I have explored non-classical logics recently, and I was wondering if three-valued relevant intuitionistic was/could be a thing.
It seems to be an interesting combination to me since it is closer to my intuition of truth/implication/etc. than classical logic.
According to my unverified studies, the three valued and intuitionisic possibilities can be combined. I have not yet found a "relevance" approach to be fruitful. I am not aware that this possibility has been explored much. The ordinary material conditional does not suffice for three valued logic, and there is more than one possible definition of negation to be considered, as well rejecting the Law of the Excluded Middle as necessary truth.