I hold the somewhat rare opinion that Consciousness and Intelligence in humans are "emergent properties", similar to a traffic jam as an emergent property of cars and roads.
I am also of the opinion that this "emergent mind" does not follow any known logic but has its own "emergent logic".
By analogy, cars logically can go from one place to another without stopping but traffic jams can cause a car to stop even though the road ahead and behind are still flowing.
Emergent rules do not follow from the substrate rules.
Emergent properties arise from complexity. I am of the opinion that the difference between an intelligent animal such as a monkey and a human is directly related to the complexity of brain structure. Since intelligence is assumed to emerge from complexity. The "logic" (bad word) of each is of "a different order", somewhat like the difference between a car traffic jam and a bicycle traffic jam.
What this "emergent logic" is, though, I cannot say.
The closest I have come is by analogy to chaos theory. Nonlinear equations can exhibit states that never repeat from very simple nonlinear equations. Current "logics" seem "linear" to me and thus cannot be chaotic.