This blog talks about trivalence with several posts I want to read more and maybe respond to someday when I have a little time to spare.
Looking at Kratzer’s lumping problem, or the ill fit of the material conditional with natural language, I get the impression that logic is in its infancy. Beginning with Frege there has been rapid innovation in logic. Unlike technology, which responds with increasing rapidity to a fiercely competitive market, logic hasn’t found its market value, so its progress will seem slow in comparison — unless someone can discover a logical structure that solves AI challenges better than the Aristotelean models.