Quantum Probabilities as Bayesian Probability, Quantum probabilities as degrees of belief Above are two articles about quantum Bayesianism. I don't know why quantum Bayesianism use some results from quantum logic. I think in quantum logic, some physical phenomena, like collapse of state, have been transformed to some requirements of the structure. Quantum Bayesianism, as an interpretation, may want to interpret some phenomena like collapse of state, then they should not borrow the results from quantum logic. If they borrow some results,which come from some requirements , to derive some other results related to these requirements, then it can't be a logical theory.
By the way, is it possible to build a logical theory based on quantum logic? Or is any promising way to make quantum mechanic more logical?