Does the Chalcedonian Definition mean Christ has two minds?

In the seventh century two Christological doctrines [were determined to be un-orthodox and in contradiction to the Chalcedonian Definition](https://en.wikipedia.org/wiki/Monothelitism#First_attempt:_Doctrine_of_one_energy) : that Christ has one "energy", and then that Christ has one will. Chalcedonian Christianity teaches that Jesus has two complete divine and human natures, united in one person, and as the will was understood to be a property of a nature and not a person, he must necessarily have two wills, otherwise he would not have two complete natures. How far is this model to be extended? I have heard it said that not only does Christ have two wills, but also two minds. Is this an accurate interpretation of Chalcedonian theology? Previous questions have asked if the Trinity possesses the faculties of [will](https://christianity.stackexchange.com/q/1878/6071) and [mind](https://christianity.stackexchange.com/q/2548/6071) by nature or persons; possessing these by nature means the three persons would each possess the one singular will or mind, possessing them by person means each have a distinct will or mind. My understanding is that Chalcedonian theology should strictly be understood as teaching that these faculties are possessed by nature. (Not all who take the label of Chalcedonian would agree though.) This leads to the confusing situation where Chalcedonians teach one will in the Godhead and two wills in Christ, and those who disagree teach three wills in the Godhead and one will in Christ! If this is an accurate summary of Chalcedonian theology, are all such faculties properties of nature rather than person?