


Best regards,
Adam Sobieski

________________________________
From: Adam Sobieski <adamsobieski@hotmail.com>
Sent: Monday, February 19, 2024 8:20 PM
To: www-math@w3.org <www-math@w3.org>
Subject: Epistemological Justification via Metadata

Math Working Group,

Hello. I am excited to share some ideas pertaining to the uses of attached and referenced metadata to enable resources, e.g., mathematical expressions, to provide epistemological justification for themselves.

Introduction

Considered here is a thought experiment about one or more HTTP-based services. These services would receive as inputs resources which would be either: (1) MathML, (2) HTML + MathML, or (3) images of mathematical expressions. These services would return contents in these same formats but with updated metadata. With the services under discussion, users or their software tools could, incrementally, build content which provides epistemological justification for itself in its metadata.

The simplest cases, or base cases, for such services would be those where users or their software tools would POST content and then receive that same content back with updated embedded or referenced metadata indicating that the content were a tautology, assumption, or assertion.

A next case to consider are those where users or their software tools would POST multiple input resources, each already bearing or referencing the type of metadata under discussion, and a special input resource which is to be the resultant content, and also the rule by which the provided result input was produced from the other inputs. Rules could be referred to by URL. If the service's operation were successful, the result input would be returned with updated metadata. In this case, the output resource would bear or reference metadata including the utilized input ingredients and the rule utilized to produce the resource.

A third case to consider involves parallel justifications or derivations and how to go about attaching these to resources. For these scenarios, users or their software tools would provide two or more resources with equivalent data but differing metadata and would receive one resource with merged metadata.

Discussion

How might metadata be securely attached to resources? With respect to images, options include C2PA manifests.

Instead of resources (and sub-resources utilized in justifications) each having to bear attached metadata, resources could provide enough attached metadata to securely reference more URL-addressable metadata, detached metadata. How might metadata be securely referenced by resources?

Some resources cannot be or are not desired to be separated from their documents' contexts to bear or to reference metadata and, for these scenarios, Web Annotations selectors could be utilized.

How should the freshness of the justifications attached to or referenced by resources be maintained as mathematical knowledge progresses?

How should mathematical expressions be distinguished from one another and canonicalized? One approach could be to use URIs, GUIDs, or OIDs with numbered parameters and symbol arguments for indicating those symbols to substitute in to instantiate an expression.

Conclusion

By means of incrementally utilizing one or more envisioned HTTP-based services, users or their software tools could create resources with metadata providing epistemological justifications for them.

Thank you. I hope that these ideas were of some interest to you.


Best regards,
Adam Sobieski