According to wikipedia
Rarely, applications such as Aviary’s Peacock will supply boolean arithmetic blend modes. These combine the binary expansion of the hexadecimal color at each pixel of two layers using boolean logic gates. The top layer’s alpha controls interpolation between the lower layer’s image and the combined image.
I would like to explore what they actually do. However, there’s so little information that exist here. The only software that use this concept is Nodewerk and that used to be the software mentioned here.
The closest I can think of is that it uses different blending mode depending on the alpha. I guess it would be possible to recreate it in g’mic, but I have not explored that yet.