The book I mentioned (Thinking in Promises) is the introductory-level public book.
https://www.amazon.com/Promise-Theory-Principles-Application... is the heavy-duty scientific stuff.
"In Search of Certainty" (https://www.amazon.com/Search-Certainty-Science-Information-...) is somewhere in-between.
I would say promise theory is its own kind of logic and notation. Thanks for the correction @dozzie.