> related to mathematical theories like model theory, which give precise accounts of what it means to describe something

Perhaps too precise? APoSD is about the practical challenges of large groups of people creating and maintaining extensive written descriptions of logic. Mathematical formalisms may be able to capture some aspects of that, but I'm not sure they do so in a way that would lend real insight.

"How can I express a piece of complicated logic in an intuitive and easy-to-understand way" is fundamentally closer to writer's craft than mathematics. I don't think a book like this would ever be mathematically grounded, any more than a book about technical writing would be. Model theory would struggle to explain how to write a clear, legible paragraph.