Speaking as an unreconstructed Platonic realist, I am tempted to say that Boolean functions are mathematical objects that cannot be invented, only discovered. But speaking as a semiotic constructivist I would have to concede that we do indeed invent all sorts of syntactic systems for talking and thinking about these mathematical objects. And some calculi can even be better than others for the purpose of calculation, a fact that repays us to consider the alternatives as they work out in practice.
On the third hand, I have more lately been thinking that the concepts of discovery and invention, being human constructs like the proverbial concepts of particles and waves, may not be adequate in the final analysis to articulate the reality of the process at hand. It may well be that all of these questions are more like the question —
Who discovered Orion in the night sky?