Since you are asking this question on a Boost distribution list, I assume that you would like to get a Boost-like review of your library. One criterion for a Boost-quality library that I can offer is the quality of the documentation. A good documentation should:
* Briefly (in five minutes or less) convince the reader that it is worth investing time in studying the library, * Describe what computational problems it helps solving, * Convince that it will be a good fit in users' programs, * Demonstrate the usage, * Provide enough information that I know how to use it in my programs.
I agree with this, but tribool's documentation could also be better in that regard. It addresses points 4 and 5, but I have to distill 1-3 myself from its tutorial. Apart from the more refined logical operators, tribool acts like a optional<bool>. I assume tribool has a size of 1 byte (that should be stated in the docs), while optional<bool> would have a size of 2 byte unless this case was specialised in the implementation. A motivation of bool3 could point out how it adds value compared to a generic template type like optional.